homework and practice 3 2 estimate products

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Course: 4th grade   >   Unit 4

• Estimating 2-digit multiplication

Estimate products (2-digit numbers)

• (Choice A)   36 ‍   A 36 ‍  
• (Choice B)   360 ‍   B 360 ‍  
• (Choice C)   3,600 ‍   C 3,600 ‍  
• (Choice D)   36,000 ‍   D 36,000 ‍  

How to Estimate Products

Multiples of 10 Review 

Use rounding to estimate products.

Estimate 6 × 34.

Another Example

Estimate 216 × 28.

One More Example

Estimate 73 × 389

Lesson Streak

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Topic C: Estimating Products

Before you practice estimating products, look at the easy multiplication that can be done when the factors end in zeros.

You already know how to quickly multiply by 10, 100, 1 000 , etc…

You can find the products in questions like these using regular multiplication:

But here is a shortcut:

• Count all the zeros at the end of the numbers in both factors.
• Write down that many zeros at the end of the product.
• Multiply the other digits in the usual way and put them before the zeros.
• How many zeros at the end of the factors? 3
• Write them down. 000
• Multiply the other digits and put them before the zeros. 3 × 5 = 15

30 × 500 = 15 000

400 × 3 000 =

• How many zeros at the end of the factors? 5
• Write them down. 00 000
• Multiply the other digits and put them before the zeros. 4 × 3 = 12

400 × 3 000 = 1 200 000

Find the products using the shortcut. Check your work using the answer key at the end of the exercise.

• [latex]\begin{array}{rr}&300\\\times&20\\\hline&6000\end{array}[/latex]
• [latex]\begin{array}{rr}&6000\\\times&200\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&210\\\times&20\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&800\\\times&600\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&400\\\times&500\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&6000\\\times&90\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&50000\\\times&6000\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&80000\\\times&30\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&5000\\\times&50\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&70\\\times&80\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&3000\\\times&700\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&50000\\\times&900\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&9000\\\times&8000\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&60000\\\times&90\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&90000\\\times&2000\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&600\\\times&600\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&40000\\\times&800\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&2400\\\times&70\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&390\\\times&40\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&7200\\\times&5000\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&7000\\\times&7000\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&61000\\\times&400\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&5200\\\times&300\\\hline\\\end{array}[/latex]
• [latex]\begin{array}{rr}&40\\\times&60\\\hline\\\end{array}[/latex]

Answers to Exercise 1

• 300 000 000
• 180 000 000

To find an estimated product, round the factors before you multiply. If a factor has only one digit, do not round it.

[latex]\begin{array}{rr}&6258\\\times&3\\\hline\end{array}[/latex]

6 258 rounds to 6 000 . Leave 3 as is.

[latex]\begin{array}{rr}&6000\\\times&3\\\hline&18000\end{array}[/latex]

18 000 is the estimated product.

[latex]\begin{array}{rr}&491\\\times&24\\\hline\end{array}[/latex]

491 rounds to 500. 24 rounds to 20.

[latex]\begin{array}{rr}&500\\\times&20\\\hline&10000\end{array}[/latex]

10 000 is the estimated product.

Topic C: Self-Test

Mark  /18    Aim  15/18

A. Multiply these numbers.

• [latex]\begin{array}{rr}&600\\\times&70\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&9000\\\times&30\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&5000\\\times&600\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&3000\\\times&500\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&400\\\times&50\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&8000\\\times&1000\\\hline\end{array}[/latex]

B. Find an estimated product.

• [latex]\begin{array}{rr}&87\\\times&23\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&268\\\times&25\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&9421\\\times&75\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&2632\\\times&49\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&365\\\times&455\\\hline\end{array}[/latex]
• [latex]\begin{array}{rr}&7264\\\times&590\\\hline\end{array}[/latex]

Answers to Topic C Self Test

• 90 × 20 = 1 800
• 300 × 30 = 9 000
• 9 000 × 80 = 720 000
• 3 000 × 50 = 150 000
• 400 × 500 = 200 000
• 7 000 × 600 = 4 200 000

Fundamentals of Mathematics 3 Copyright © 2023 by Wendy Tagami and Liz Girard is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Estimating products

Common Core Standards: Grade 4 Number & Operations in Base Ten

CCSS.Math.Content.4.NBT.A.3, CCSS.Math.Content.4.NBT.B.5

This worksheet originally published in Math Made Easy for 5th Grade by © Dorling Kindersley Limited .

Related worksheets

Estimating quotients, rounding to the nearest 10, 100, and 1,000, rounding whole numbers, rounding to the nearest whole number.

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Estimating Products – 3 digit by 2 digit – using Rounding

These worksheets are a great way to help your students learn and practice estimating products using rounding.

In these worksheets, students will estimate using rounding and mental math. Then, they will find the actual product. The teacher can then ask students to check the reasonableness of their estimated answer.

The prerequisites for this packet are:

• Mental math
• Calculating products of 3-digit by 2-digit numbers

These worksheets can be used for classwork, homework, or math centers. The answer key is included, so you can easily assess your student’s progress.

Includes 4 worksheets plus the answer key.

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Big Ideas Math Answers Grade 4 Chapter 3 Multiply by One-Digit Numbers

Big Ideas Math Book 4th Grade Answer Key Chapter 3 Multiply by one – Digit Numbers answer key is helpful for students who are willing to do their best in exams and can Acknowledge these topics by downloading this pdf for free of cost. In this chapter, each and every question was explained in clean and clear cut manner to help the students in a better way to understand these Math problems easily. Big Ideas Math Answers Grade 4 Chapter 3 explains different types of questions with examples and references by which one can grasp different methods in easy and fun way.

Big Ideas Math Book 4th Grade Answer Key Chapter 3 Multiply by One-Digit Numbers

The chapter 3 Multiply by one – digit numbers covers the various topics such as  Multiplying the one or more digit numbers with on digit numbers , Rounding the numbers, Estimating the product of Two  numbers , Finding the products using the different methods such as Expanded form , Distributive property , commutative property, Associative property, Using partial products to find the final product of two numbers with examples to make it easy for the students who finds math as complex task, This chapter is useful for students for easy Growth in their Academics.

Lesson 1 Understand Multiplicative Comparisons

Lesson 3.1 understand multiplicative comparisons, understand multiplicative comparisons homework & practice 3.1, lesson 2 multiply tens, hundreds, and thousands, lesson 3.2 multiply tens, hundreds, and thousands, multiply tens, hundreds, and thousands homework & practice 3.2, lesson 3 estimate products by rounding.

• Lesson 3.3 Estimate Products by Rounding 
• Estimate Products by Rounding Homework & Practice 3.3

Lesson 4 Use the Distributive Property to Multiply

• Lesson 3.4 Use the Distributive Property to Multiply   

Use the Distributive Property to Multiply Homework & Practice 3.4

Lesson 5 use expanded form to multiply, lesson 3.5 use expanded form to multiply, use expanded form to multiply homework & practice 3.5, lesson 6 use partial products to multiply, lesson 3.6 use partial products to multiply, use partial products to multiply homework & practice 3.6, lesson 7 multiply two-digit numbers by one-digit numbers, lesson 3.7 multiply two-digit numbers by one-digit numbers, multiply two-digit numbers by one-digit numbers homework & practice 3.7, lesson 8 multiply three- and four-digit numbers by one-digit numbers.

• Lesson 3.8 Multiply Three- and Four-Digit Numbers by One-Digit Numbers
• Multiply Three- and Four-Digit Numbers by One-Digit Numbers Homework & Practice 3.8

Lesson 9 Use Properties to Multiply

Lesson 3.9 use properties to multiply, use properties to multiply homework & practice 3.9, lesson 10 problem solving: multiplication, lesson 3.10 problem solving: multiplication, problem solving: multiplication homework & practice 3.10, multiply by one-digit numbers performance task, multiply by one-digit numbers activity, multiply by one-digit numbers chapter test, multiply by one-digit numbers cumulative practice.

• Multiply by One-Digit Numbers STEAM Performance Task 

Explore and Grow

Model the counters. Draw to show your model.

There are 20 counters. Five of the counters are yellow. The rest are red.

How many more red counters are there than yellow counters? How many times as many red counters are there as yellow counters? Answer: model

15 red counters, 3 times the yellow cou nters.

Explanation: Totally there are 20 counters in which 5 of them are yellow counters and the remaining 15 of them are red counters. So, red counters are three times the yellow counters.

Structure Explain how you can use an addition equation or a multiplication equation to compare the numbers of yellow counters and red counters. Answer:  Number of yellow counters = 5 and number of red counters =15, There are red counters as 3 times of yellow counters that is, 3 × 5 = 15  or 5 + 5 + 5 = 15.

Explanation: Given the total number of yellow counters and the number of red counters so, simply we should use our basic addition rule and basic multiplication rule to explain the mathematical equation for the number of yellow counters and number of red counters.

Think and Grow: Understand Multiplicative Comparisons

You can compare two numbers using addition or multiplication. • Use addition to find or how many more how many fewer • Use multiplication to find as much. how many times

Show and Grow

Write two comparison sentences for the equation Question 1. 15 = 3 × 5 Answer:  15 is 3 times as many as 5. or 15 is 5 times as many as 3.

Explanation: we should multiply the numbers 3 and 5 , to get the multiplication result as 15.

Question 2. 32 = 4 × 8 Answer: 32 is 4 times as many as 8. or 32 is 8 times as many as 4.

Explanation: we should multiply the numbers 4 and 8 , to get the multiplication result as 32.

21 = 14 + 7.

Explanation: The term more than is referred  to addition , we should add the numbers 14 and 7, to get the addition result as 21.

40 = 8 × 5.

Explanation: The term as many as is referred  to multiplication , we should multiply the numbers 5and 8 , to get the multiplication result as 40.

Apply and Grow: Practice

Write two comparison sentences for the equation . Question 5. 48 = 6 × 8 Answer: 48 is 6 times as many as 8. or 48 is 8 times as many as 6.

Explanation: The term as many as is referred  to multiplication , we should multiply the numbers 6and 8 , to get the multiplication result as 48.

Question 6. 63 = 7 × 9 Answer:  63 is 7 as many as 9. or 63 is 9 as many as 7.

Explanation: The term as many as is referred  to multiplication , we should multiply the numbers 7and 9 , to get the multiplication result as 63.

Write an equation for the comparison sentence. Question 7. 20 is 2 times as many as 10. Answer: 20 = 2 × 10.

Explanation: we should multiply the numbers 2 and 10 , to get the multiplication result as 20.

Question 8. 18 is 10 more than 8. Answer: 18 = 10 + 8.

Explanation: we should add the numbers 10 and 8, to get the addition result as 18.

Question 9. 35 is 7 times as many as 5. Answer: 35 = 7 × 5.

Explanation: we should multiply the numbers 7and 5 , to get the multiplication result as 35.

Question 10. 16 is 4 times as many as 4. Answer: 16 = 4 × 4.

Explanation: we should multiply the numbers 4 and 4 , to get the multiplication result as 16.

Question 11. Earthworms have four more hearts than humans. How many hearts do earth worms have? Answer: 5.

Explanation: Humans have one heart and question implies that, Earthworms have four more hearts than humans. So 1 + 4 = 5.

Answer:  250 milligrams.

Explanation: Ant body weight = 5 milligrams and it can lift 50 times their body weight. So, ant can lift 50 times the 5 milligrams, that is 5 × 50 = 250 milligrams.

Question 13. Writing Explain how you know the statement “32 is 8 times as many as 4”is a comparison involving multiplication. Answer:  Multiplication is used to find as  much or how many times, and the two factors 8 &  4 gives the product of 32 . So, 32  = 8 × 4.

Question 14. Number Sense Write an addition comparison statement and a multiplication comparison statement for the numbers 8 and 24. Answer: Addition comparison statement  for 24 = 16 + 8  is , 24 is 16 more than 8. multiplication comparison statement for 24 = 3 × 8 is , 24 is 3 times as many as 8.

Think and Grow: Modeling Real Life

Explanation: Given, hydrogen peroxide used in this solution is 4 times as many as water , so let us say that , Hydrogen peroxide is represented as H and water as W, then we have H = 4W, from the model given we can say that Hydrogen peroxide + water = 10 tablespoons of liquid, we get H + W = 10 from above details we can write it as, 4W + W = 10 5W = 10 W = 10/5 w = 2. Replace this value in assumed equation H = 4W that is H = 4(2) H = 4 ×2 H = 8. Hydrogen peroxide (H) = 8 Water (W) = 2, in total 8 + 2 = 10. Given equation is balanced. so here we are using 8 tablespoons of Hydrogen peroxide and 2 tablespoons of water to get the required 10 table spoons of liquid.

Find the number of tablespoons of water. The model shows ______ equal parts. There are ______ tablespoons of liquid in all. Answer: The model shows 2 tablespoons of water . There are 10 tablespoons of liquid in all.

5 × ? = 10 Think: 5 times what number equals 10? Answer: 5 × 2 = 10. Explanation: 10 is 5 times as many as 2.

You use _______ tablespoons of water. Answer: we use 2 tablespoons of water in the liquid.

Find the number of tablespoons of hydrogen peroxide. You use ________ times as much hydrogen peroxide as water. Answer: we use 4 times as much Hydrogen peroxide as water.

2 × 4 = ______ Answer: 2 × 4 = 8. 8 is 2 times as many as 4.

So, you use _______ tablespoons of hydrogen peroxide. Answer: we use 8 tablespoons of Hydrogen peroxide.

Question 15. A bicycle-sharing station on Main Street has 5 times as many bicycles as a station on Park Avenue. There are 24 bicycles at the two stations. How many bicycles are at the Main Street station? Answer: 20

Explanation: Let us say ,Main street as M and Park Avenue as P, Given that main street has 5 times as many bicycles as a station on Park Avenue so we get, M = 5P And there are 24 bicycles at the two stations from that we have M + P = 24, by replacing the M value in the equation M + P = 24 we get, 5P + P = 24 6P = 24 P = 24/6 P = 4. replace this P value in the above equation M = 5P to get M value, then M = 5(4) M = 5 × 4 M = 20. so we have M = 20 and P = 4, in total 20 + 4 = 24. the given equation is balanced. Finally, we have 20 bicycles at the Main street station and 4 bicycles at the Park Avenue station.

Question 16. In the 2016 Olympics, Brazil won 6 silver medals. France won 3 times as many silver medals as Brazil. How many silver medals did France win? Answer: 18 silver medals.

Explanation: Brazil = 6 silver medals, France = 3 times as many as brazil , so 3 × 6 = 18. France has won 18 silver medals.

Question 17. Of all the national flags in the world, there are 3 times as many red, white, and blue flags as there are red, white, and green flags. There are 40 flags with these color combinations. How many more flags are red, white, and blue than red, white, and green? Answer:

Write two comparison sentences for the equation. Question 1. 24 = 8 × 3 Answer: 24 is 8 times as many as 3. or 24 is 3 times as many as 8.

Explanation: we should multiply the numbers 8 and 3 , to get the multiplication result as 24.

Question 2. 14 = 7 × 2 Answer: 14 is 7 times as many as 2. or 14 is 2 times as many as 7.

Explanation: we should multiply the numbers 7 and 2 , to get the multiplication result as 14.

Write an equation for the comparison sentence. Question 3. 30 is 6 times as many as 5. Answer: 30 = 6 × 5

Explanation: we should multiply the numbers 6 and 5, to get the multiplication result as 30.

Question 4. 27 is 3 times as many as 9. Answer: 27 = 3 × 9

Explanation: we should multiply the numbers 3 and 9, to get the multiplication result as 27.

Question 5. 12 is 7 more than 5. Answer: 12 = 7 + 5

Explanation: we should add the numbers 7 and 5, to get the Addition result as 12.

Question 6. 10 is 2 times as many as 5. Answer: 10 = 2 × 5

Explanation: we should multiply the numbers 2 and 5, to get the multiplication result as 10.

Question 7. The House of Representatives has 335 more members than the Senate. The Senate has 100 members. How many members does the House of Representatives have? Answer: 435 members.

Explanation: senate has 100 members so, 335 + 100 = 435 . House of representatives have 435 members.

Question 8. A lion’s roar can be heard 5 miles away. The vibrations from an elephant’s stomp can be felt 4 times as many miles away as the lion’s roar can be heard. How many miles away can the vibrations be felt? Answer: 20 miles.

Explanation: a lion’s roar can be heard from 5 miles away Elephant’s stomp can be felt 4 times as many miles away from the lion’s roar , that is 4 × 5 = 20.

Question 9. Reasoning Newton says the equation 270 = 30 × 9 means 270 is 30 times as many as 9. Descartes says it means 270 is 9 times as many as 30. Explain how you know they are both correct.

Answer: Multiplication is used to find as much or how, many times. Since the two numbers 30 and 9 are the  factors of  multiplication they remain constant, Even their position in the factors place changes, The result will be the same product , that is 270.

Question 11. Open-Ended Write a comparison statement for a sum of 28. Answer:  28 is  20 more than 8. Explanation: 28  = 20 + 8 . The term sum here refers to addition of two number to get the total number.

Question 12. Modeling Real Life There are 12 shepherds and retrievers in all at a dog park. There are 2 times as many shepherds as retrievers. How many retrievers are there? Answer: 8 retrievers.

Explanation:  Total count of dogs at a dog park is 12. Let us say that shepherds as S and retrievers as R , Given that, S + R = 12. There are 2 times as many shepherds as retrievers. we have S = 2R,  by replacing this value in equation S + R = 12 we get, 2R + R = 12 3R = 12 R = 12/3 R = 4.  To get S value substitute this value in S = 2R then S = 2(4) S = 2 × 4 S = 8. Finally we have 8 shepherds and 4 retrievers in the dog park.

Question 13. Modeling Real Life Pythons sleep 6 times as long as horses. Horses sleep3 hours each day. How many hours do pythons sleep each day? Answer: 18 hours.

Explanation: Horses sleep 3 hours  and Python sleep 6 times as long as horses , so 6 x 3 =  18. therefore python sleeps 18 hours each day.

Question 14. DIG DEEPER! You have 8 times as many dimes as nickels. You have18 dimes and nickels altogether. How much money do you have in all? Answer: I have 16 dimes and 2 nickels.

Explanation: You have 8 times as many dimes as nickels You have18 dimes and nickels altogether Let us say, dimes as D and nickels as N then we have, D = 8N, so, D + N = 18 8N + N = 18 9N = 18 N = 18/9 N = 2. replace the value in D = 8N , we get  D = 8 × 2 = 16 .

So, I have 16 dimes and 2 nickels.

Review & Refresh

Find the missing factor. Question 15. 7 × _____ = 280 Answer: 40

Explanation:    280 is 7 times as many as 40 , 7 × 40 = 280. we should multiply the numbers 7 and 40, to get the multiplication result as 280.

Question 16. ____ × 30 = 270 Answer: 9

Explanation: 270 is 9 times as many as 30 , 9 × 30 = 270. we should multiply the numbers 30 and 9, to get the multiplication result as 270.

Question 17. 8 × ____ = 640 Answer: 80

Explanation: 640 is 8 times as many as 80 , 8 × 80 = 640. we should multiply the numbers 8 and 80, to get the multiplication result as 640.

Question 18. ____ × 90 = 540 Answer: 6

Explanation: 540 is 6 times as many as 90 , 6 × 90 = 540. we should multiply the numbers 6 and 90, to get the multiplication result as 540.

Question 19. 2 × _____ = 40 Answer: 20

Explanation: 40 is 2 times as many as 20, 2 × 20 = 40. we should multiply the numbers 2 and 20, to get the multiplication result as 40.

Question 20. _____ × 50 = 350 Answer:  7

Explanation: 350 is 7 times as many as 50 , 7 × 50 = 350. we should multiply the numbers 7 and 50, to get the multiplication result as 350.

The Place- value method. From the above pattern, we can conclude that the result has different place-values of 12

Explanation: The position of 3 is different in the given 4 multiplications. So, 4 × 3 = 12 4 × 30 = 120 4 × 300 = 1200 4 × 3000 = 12,000 From the above pattern, we can conclude that the result has different place-values of 12.

Repeated Reasoning How does 3 × 7 help you to find 3 × 7,000? Explain. Answer: 3× 7 = 21 3 × 7000 = 21000

Explanation:   When multiplying 3 by 7 we get 21 , same as that when we multiply 3 by 7000 we get 21000. the number moves to the left and a zero is put in, , the number moves three places to the left and zeros are put in, so the number would become 21000.

Think and Grow: Multiply Tens, Hundreds, and Thousands

You can use place value to multiply by tens, hundreds, or thousands. Example Find each product. 7 × 200 = 7 × _____ hundreds = _____ hundreds = ______ So, 7 × 200 = _____.

Answer: 1400

Explanation: Using the Place-value method, 7 × 200 = 7 × 2 hundreds = 14 hundreds = 1400 So, 7 × 200 = 1400.

3 × 4,000 = 3 × ______ thousands = _____ thousands = _____ So, 3 × 4,000 = ______.

Answer: 12000.

Explanation: Using the Place-value method, 3 × 4,000 = 3 × 4 thousands = 12 thousands = 12000 So, 3 × 4,000 = 12000.

Example Find each product. 8 × 5 = 40 Multiplication fact 8 × 50 = 400 Find 8 × 5; write 1 zero to show tens. Answer: 8 × 5 = 40 .

Explanation: By using the place-value method, 8 × 50 = 8 × 5 tens = 40 × tens = 400 So, 8 × 50 = 400.

8 × 500 = _____ Find 8 × 5; write 2 zeros to show hundreds. Answer: 8 × 5 = 40 , 8 × 500 = 4000.

Explanation: By using the place-value method, 8 × 500 = 8 × 50 tens = 8 × 5 × tens ×  tens = 40 × tens × tens = 4000 So, 8 × 500 = 4000.

8 × 5,000= ______ Find 8 × 5; write 3 zeros to show thousands. Answer : 8 × 5 = 40, 8 × 5,000 = 40,000.

Explanation: By using the place-value method, 8 × 5000 = 8 × 500 tens = 8 × 5 × tens ×  tens ×tens = 40 × tens × tens × tens = 40,000 So, 8 × 5000 = 40,000. Notice the Pattern: Write the multiplication fact and the same number of zeros that are in the second factor.

Find each product. Question 1. 6 × 9 = ____ 6 × 90 = ____ 6 × 900 = ______ 6 × 9,000 = _____ Answer: 6 × 9 = 54 6 × 90 = 540 6 × 900 =5400 6 × 9,000 = 54,000

Explanation:  6 × 9 = 54

By using the place-value method, 6 × 90 = 6× 9 tens = 6 × 9 × tens = 54 × tens = 540 So, 6 × 90= 540.

By using the place-value method, 6 × 900 = 6× 90 tens = 6 × 9 × tens × tens = 54 × tens × tens = 5400 So, 6 × 900= 5400.

By using the place-value method, 6 × 9,000 = 6× 900 tens = 6 × 90 × tens × tens = 6 × 9 × tens ×  tens × tens = 54 × tens × tens × tens = 54,000 So, 6 × 9,000 = 54,000.

Question 2. 5 × 2 = ____ 5 × 20 = ____ 5 × 200 = ______ 5 × 2,000 = _____ Answer: 5 × 2 = 10 5 × 20 = 100 5 × 200 = 1000 5 × 2,000 = 10,000.

Explanation: 5 × 2 = 10.

By using the place-value method, 5 × 20 = 5 × 2 tens = 10 × tens = 100 So, 5 × 20 = 100.

By using the place-value method, 5 × 200 = 5 × 20 tens = 5 × 2 × tens × tens = 10 ×  tens × tens = 1000 So, 5 × 200 = 1000.

By using the place-value method, 5 × 2,000 = 5× 200 tens = 5 × 20 × tens × tens = 5 × 2 × tens ×  tens × tens = 10× tens × tens × tens = 10,000 So, 5 × 2,000 = 10,000.

Question 3. 2 × 3 = _____ 2 × 300 = _____ Answer: 2 × 3 = 6 2 × 300 = 600

Explanation:  we should multiply 2 by 3 to get 6.

By using the place-value method, 2 × 300 = 2 × 30 tens = 2 × 3 × tens × tens = 6 ×  tens × tens = 600 So, 2 × 300 = 600.

Question 4. 9 × 8 = _____ 9 × 8,000 = _____ Answer: 9 × 8 = 72 9 × 8,000 = 72,000

Explanation: we should multiply 9 by 8 to get 72.

By using the place-value method, 9 × 8,000 = 9 × 800 tens = 9 × 80 × tens × tens = 9 × 8 × tens ×  tens × tens = 72× tens × tens × tens = 72,000 So, 9 × 8,000 = 72,000.

Find the product Question 5. 7 × 700 = _____ Answer: 4900

Explanation:

By using the place-value method, 7 × 700 = 7 × 70 tens = 7 × 7 × tens × tens = 49 ×  tens × tens = 4900 So, 7 × 700 = 4900.

Question 6. 3 × 100 = _____ Answer: 300

Explanation: By using the place-value method, 3 × 100 = 3 × 10 tens = 3 × tens × tens = 30× tens = 300 So, 3 × 100 = 300.

Question 7. 8,000 × 3 = _____ Answer: 24,000

Explanation : By using the place-value method, 3 × 8,000 = 9 × 800 tens = 3 × 80 × tens × tens = 3 × 8 × tens ×  tens × tens = 24× tens × tens × tens = 24,000 So, 3 × 8,000 = 24,000.

Question 8. 60 × 2 = _____ Answer: 120

Explanation: By using the place-value method, 2 × 60 = 2 × 6 tens = 12 × tens = 120 So, 2 × 60 = 120.

Question 9. 4 × 4,000 = ______ Answer: 16,000.

Explanation : By using the place-value method, 4 × 4,000 = 4 × 400 tens = 4 × 40 × tens × tens = 4 × 4 × tens ×  tens × tens = 16 × tens × tens × tens = 16,000 So, 4 × 4,000 = 16,000.

Question 10. 700 × 5 = _____ Answer: 3500

Explanation: By using the place-value method, 5 × 700 = 5 ×70 tens = 5 ×7 × tens × tens = 350× tens = 3500 So, 5 × 700 = 3500.

Question 11. 900 × 7 = _____ Answer: 6300

Explanation: By using the place-value method, 7 × 900 = 7 × 90 tens = 7 × 9 × tens × tens = 63 × tens × tens = 6300 So, 7  × 900 = 6300.

Question 12. 50 × 3 = _____ Answer: 150

Explanation: By using the place-value method, 3 × 50 = 3 × 5 × tens = 15 × tens = 150 So, 3 × 50 = 150.

Question 13. 1,000 × 8 = ______ Answer: 8000

Explanation : By using the place-value method, 8 × 1,000 = 8 × 100 tens = 8 × 10 × tens × tens = 8 × tens ×  tens × tens = 8,000 So, 8 × 1,000 = 8,000.

Find the missing factor Question 14. _____ × 6,000 = 24,000 Answer:  4 × 6,000 = 24,000

Explanation :Let the missing number be X So, X × 6,000 = 24,000 X = 24,000 / 6,000 = 4 Hence, the value of X is: 4.

Question 15. 9 × ____ = 450 Answer: 9 × 50 = 450

Explanation : Let the missing number be X So, 9 × X = 450 X = 450 / 9 = 50 Hence, the value of X is: 50.

Question 16. _____ × 30 = 210 Answer: 7 × 30 = 210

Explanation: Let the missing number be X So, X × 30 = 210 X = 210 / 30 = 7 Hence, the value of X is: 7

Question 17. 2 × _____ = 800 Answer: 2 × 400 = 800

Explanation: Let the missing number be X So, 2 × X = 800 X = 800 / 2 = 400 Hence, the value of X is: 400.

Question 18. _____ × 1,000 = 9,000 Answer: 9 × 1,000 = 9,000

Explanation: Let the missing number be X So, X × 1,000 = 9,000 X = 9,000 / 1,000 = 9 Hence, the value of X is: 9.

Question 19. 8 × ____ = 640 Answer: 8 × 80 = 640.

Explanation : Let the missing number be X So, 8 × X = 640 X = 640 / 8 = 80 Hence, the value of X is: 80

Explanation: 7 × 60 = 420 Given numbers are: 420 and 400 By comparing 2 values, we can conclude that 420 is greater than 400

Explanation: 500 × 4 = 2,000 Given numbers are: 2,000 and 2,000 By comparing 2 values, we can conclude that 2,000 is equal to 2,000

Explanation : 3 × 9,000 = 27,000 Given numbers are: 27,000 and 39,000 By comparing 2 values, we can conclude that 27,000 is less than 39,000.

Explanation: Let us say North Canadian river as N and Amazon river as A , Given that Amazon river is 5 times longer than North Canadian river so A = 5N N = 800 miles, get this value into above equation then, A = 5(800) = 5 × 800 = 4,000. so Amazon river is 4,000 miles long.

Question 24. One reusable bag can prevent the use of 600 plastic bags. Six reusable bags can prevent the use of how many plastic bags? Answer: 3600 plastic bags

Explanation: Given that , One reusable bag can prevent the use of 600 plastic bags. if one bag = 600 plastic bags then six bags  = ? let us multiply the bags then we have 6 × 600 = 3600. so, answer is 3600 plastic bags.

Question 25. YOU BE THE TEACHER Your friend says the product of 6 and 500 will have2 zeros. Is your friend correct? Explain. Answer: NO

Explanation:  6 × 500 = 3,000. they mentioned that result will have 2 zero’s, but the actual product gives 3 zero’s.

Explanation: Let us say Aquarium as A and Dolphins as D Given that A = 7D, Aquarium has 510 pounds of fish Each D = 60 pounds, we get A = 7 (60) = 7 × 60 = 420. All the dolphins will eat 420 pounds of fish and the Aquarium has 510 pounds.510 is greater than 420

Think: What do you know? What do you need to find? How will you solve? Step 1: How many pounds of fish do all of the dolphins eat? 7 × 60 = _____ Answer: 7 × 60 = 420. All of the dolphins eat _______ pounds of fish. Answer: 420 pounds. Step 2: Compare the number of pounds of fish all of the dolphin seat to the number of pounds of fish the aquarium has. Answer: Aquarium has 510 pounds of fish and all the dolphins will eat 420 pounds of fish so, 510 is greater than 420 The aquarium _______ have enough fish to feed the dolphins. Answer: 510 pounds of fish.

Explanation: Let us say Dream catcher as D and Feathers as F, total Dream catchers we want are 400 and Each Dream catcher needs 8 Feathers  so D = 8F, students have 3,100 Feathers Then , by calculating , 3,100 /8 = 387.5. to get up to the total count of required 400 Dream catchers Feathers are not sufficient as 400 is greater than 387.

Question 27. A principal has 3 rolls of 800 raffle tickets each and 5 rolls of 9,000 raffle tickets each. How many raffle tickets does the principal have? Answer: 47,400 raffle tickets are there with the principal.

Explanation: A principal has 3 rolls of 800 raffle tickets each and 5 rolls of 9,000 raffle tickets each. Then we have 3 × 800 and 5 × 9,000 = 2,400 and 45,000 Totally , 45,000 + 2,400 = 47,400 .

So, 47,400 raffle tickets are there with the principal.

Question 28. You have 2 sheets of 4 stickers each. Your friend has 20 times as many stickers as you. Your teacher has 700 times as many stickers as you. How many stickers do the three of you have in all? Answer: Three of us have  5,768 stickers in all.

Explanation: You have 2 sheets of 4 stickers each. that is 2 × 4 = 8 stickers. Your friend has 20 times as many stickers as you. that is 20 × 8 = 160 stickers. Your teacher has 700 times as many stickers as you. that is 700 × 8 = 5,600 stickers. Then 5,600 + 160 + 8 = 5,768 stickers.

So, Three of us have  5,768 stickers in all.

Find each product Question 1. 3 × 3 = ____ 3 × 30 = ____ 3× 300 = ______ 3 × 3,000 = _____ Answer: 3 × 3 = 9 3 × 30 = 90 3× 300 = 900 3 × 3,000 = 9,000

Explanation:  3 × 3 = 9

By using the place-value method, 3 × 30 = 3× 3 × tens = 9 × tens = 90 So, 3 × 30= 90.

By using the place-value method, 3 × 300 = 3× 30 tens = 3 × 3 × tens × tens = 9 × tens × tens = 900 So, 3 × 300= 900.

By using the place-value method, 3 × 3,000 = 3 × 300 tens = 3 × 30 × tens × tens = 3 × 3 × tens ×  tens × tens = 9 × tens × tens × tens = 9,000 So, 3 × 3,000 = 9,000.

Question 2. 8 × 7 = ____ 8 × 70 = ____ 8 × 700 = ______ 8 × 7,000 = _____ Answer: 8 × 7 = 56 8 × 70 = 560 8 × 700 = 5600 8 × 7,000 = 56,000

Explanation:  8 × 7 = 56

By using the place-value method, 8 × 70 = 8 × 7 tens = 8 × 7 × tens = 56 × tens = 560 So, 8 × 70= 560.

By using the place-value method, 8 × 700 = 8 × 70 tens = 8 × 7 × tens × tens = 56 × tens × tens = 5600 So, 8 × 700= 5600.

By using the place-value method, 8 × 7,000 = 8 × 700 tens = 8 × 70 × tens × tens = 8 × 7 × tens ×  tens × tens = 56 × tens × tens × tens = 56,000 So, 8 × 7,000 = 56,000.

Find the product. Question 3. 9 × 90 = ____ Answer: 9 × 90 = 810

Explanation:  we should multiply 9 by 9 to get 81 that implies 9 × 90 = 810. By using the place-value method, 9 × 90 = 9 × 9 tens = 81 × tens = 810 So, 9 × 90 = 810.

Question 4. 6,000 × 1 = _____ Answer: 6,000 × 1 = 6,000.

Explanation : By using the place-value method, 1 × 6,000 = 1× 600 tens = 1 × 60 × tens × tens = 1 × 6 × tens ×  tens × tens = 6 × tens × tens × tens = 6,000 So, 1 × 6,000 = 6,000.

Question 5. 8 × 200 = _____ Answer: 8 × 200 = 1600.

Explanation: By using the place-value method, 8 × 200 = 8 ×20 tens = 8 ×2 × tens × tens = 160× tens = 1600 So, 8 × 200 = 1600.

Question 6. 3,000 × 6 = _____ Answer: 3,000 × 6 = 18,000.

Explanation : By using the place-value method, 6 × 3,000 = 6 × 300 tens = 6 × 30 × tens × tens = 6 × 3 × tens ×  tens × tens = 18 × tens × tens × tens = 18,000 So, 6 × 3,000 = 18,000.

Question 7. 5 × 500 = _____ Answer: 5 × 500 = 2500.

Explanation: By using the place-value method, 5 × 500 = 5 ×50 tens = 5 ×5 × tens × tens = 250× tens = 2500 So, 5 × 500 = 2500.

Question 8. 2 × 90 = ______ Answer: 2 × 90 = 180

Explanation: By using the place-value method, 2 × 90 = 2 × 9 × tens = 18 × tens = 180 So, 2 × 90 = 180.

Question 9. 7 × 300 = ______ Answer: 7 × 300 = 2100

Explanation: By using the place-value method, 7 × 300 = 7 × 30 tens = 7 × 3 × tens × tens = 21 × tens × tens = 2100 So, 7  × 300 = 2100.

Question 10. 20 × 2 = _____ Answer:  20 × 2 = 40

Explanation: By using the place-value method, 2 × 20 = 2 × 2 × tens = 4 × tens = 40 So, 2 × 20 = 40.

Question 11. 6,000 × 5 = _____ Answer:  6,000 × 5 = 30,000.

Explanation : By using the place-value method, 5 × 6,000 = 5 × 600 tens = 5 × 60 × tens × tens = 5 × tens ×  tens × tens = 30,000 So, 5 × 6,000 = 30,000.

Find the missing factor. Question 12. _____ × 400 = 3,200 Answer:  8 × 400 = 3,200

Explanation: Let the missing number be X So, X × 400 = 3,200 X = 3,200 / 300 = 8 Hence, the value of X is: 8

Question 13. 1 × _____ = 500 Answer: 1 × 500 = 500.

Explanation: Let the missing number be X So, 1 × X = 500 X = 500 / 1 = 500 Hence, the value of X is: 500

Question 14. _____ × 300 = 1,200 Answer:  4 × 300 = 1,200

Explanation: Let the missing number be X So, X × 300 = 1,200 X = 1,200 / 300 = 4 Hence, the value of X is: 4

Question 15. 8 × ____ = 720 Answer: 8 × 90 = 720

Explanation: Let the missing number be X So, 8 × X = 720 X = 720 / 8 = 90 Hence, the value of X is: 90

Question 16. _____ × 1,000 = 7,000 Answer:   7 × 1,000 = 7,000

Explanation : Let the missing number be X So, X × 1,000 = 7,000 X = 7,000 / 1,000 = 7 Hence, the value of X is: 7

Question 17. 8 × _____ = 4,800 Answer: 8 × 600 = 4,800

Explanation: Let the missing number be X So, 8 × X = 4,800 X = 4,800 / 8 = 600 Hence, the value of X is: 600

Explanation: 9 × 400 = 3,600 Given numbers are: 3,600 and 3,600 By comparing 2 values, we can conclude that 3,600 is equal to 3,600

Explanation: 6 × 60 = 360 Given numbers are: 360 and 660 By comparing 2 values, we can conclude that 360 is less than 660.

Explanation: 8,000 × 2 = 16,000 Given numbers are: 16,000 and 10,000 By comparing 2 values, we can conclude that 16,000 is greater than 10,000

Question 21. Patterns Describe and complete the pattern. 1 × 4 = _____ 2 × 40 = _____ 3 × 400 = ____ _____ × _____ = _____ _____ × _____ = ______ Answer:  1 × 4 = 4 2 × 40 = 80 3 × 400 = 1200 4 × 4,000 = 16,000 5 × 40,000 = 200,000 Explanation :  we should multiply the numbers 1 and 4 to get 4 . By using the place-value method, 2 × 40 = 2 × 4 tens = 8 × tens = 80 So, 2 × 40 = 80.

By using the place-value method, 3 × 400 = 3 × 40 tens = 3 × 4 × tens × tens = 12 ×  tens × tens = 120× tens = 1200 So, 3 × 400 = 1200.

By using the place-value method, 4 × 4,000 = 4 × 4,000 tens = 4 × 40 × tens × tens = 4 × 4 × tens ×  tens × tens = 16× tens × tens × tens = 16,000 So, 4 × 4,000 = 16,000.

By using the place-value method, 5 × 40,000 = 5 × 4,000 tens = 5 × 400 × tens × tens = 5 × 40 × tens ×  tens × tens = 5 × 4 × tens × tens × tens × tens = 200,000 So, 5 × 40,000 = 200,000.

Question 22. DIG DEEPER! Without calculating, tell whether the product of 5 and 700 or the product of 5 and 7,000 is greater. Explain how you know. Answer: The place value method. This is a common  method used to know how to multiply by ten: When multiplying 5 by ten, the number moves to the left and a zero is put in, so the number becomes 50. If you multiply 5 by 100, the number moves two places to the left and zeros are put in, so the number would become 500.

Explanation: This shows that to know the greater value of the product of 5 and 700 or the product of 5 and 7,000 is determined by the place of the zero’s in the number. So, product of 5 and 7,000 is greater than the product of 5 and 700.

Question 23. Writing How does 3 × 6 help you to find 3,000 × 6? Explain. Answer: 3 × 6 = 18   so 3,000 × 6 = 18000.

Explanation: we should multiply the 3 and 6 to get 18 ,like wise the zero’s value increases when they start to move left side adding another zero until  the thousands place is filled so we have 3,000 × 6 = 18,000.

Question 24. Open-Ended Write a multiplication equation with a product of 120. Answer: 4 × 30 = 120 or 3 × 40 = 120

Explanation: the product of the two numbers 4 and 3 is 12 that implies if the zero, is in tens place in any one of the number in multiplying we get the same number as a product so, 4 × 30 = 120 or 3 × 40 = 120.

Question 25. Modeling Real Life A second grade student answers about 2,000 math problems each month. A fourth grade student answers about 7,000 math problems each month. How many total problems would 8 second grade students and 9 fourth grade students answer in one month? Answer: Totally they both answer 79,000 math problems in one month.

Explanation: A second grade student answers about 2,000 math problems each month. For 8 students to solve in 1 month we have, 8 × 2,000 = 16,000.

A fourth grade student answers about 7,000 math problems each month. For 9 students to solve in 1 month we have, 9 × 7,000 = 63,000.

They both have answered, 63,000 + 16,000 = 79,000. Totally they both answer 79,000 math problems in one month.

Explanation: A teacher has 5 boxes with 50 pencils in each box.  so, 5 × 50 = 250 pencils He also has 3 boxes with 20 pens in each box. so, 3 × 20 = 60 pens. A student donates 25 pencils. so 250 + 25 = 275 pencils.

So, He has 275 pencils and 60 pens.

Lesson 3.3 Estimate Products of Rounding

Round 92 to the nearest ten. Answer:  90 Explanation: Round the nearest tens , so 92 is close to 90.

Round 92 to the nearest hundred. Answer: 100 Explanation: Round the nearest tens , so 92 is close to 100.

Which estimate do you think is closer to the total number of marbles? Explain. Answer:   540. The one 92 is closer to 90. Because marbles in all jars are calculated as 552 by multiplying the 6 and 992.

Explanation: 1 jar has 92 marbles, then 6 jars has  6 × 92 marbles Round to the nearest tens. 92 is close to 90; 6 x 90 = 540. and Round to the nearest tens. 92 is close to 100; 6 x 100 = 600. So the total number of marbles count is in between 540 and 600.

Repeated Reasoning Would your answer to the question above change if there were 192 marbles in each jar? Explain Answer: Yes. 1,140 and 1200.

Explanation: 1 jar has 192 marbles, then 6 jars has  6 × 192 marbles Round to the nearest tens. 192 is close to 190; 6 x 190 = 1,140. and Round to the nearest tens. 192 is close to 200; 6 x 200 = 1200. So the total number of marbles count is in between 1,140 and 1200.

Think and Grow: Estimate Products

Explanation: Round to the nearest tens. 76 is close to 70; 4 x 70 = 280. or Explanation: Round to the nearest tens. 76 is close to 80; 80 x 4 = 320

Estimate the product. Question 1. 3 × 89 Answer: 270

Explanation: Round to the nearest tens. 89 is close to 90; 3 x 90 = 270

Question 2. 8 × 721 Answer: 5,760

Explanation: Round to the nearest tens. 721 is close to 720; 8 x 720 = 5,760

Question 3. 5 × 7,938 Answer: 39,700

Explanation: Round to the nearest tens. 7,938 is close to 7,940; 5  x  7,940 = 39,700

Find two estimates that the product is between Question 4. 9 × 44 Answer: 360 and 450

Explanation: Round to the nearest tens. 44 is close to 40; 9 x 40 = 360 and Explanation: Round to the nearest tens. 44 is close to 50; 9 x 50 = 450 The product is in between 360 and 450.

Question 5. 2 × 657 Answer:  1,300 and  1,320

Explanation: Round to the nearest tens. 657 is close to 650; 2 x 650 = 1,300 and Explanation: Round to the nearest tens. 657 is close to 660; 2 x 660 = 1,320 The product is in between 1,300 and  1,320

Question 6. 6 × 4,243 Answer:  25,440 and 25,500

Explanation: Round to the nearest tens. 4,243 is close to 4,240; 6 x 4,240 = 25,440 and Explanation: Round to the nearest tens. 4,243 is close to 4,250; 6 x 4,250 = 25,500 The product is in between 25,440 and 25,500

Estimate the product. Question 7. 4 × 65 Answer: 240

Explanation: Round to the nearest tens. 65 is close to 60; 4 x 60 = 240

Question 8. 248 × 7 Answer:  1,750

Explanation: Round to the nearest tens. 248 is close to 250; 250 x 7 = 1,750

Question 9. 3 × 9,032 Answer: 27,090

Explanation: Round to the nearest tens. 9,032 is close to 9,030; 3 x 9,030 = 27,090

Find two estimates that the product is between. Question 10. 32 × 9 Answer:  270 and  360

Explanation: Round to the nearest tens. 32 is close to 30; 9 x 30 = 270 and Explanation: Round to the nearest tens. 32 is close to 40; 9 x 40 = 360 The product is in between 270 and 360

Question 11. 970 × 5 Answer: 4,850

Explanation: There is no need to Round to the nearest tens. Because the number 970 is already has its tens value 970 x 5 = 4,850 .

Question 12. 6 × 5,328 Answer:  31,920 and 31,968

Explanation: Round to the nearest tens. 5,328 is close to 5,320; 6 x 5,320 = 31,920

Explanation: Round to the nearest tens. 5,328 is close to 5,330; 6 x 5,330 = 31,968

Explanation: if each watch cost $199, 4 × 199 then 4 watches costs $ 800 Round to the nearest tens. 199 is close to 200; 4 x 200 = 800 The estimated cost is $800.

Explanation: The given number is already at its tens place so, There is no need to Round to the nearest tens. 480 x 8 = 3,840

Explanation: Round to the nearest tens. 1,904 is close to 1,900; 1,900 x 4 = 7,600

Explanation: Round to the nearest tens. 8,932 is close to 8,930; 5 x 8,930 = 44,650 The product is estimated as the nearest to 40,000

Question 17. Estimate: 9,000 _____ × ____ Answer:  3 and  2,842 are used here. Explanation: Round to the nearest tens. 2,842 is close to 2,850; 3 x 2,850 = 8,550 The product is estimated as the nearest to 9,000

Question 18. Estimate: 72,000 _____ × ______ Answer: 8 and 8,932  are used here.

Explanation: Round to the nearest tens. 8,932 is close to 8,930; 8 x 8,930 = 71,440 The product is estimated as the nearest to 72,000.

Question 19. Estimate: 45,000 _____ × ______ Answer:   5 and 8,932  are used here.

Explanation: Round to the nearest tens. 8,932 is close to 8,930; 5 x 8,930 = 44,650 The product is estimated as the nearest to 45,000.

Explanation: Estimation of the amount of money earned from new release rentals is Round to the nearest tens. 3,047 is close to 3,050; $5 x 3,050 = $15,250

Estimation of the amount of money earned from top pick rentals is Round to the nearest tens. 3,986 is close to 3,990; $3 x 3,990 = $11,970

Use the graph above. Question 20. About how much more money was earned from top pick rentals than from television episode rentals? Answer:  Estimation of the amount of money earned from top pick rentals is  $11,970 Estimation of the amount of money earned from to television episode rentals is $1,700 Money was earned from top pick rentals than from television episode rentals is $10,270

Explanation:   Estimation of the amount of money earned from top pick rentals is Round to the nearest tens. 3,986 is close to 3,990; $3 x 3,990 = $11,970

Estimation of the amount of money earned from to television episode rentals is Round to the nearest tens. 849 is close to 850; $2 x 850 = $1,700

Money was earned from top pick rentals than from television episode rentals is subtract $1,700 from $11,970 we get  $10,270.

Question 21. Your friend says that the number of top picks rented is about 5 times as many as the number of television episodes rented. Is your friend correct? Explain. Answer: yes. The number of top picks rented is about 5 times as many as the number of television episodes rented.

The number of top picks rented is about 5 times as many as the number of television episodes rented. 5 × $1,700 = $8,500

Explanation: Estimation of the amount of money earned from new release rentals is Round to the nearest tens. 3,047 is close to 3,040; $5 x 3,040 = $15,200 Estimation of the amount of money earned from new release rentals is Round to the nearest tens. 3,047 is close to 3,050; $5 x 3,050 =  $15,250 The estimated product should be in between  $15,200 and $15,250

Estimate Products of Rounding Homework & Practice 3.3

Estimate the product Question 1. 7 × 42 Answer: 280

Explanation: Round to the nearest tens. 42 is close to 40; 7 x 40 = 280

Question 2. 85 × 4 Answer: 320

Explanation: Round to the nearest tens. 85 is close to 80; 4 x 80 = 320

Question 3. 2 × 698 Answer: 1,400

Explanation: Round to the nearest tens. 698 is close to 700; 2 x 700 = 1,400

Question 4. 6 × 705 Answer: 4,200

Explanation: Round to the nearest tens. 705 is close to 700; 6 x 700 = 4,200

Question 5. 1,834 × 9 Answer: 16,470

Explanation: Round to the nearest tens. 1,834 is close to 1,830; 9 x 1,830 = 16,470

Question 6. 7,923 × 8 Answer: 63,360

Explanation: Round to the nearest tens. 7,923 is close to 7,920; 8 x 7,920 = 63,360

Find two estimates that the product is between Question 7. 3 × 95 Answer: 270 and 300

Explanation: Round to the nearest tens. 95 is close to 90; 3 x 90 = 270 and Explanation: Round to the nearest tens. 95 is close to 100; 3 x 100 = 300 The product is in between 270 and 300

Question 8. 23 × 5 Answer: 100 and 150

Explanation: Round to the nearest tens. 23 is close to 20; 20 x 5 = 100 and Explanation: Round to the nearest tens. 23 is close to 30; 5 x 30 = 150 The product is in between 100 and 150

Question 9. 537 × 6 Answer: 3,240 and 3,180

Explanation: Round to the nearest tens. 537 is close to 530; 6 x 530 = 3,180 and Explanation: Round to the nearest tens. 537 is close to 540; 6 x 540 = 3,240 The product is in between 3,240 and 3,180

Question 10. 8 × 309 Answer: 2,400 and 2,4800

Explanation: Round to the nearest tens. 309 is close to 300; 8 x 300 = 2,400 and Explanation: Round to the nearest tens. 309 is close to 310; 8 x 310 = 2,480 The product is in between 2,400 and 2,4800

Question 11. 1,649 × 7 Answer:

Explanation: Round to the nearest tens. 1,649 is close to 1,640; 1,640 x 7 = 11,480 and Explanation: Round to the nearest tens. 1,649 is close to 1,650; 1,650 x 7 = 11,550 The product is in between 11,480  and  11,550.

Question 12. 4 × 6,203 Answer: 24,800  and  24,840.

Explanation: Round to the nearest tens. 6,203 is close to 6,200; 4 x 6,200 = 24,800

Explanation: Round to the nearest tens. 6,203 is close to 6,210; 4 x 6,210 = 24,840

The product is in between  24,800  and  24,840.

Question 13. Construction workers build 54 feet of a bridge each day for 9 days. To determine whether the bridge is at least 490 feet long, can you use an estimate, or is an exact answer required? Explain. Answer: exact answer is 9 × 54 = 486 feet long .which is close to the target of 490 feet long

Explanation: if 54 feet of a bridge  each day for 9 days, we get 9 × 54 Round to the nearest tens. 54 is close to 500; 9 x 50 = 450. The estimated product 450 feet is close to given target of 490 feet long and an exact answer can also satisfies.

Question 15. DIG DEEPER! An astronaut earns $5,428 each month. You estimate that she will earn $35,000 in 7 months. Is the amount she earns in 7 months greater than or less than your estimate? Explain. Answer: The estimated product  $38,010 is greater than the given $35,000.

Explanation: if astronaut earns $5,428 each month then , Estimation of the amount of money earned for 7 months is $5,428 × 7 Round to the nearest tens. 5,428 is close to 5,430; $5,430 x 7 = $38,010 The estimated product  $38,010 is greater than the given $35,000.

Question 16. Writing Explain how estimating by rounding can be helpful as a check when finding a product. Answer:  sTo find the actual product of the two factors of numbers are quite hard for larger digit numbers so by rounding the higher digit numbers which have nearest to 10’s or 100’s. We will get the estimated product easily and fast . To get the actual product we have to use the normal method .

Explanation: whale has heart rate of 20 Bpm Horse has around 40 Bpm as per the given details, so Horse = 2(20) Bpm Horse has a heart rate that is about 2 times as fast as a whale’s

Question 18. About how many times does a giraffe’s heart beat in 5 minutes? Find two estimates that the answer is between. Answer:  300 and 350 times Explanation: Giraffe’s heart beat is in between 60  and 70 as per the details so to find for 5 min we have to multiply 5 × 60  and 5 × 70 so, 300 and 350 is the estimation times.

Use the Distributive Property to find the product. Question 19. 9 × 6 = ____ × (5 + ____) = (9 × 5) + (____ + _____) = ____ + ____ = _____ Answer: 54

Explanation: by using Distributive property 9 × 6 = 9 × (5 + 1) = (9 × 5) + (9 × 1) = 45 + 9 = 54

Question 20. 7 × 7 = 7 × (5 + ____) = (_____ × 5) + (7 × _____) = _____ + _____ = _____ Answer: 49

Explanation: by using Distributive property 7 × 7 = 7 × (5 + 2) = (7 × 5) + (7 × 2) = 35 + 14 = 49

Lesson 3.4 Use the Distributive Property to Multiply

Reasoning How does this strategy relate to the Distributive Property? Explain. Answer: Because of the evenly distributed  numbering among the place – values of the numbers. This property helps to find the product in a easy way.

Think and Grow: Use the Distributive Property to Multiply

Find the product. Question 6. 3 × 46 = _____ Answer: 129 Explanation: by using distributive property 3 × 43 = 3 × (40 + 3) = (3 × 40) + (3 × 3) = 120 + 9 = 129

Question 7. 8 × 35 = ____ Answer: 280

Explanation: by using distributive property 8 × 35 = 8× (30 + 5) = (8 × 30) + (8 × 5) = 240 + 40 = 280

Question 8. 5 × 72 = _____ Answer: 360

Explanation: by using distributive property 5 × 72 = 5 × (70 + 2) = (5 × 70) + (5 × 2) = 350 + 10 = 360

Explanation: by using distributive property 9 × 78 = 9× (70 + 8) = (9 × 70) + (9 × 8) = 630 + 72 = 702 Compare the number of spaces to the number of cars trying to park in the garage. There _____ enough parking spaces. Explain: Answer:  Total number of spaces in the garage are 702 but as per the given details 705 are trying to park in the garage . There are not enough parking spaces.

Question 10. Your piano teacher wants you to practice playing the piano 160 minutes this month. So far, you have practiced 5 minutes each day for 24 days. Have you reached the goal your teacher set for you? Explain. Answer: 150 minutes Explanation : practice for 160 minutes in a month ,say that 30 days So far, you have practiced 5 minutes each day for 24 days. then, 5 × 24, By using distributive property = 5 × (20+ 4) = (5 × 20) + (5 × 4) = 100 + 20 = 120 Remaining 6 days have to be practiced so ,5 × 6, By using distributive property = 5 × (4 + 2) = (5 × 4) + (5 × 2) = 20 +10 = 30 Totally we have 120 + 30 = 150

Explanation: Baby orangutan  = 3 pounds Mother orangutan weighs 27 times as much as the baby , 27 × 3, By using distributive property 3 × 27 = 3 × (20 + 7) = (3 × 20) + ( 3 × 7) = 60+21 = 81. father orangutan weighs 63 times as much as the baby, 63 × 3, By using distributive property 63 × 3 = 3 × (60 + 3) = (3 × 60) + (3 × 3) = 180 + 9 = 189.

Find the product. Question 4. 9 × 56 = ____ Answer: 504

Explanation: 9 × 56= 9 ×(50+6) =(9×50)+ (9×6) =450 + 54 =504

Question 5. 71 × 2 = _____ Answer:  142

Explanation:  71 × 2 = 2 × (70+ 1) =(2×70)+ (2×1) = 140+2 =142

Question 6. 3 × 77 = ____ Answer:  231

Explanation:  77 × 3 = 3 × (70+ 7) =(3×70)+ (3×7) = 210 + 21 =231

Question 7. Writing Explain how you can use the Distributive Property to find a product. Answer: The Distributive   Property states that when you multiply the sum of two or more addends by a factor, the product  is the same as if you multiplied each addend by the factor and then added the partial products .

Question 8. Structure Use the Distributive Property to find 6 × 18 two different ways. Answer: 108 Explanation: 6 ×18 = 6 ×(10+8) =(6×10)+ (6×8) =60 + 48 = 108 or Explanation: 6 ×18= 6 ×(9 + 9) =(6×9)+ (6 ×9) =54 +54 = 108

Question 9. Reasoning To find 4 × 22, would you rather break apart the factor 22 as 20 + 2 or as 11 + 11? Explain. Answer:  88. I would rather prefer to break apart the factor 22 as 20 + 2 . as it has zero’s in the tens place it would be easier to calculate and both of them are correct and anyone can use it on their Explanation: 4× 22 = 4 ×(20+2) = (4×20)+ (4×2) = 80 + 8 = 88 or Explanation: 4× 22 = 4 ×(11+11) = (4×11)+ (4×11) = 44 + 44 = 88

Explanation: The diameter of a firework burst, in feet, is 45 times the height of the shell in inches You have an 8-inch firework shell converting into feet e get 0.66 feet so diameter = 45 × 0.66 =  29.7 feet The shell  does not produce a firework burst that has a diameter greater than 375 feet

Explanation:  juvenile bearded dragon should eat 48 crickets each day To feed 3 juvenile bearded dragons , 3 × 48 = 3 × (40 + 8) = ( 3 × 40) + (3 × 8) = 120 + 24 = 144. You have150 crickets , we can feed them by 144 crickets

Repeated Reasoning Explain to your partner how you can use expanded form to find 364 × 8. Answer:  2,912 Explanation: 364 × 8 , by expanding we get = (300 + 60 + 4) × 8, by using distributive property, we get = (8 × 300) + ( 8 × 60) + ( 8× 4), Area model = 2400 + 360  + 32 The sum of the partial products is 2,912.

Think and Grow: Use Expanded Form to Multiply

Find the product. Question 1. 4 × 306 = 4 × (_____ + _____) = (4 × _____) + (4 × _____) = ____ + _____ = ______ Answer: 1,224 Explanation :  4 × 306 = 4 × ( 300 + 6 ) = (4 × 300 ) + (4 × 6 ) by using distributive property we get = 1200 + 24 = 1,224

Question 2. 7 × 549 Answer:  3,843

Explanation :  7 × 549 = 4 × ( 500 + 40 + 9 ) = (7 × 500 ) + (7 × 40 ) + (7 × 9)  by using distributive property we get = 3,500 + 280 + 63 = 3,843

Explanation :  6 × 85 = 6 × ( 80 + 5 ) = (6 × 80 ) + (6 × 5 ) by using distributive property we get = 480 + 30 = 510

Explanation :  2 × 932 = 2 × ( 900 + 30 + 2 ) = (2 × 900 ) + (2 × 30 ) + ( 2 ×2)  by using distributive property we get = 1800 + 60 + 4 = 1,864

Question 5. 4 × 690 = 4 × (_____ + ______) = (4 × _____) + (4 × ____) = _____ + _____ = _____ Answer: 2,760

Explanation: 4 × 690 = 4 × (600 + 90) = (4 × 600) + (4 × 90) = 2,400 + 360 = 2,760

Question 6. 1,027 × 9 = (_____ + _____ + ______) × 9 = (____ × 9) + (_____ × 9) + (_____ × 9) = _____ + ______ + _____ = _____ Answer: 9,243

Explanation: 1,027 × 9 = (1000+ 20 + 7) × 9 = (1000 × 9) + (20 × 9) + (7 × 9) = 9000 + 180 + 63 = 9,243

Question 7. 487 × 5 = _____ Answer: 2,435

Explanation :  5 × 487 = 5 × ( 400 + 80 + 7 ) = (5 × 400 ) + (5 × 80 ) + ( 5 ×7 )  by using distributive property we get = 2000 + 400 + 35 = 2,435

Question 8. 8 × 2,483 = ______ Answer: 19,864

Explanation :  8 × 2,483 = 8 × (2000 + 400 + 80 + 3 ) = (8 × 2000 ) + (8 × 400 ) + ( 8 ×80) + (8 ×3)   by using distributive property we get = 16,000 + 3200 + 640 +24 = 19,864

Question 9. A basketball player made 269 three-point shots in a season. How many points did he score from three-point shots? Answer:

Question 10. Your cousin runs 6 miles each week. There are 5,280 feet in a mile. How many feet does your cousin run each week? Answer: 6 × 5,280 = 31,680

Explanation :  cousin runs 6 miles each week. There are 5,280 feet in a mile.so we have 6 × 5,280 6 × 5,280 = 6 × (5000 + 200 + 80 ) = (6 × 5000 ) + (6 × 200 ) + ( 6 ×80)  by using distributive property we get = 30,000 + 1200 + 480 = 31,680.

Question 11. YOU BE THE TEACHER Your friend finds 744 × 3. Is your friend correct? Explain. 744 × 3 = (700 + 40 + 4) × 3 = (700 × 3) + (40 × 3) + (4 × 3) = 2,100 + 120 + 12 = 2,232 Answer: Yes

Explanation: By using expanding form and distributive property we get, 744 × 3 = (700 + 40 + 4) × 3 = (700 × 3) + (40 × 3) + (4 × 3) = 2,100 + 120 + 12 = 2,232

Question 12. DIG DEEPER! What is the greatest possible product of a two-digit number and a one-digit number? Explain. Answer:  891 The greatest two digit number is 99 and the greatest single digit number is 9. The products when the two are multiplied. Multiply 99 by 9 to get 891.

Explanation : 99 × 9 = 891

Find the number of fluid ounces of milk the baby hippo drinks in 1 day. 5 × 77 = 5 × (70 + 7) = (5 × 70) + (5 × 7) = _____ +____ = _____

Answer : 385 Explanation: baby hippo is fed 77 fluid ounces of milk 5 times each day that is, 5 × 77 = 5 × (70 + 7 ) = (5 ×70) + (5 ×7) = 350 + 35 = 385

Find the number of fluid ounces in 2 gallons 2 × 128 = 2 × (100 + 20 + 8) = (2 × 100) + (2 × 20) + (2 × 8) = ___ + _____ + _____ = _____ Answer: 256 Explanation: 2 × 128 = 2 × (100 + 20 + 8) = (2 × 100) + (2 × 20) + (2 × 8) = 200 +40 + 16 = 256. Compare the products. Answer: Baby hippo is fed 77 fluid ounces of milk 5 times each day that is, 5 × 77 is 385 ounces There are 128 fluid ounces in 1 gallon , then for 2 gallons it will 256 fluid ounces So, 385 ounces is greater than 256 ounces.

So, 2 gallons of milk ______ enough to feed the baby hippo for 1 day. Answer: 2 gallons of milk is not enough to feed the baby hippo for 1 day.s

Question 13. A school with 6 grades goes on a field trip. There are 64 students in each grade. One bus holds 48 students. Will 8 buses hold all of the students? Answer: YES , there are 384 students in total.

Explanation : A school with 6 grades goes on a field trip. There are 64 students in each grade. so we have 6 × 64 = 6 × ( 60 + 4 ) = (6 × 60) + ( 6 × 4) = 360 + 24 = 384. There are 8 buses in total One bus holds 48 students.so 8 × 48 = 8 × ( 40 + 8 ) = (8 × 40) + ( 8 × 8) = 320 + 64 = 384.

So, 8 buses are enough to carry the 384 students of all 6 grades.

Explanation: The average life span of a firefly is 61 days. The average life span of a Monarch butterfly is 4 times as long as that of a firefly. so, we have 4 × 61 = 4 × ( 60 + 1 ) = (4 × 60) + ( 4 × 1) = 240 + 4 = 244. Then 244 – 61 (The average life span of a firefly) is 183. So 183 days longer is the average lifespan of a Monarch butterfly than a firefly.

Explanation: His car can travel 337 miles using 1 tank of gasoline. He wants to travel to a city using no more than 3 tanks of gasoline. we have 3 × 337 = 3 × (300 + 30 + 7) = (3 × 300) + (3 × 30) + (3 × 7) = 900 +90 + 21 = 1,011. From the given details Los Angeles is the nearest one which he can drive with 3 tanks of gasoline  that is 1,016 miles.

Explanation: 7 × 803 = 7 × (800 + 3) = (7 × 800) + (7 × 3) = 5600 + 21 = 5,621.

Explanation: 9 × 1,024 = 9 × (1000 + 20 + 4) = (9 × 1000) + (9 × 20) + (9 × 4) = 9000 +180 + 36 = 9,216.

Question 3. 43 × 8 = (40 + 3) × 8 = (____ × 8) + (____ × 8) = ____ + ____ = _____ Answer: 344

Explanation: 8 × 43 = (40 + 3) × 8 = (40 × 8) + (3 × 8) = 320 + 24 = 344.

Question 4. 4 × 742 = 4 × (____ + ____ + _____) = (4 × ____) + (4 × _____) + (4 × _____) = ____ + _____ + _____ = _____ Answer: 2,968

Explanation: 4 × 742 = 4 × (700 + 40 + 2) = (4 × 700) + (4 × 40) + (4 × 2) = 2800 +160 + 8 = 2,968.

Question 5. 3 × 482 = _____ Answer: 1,446

Explanation: 3 × 482 = 2 × (400 + 80 + 2) = (3 × 400) + (3 × 80) + (3 × 2) = 1200 + 240 + 6 = 1,446.

Question 6. 4,591 × 6 = _____ Answer: 27,546

Explanation: 6 × 4,591 = 6 × (4,000 + 500 + 90 + 1) = (6 × 4,000) + ( 6 × 500) +(6 × 90) + ((6 × 1) = 24,000 + 3,000 + 540 + 6 = 27,546.

Explanation: A Venus flytrap has 128 lobes Each lobe on a Venus flytrap has 6 trigger hairs, we have 6 × 128 = 6 × (120 + 8) = (6 × 120) + (6 × 8) = 720 + 48 = 768 So, it has 768 trigger hairs.

Question 8. A human skeleton has 206 bones. How many bones do 4 skeletons have in all? Answer: 824

Explanation:  A human skeleton has 206 bones so 4 × 206 = 4 × ( 200 + 6) = (4 × 200) + ( 4 × 6) = 800 + 24 =824. So, 4 skeletons have 824 bones.

Question 9. Writing Explain how you can find 5 × 7,303 using expanded form. Answer: 36,515

Explanation: 5 × 7,303 = 5 × (7,000 + 300 + 3) = (5 × 7,000) + ( 5 × 300) + (5 × 3) = 35,000 + 15,000 + 15 = 36,515.

Question 10. Structure Rewrite the expression as a product of two factors. (6,000 × 3) + (70 × 3) + (4 × 3) Answer: 18,222

Explanation: (6,000 × 3) + (70 × 3) + (4 × 3) = (6,000 + 70 + 4) × 3 = 3 × 6,074 = 18,222.

Explanation:  A summer camp has 8 different groups of students. There are 35 students in each group, we have 8 × 35 = 8 × (30 + 5) = (8 × 30) + ( 8 × 5) = 240 + 40 =280. There are 24 shirts in a box for 9 boxes we have , 9 × 24 = 9 × (20 + 4) = (9 × 20) + ( 9 × 4) = 180 + 36 =216. So, there are not enough shirts for all the students.

Question 12. Modeling Real Life Firefighters respond to 65 calls in 1 week. Police officers respond to 8 times as many calls as firefighters in the same week. How many more calls do police officers respond to than firefighters in that week? Answer: 455 calls.

Explanation: Firefighters respond to 65 calls in 1 week. Police officers respond to 8 times as many calls as firefighters in the same week. we have, 8 × 65 = 8 × (60 + 5) = (8 × 60) + ( 8 × 5) = 480 + 40 =520. Then 520 – 65 (Firefighters respond to 65 calls in 1 week.) = 455. So, 455 calls do police officers respond to than firefighters in that week.

Explanation: Total mass = 500 +100 + 100 + 100 +100 +1 + 1 + 1 +10 =500 + 400 + 3 + 10 =913g

Explanation: 1 kg = 1000g Total mass = 1000 + 5 + 100 +100 + 100 + 10 + 10 +10 + 1g =1000 + 300 + 40 + 6 =1,346g

Explanation:  The product of the two numbers does not change as long as the factor numbers are same in the multiplication products that is (3 × 4 ) + ( 60 × 4) + ( 200 × 4) = 12 + 240 + 800 = 1,052.

Think and Grow: Practice

Answer: 194 × 3 = 582.

Example 2 Answer: 3,190 × 2 = 6,380

Question 15. Writing Write a multiplication word problem using the numbers 506 and 8. Then solve. Answer: 506 × 8 = 4,048

Question 17. Newton replaces all 4 tires on his car and pays $159 for each tire. Descartes replaces all 4 tires on his truck and pays $227 for each tire. How much more does Descartes pay to replace his tires? Answer:  $272 more has to pay to replace the tires.

Question 18. There are 52 weeks and 1 day in a year. There are 52 weeks and 2 days in a leap year. How many weeks are there in 6 years if one of the years is a leap year? Answer: There are 313 weeks are there for 6 years .

Question 11. DIG DEEPER! The sum of a four-digit number and a one-digit number is 7,231. The product of the numbers is 28,908. What are the numbers? Answer: 7227 and 4

Explanation: In geometry, a quadrilateral can be defined as a closed, two dimensional shape which has four straight sides. We can find the shape of quadrilaterals in various things around us, like in a chess board, a deck of cards, a kite, a tub of popcorn, a sign board and in an arrow.

Explanation: All sides are equal. All angles are equal and measure 90°.

Precision Use a model to find 15 × 8. Answer: 120

Think and Grow: Use Regrouping to Multiply

Explanation: Because 192  is close to the estimate, 180 , the answer is reasonable.

And the Estimate product is 80, because 12 is close to 10 , we have 10 × 8 = 80 So, 12 × 8 = 96

5 × 7 ones = 35 ones regrouping 35 ones as 3 tens and 5 ones 5 × 4 tens = 20 tens 20 tens + 3 tens = 23 tens  or  2 hundreds and 3 tens ,Then we get 235

And the estimated product is 250 because 47 is close to 50,then 50 × 5 = 250 So, 47 × 5 = 235

And the estimated product is 120 because 23 is close to 20 , so 20 × 6 = 120 So, 23 × 6 = 138

And the estimated product is 140 because 25 is close to 20 , so 20 × 7 = 120 So, 25 × 7 = 175

And the estimated product is 60 because 34 is close to 30 , so 30 × 2 = 60 So, 34 × 2 = 68

And the estimated product is 540 because 56 is close to 60 , so 60 × 9 = 540 So, 56 × 9 = 504

And the estimated product is 320 because 41 is close to 40 , so 40 × 8 = 320 So, 41 × 8 = 328

And the estimated product is 280 because 73 is close to 70 , so 70 × 4 = 280 So, 73 × 4 = 292

And the estimated product is 540 because 89 is close to 90 , so 90 × 6 = 540 So, 89 × 6 = 534

Question 11. Estimate: ______ 65 × 7 = ______ Answer:  455, the Estimate product is 490

Question 12. Estimate: ____ 3 × 92 = _____ Answer: 276, the Estimate product is 270

3 × 2 ones = 6 ones 3 × 9 tens = 27 tens Then we get 235

And the estimated product is 270 because 92 is close to 90, then 90 × 3 = 270 So, 92 × 3 = 276

Question 4.

Question 13. Estimate: _____ 47 × 5 = ______ Answer:  235, the Estimate product is 250

Question 14. There are 8 questions during the first round of a game show. Each question is worth 15 points. What is the greatest number of points that a contestant can earn during the first round? Answer: 120 is the greatest number of points that a contestant can earn during the first round

8 × 5 ones = 40 ones regrouping 40 ones as 4 tens and 0 ones 1 × 8 tens = 8 tens 8 tens + 4 tens = 12 tens  or  1 hundred  and 2 tens ,Then we get 120 So, 120 is the greatest number of points that a contestant can earn during the first round.

5 × 3 ones = 15 ones regrouping 15 ones as 1 ten and 5 ones 5 × 1 ten = 5 tens 5 tens + 1 ten = 6 tens  ,Then we get  65

2 × 7 ones = 14 ones regrouping 14 ones as 1 ten and 4 ones 2 × 3 tens = 6 tens 6 tens + 1 ten = 7 tens  Then we get  74

9 × 8 ones = 72 ones regrouping 72 ones as 7 tens and 2 ones 9 × 8 tens = 72 tens 72 tens + 7 tens = 79 tens  or  7 hundreds and 9 tens ,Then we get  792 Think and Grow: Modeling Real Life

A pronghorn antelope can run up to _____ miles per hour. Answer: A pronghorn antelope can run up to 54 miles per hour.

Compare the fastest speeds of a pronghorn antelope and a cheetah. So, a _______ can run faster. Answer: A cheetah can run faster.

Question 16. A band’s goal is to produce 100 songs. The band has produced 6 albums with 13 songs on each album. Has the band reached its goal? Answer: NO , 78 songs

6 × 3 ones = 18 ones regrouping 18 ones as 1 ten and 8 ones 6 × 1 ten = 6 tens 6 tens + 1 ten = 7 ten Then we get  78 A band’s goal is to produce 100 songs but they had only 78 songs so they did not get to their goal.

4 × 4 ones = 16 ones regrouping 16 ones as 1 ten and 6 ones 4 × 1 ten = 4 tens 4 tens + 1 ten = 5 tens Then we get  56 A teenager must practice driving with an adult for 50 hours So she has practiced enough to get a license.

Finally $267 – $ 207 = $60 It cost $60 more to rent a personal water craft for 3 hours than a motor boat for 3 hours.

And the Estimate product is 60, because 24 is close to 20 , we have 20 × 3 = 60 So, 24 × 3 = 72.

And the Estimate product is 140, because 18 is close to 20 , we have 20 × 7 = 140 So, 18 × 7 = 126

And the Estimate product is 180, because 33 is close to 30 , we have 30 × 6 = 180 So, 33 × 6 = 198

And the Estimate product is 450, because 47 is close to 50 , we have 50 × 9 = 450 So, 47 × 9 = 423

And the Estimate product is 240, because 65 is close to 60 , we have 60 × 4 = 240 So, 65 × 4 = 260

And the Estimate product is 560, because 72 is close to 70 , we have 70 × 8 = 560 So, 72 × 8 = 576.

Find the product. Check whether your answer is reasonable. Question 8. Estimate: ______ 49 × 5 = _____ Answer: 245 , the Estimate product is 250,

And the Estimate product is 250, because 49 is close to 50 , we have 50 × 5 = 250 So, 49 × 5 = 250.

Question 9. Estimate: _______ 7 × 86 = _______ Answer: 602, the Estimate product is 630,

And the Estimate product is 630, because 86 is close to 90 , we have 90 × 7 = 630 So, 86 × 7 = 602.

Question 10. Estimate: ______ 93 × 3 = ______ Answer: 279 , the Estimate product is 270

And the Estimate product is 270, because 93 is close to 90 , we have 90 × 3 = 270 So, 93 × 3 = 270.

Question 11. You read 56 pages each week. How many pages do you read in 8 weeks? Answer: 448 pages.

Question 12. Number Sense The sum of two numbers is 20. The product of the two numbers is 51. What are the two numbers? Answer: 17 and 3  are the two numbers.

Question 13. Reasoning Your friend multiplies 58 by6 and says that the product is 3,048. Is your friend’s answer reasonable? Explain. Answer:  Correct answer is 348

6 × 8 ones = 48 ones regroup 48 ones as 4 tens and 2 ones Then 6 × 5 tens = 30 tens 30 tens + 4 tens = 34 tens , then we have  348 So, Correct answer is 348 .

Question 14. DIG DEEPER! How much greater is 4 × 26 than 3 × 26? Explain how you know without multiplying. Answer:  4 × 26 is greater than 3 × 26 . Explanation: The two factors of the given multiplication are 4 and 3 as 4 is greater than 3 , So , any same number multiplied by these two numbers individually will give the greatest number as a result for the number 4 . So, 4 × 26 is greater than 3 × 26.

Question 17. You spend 21 fewer minutes riding the bus to school than getting ready in the morning. You take 36 minutes to get ready. How long is the bus ride? Answer: 15 minutes to ride the bus

Explanation:  You take 36 minutes to get ready. You spend 21 fewer minutes riding the bus to school than getting ready in the morning So, 36 – 21 = 15 It takes 15 minutes to ride the bus.

Lesson 3.8 Multiply Three-and Four-Digit Numbers by One-Digit Numbers

Use any strategy to find each product. 7 × 39 = _____ 7 × 439 = ______ Answer: 273 and 3,073

Explanation: by using distributive property 7 × 39 = 7 × ( 30 + 9) = (7 × 30)+ (7 ×9) =210  + 63 = 273.

Explanation: 7 × 439 = 7 × ( 400 + 30 + 9) = ( 7 × 400) +(7 × 30)+ (7 ×9) = 2800  + 210 + 63 = 3,073.

Structure How are the equations the same? How are they different? Answer: The equations are same when the numbers in the equation are in their standard position as ones, tens, hundreds etc. And at the same time the factors of the products must not change . The equation is different when the two factor numbers are changing their position irrespective of their places.

Step 2: Multiply tens and regroup tens 2 × 8 tens = 16 tens regroup as 1 ten and 6 ones

Step 3: Multiply hundreds and regroup hundreds 2 × 0 = 0

Step 4: Multiply thousands and regroup thousands 2 × 6 thousands = 12 thousands Finally we have , 12,168. So, 6,000 × 2 = 12,000 and 6,084 × 2 = 12,168. Because 6,000  is close to the estimate, 12,000, the answer is reasonable.

Step 1:  Multiply ones and regroup 5 × 3 ones = 15 ones Regroup as 1 ten and 5 ones

Step 2: Multiply tens and regroup tens 5 × 2 tens = 10 tens 10 tens + 1 ten = 11 tens regroup 11 tens  as 1 hundreds and 1 ten

Step 3: Multiply hundreds and regroup hundreds 5 × 1 hundreds  = 5 hundreds 5 hundreds + 1 hundred = 6 hundreds

By holding all places together we get 615 .

And the estimated product is 600 because 123 is close to 120, 120 × 5 = 600 So, 123 × 5 = 615 .

Step 1:  Multiply ones and regroup 3 × 7 ones = 21 ones Regroup 21 ones  as 2 tens and 1 ones

Step 2: Multiply tens and regroup tens 3 × 0 tens = 0 tens 0 tens + 2 tens = 2 tens

  Step 3: Multiply hundreds and regroup hundreds 3 × 9 hundreds  = 27 hundreds Regroup 27 hundreds  as 2 thousands and 7 hundreds

By holding all places together we get 2,721 .

And the estimated product is 2,700 because 907 is close to 900, 900 × 3 = 2,700 So, 907 × 3 = 2,721 .

Step 1:  Multiply ones and regroup 6 × 5 ones = 30 ones regroup 30 ones as 3 tens and 0 ones

Step 2: Multiply tens and regroup tens 6 × 1 tens = 6 tens 6 tens + 3 tens = 9 tens

Step 3: Multiply hundreds and regroup hundreds 6 × 3 hundreds  = 18 hundreds regroup as 1 thousand and 8 hundreds

Step 4: Multiply thousands and regroup thousands 6 × 7 thousands = 42 thousands 42 thousands + 1 thousand = 43 thousands

By holding all the places together we get 43,890

And the estimated product is 43,800 because 7,315 is close to 7300, 7300 × 6 = 43,800 So, 7,315 × 6  = 43,890 .

Step 1:  Multiply ones and regroup 7 × 0 ones = 0 ones

Step 2: Multiply tens and regroup tens 7 × 2 tens = 14 tens regroup 14 tens  as 1 hundred and 4 tens

Step 3: Multiply hundreds and regroup hundreds 7 × 1 hundreds  = 7 hundreds 7 hundreds + 1 hundred = 8 hundreds

By holding all places together we get 840.

And the estimated product is 840 because 120 has a zero’s in ones place , so it is already close to the nearest 0’s so we don’t have to  estimate separately.

Step 1:  Multiply ones and regroup 4 × 4 ones = 16 ones regroup as 1 ten and 6 ones

Step 2: Multiply tens and regroup tens 4 × 3 tens = 12 tens 12 tens + 1 ten = 13 tens regroup as 1 hundred and 3 tens

Step 3: Multiply hundreds and regroup hundreds 4 × 5 hundreds  = 20 hundreds 20 hundreds +  1 hundred = 21 hundreds regroup as 2 thousands and 1 hundred

Step 4: Multiply thousands and regroup thousands 4 × 2 thousands = 8 thousands 8 thousands + 2 thousands = 10 thousands

By holding all the places together we get 10,136

And the estimated product is 10,000 because 2,534 is close to 2500, 2500 × 4 = 10,000 So, 2,534 × 4 = 10,136 .

Step 1:  Multiply ones and regroup 2 × 7 ones = 14 ones regroup as 1 ten and 4 ones

Step 2: Multiply tens and regroup tens 2 × 1 ten = 2 tens 2 tens + 1 ten = 3 tens

Step 3: Multiply hundreds and regroup hundreds 2 × 6 hundreds  = 12 hundreds regroup as 1 thousand  and 2 hundreds

Step 4: Multiply thousands and regroup thousands 2 × 7 thousands = 14 thousands 14 thousands + 1 thousand = 15 thousands

By holding all the places together we get 15,234

And the estimated product is 15,200 because 7,617 is close to 7600, 7,600 × 2 = 15,200 So, 7,617 × 2 = 15,234 .

Step 1:  Multiply ones and regroup 8 × 8 ones = 64 ones regroup as 6 tens and 4 ones

Step 2: Multiply tens and regroup tens 8 × 5 tens = 40 tens 40 tens + 6 tens = 46 tens regroup 46 tens  as 4 hundreds  and 6 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 4 hundreds  = 32 hundreds 32 hundreds + 4 hundreds = 36 hundreds

By holding all places together we get 3,664.

And the estimated product is 3,680 because 458 is close to 460, 460 × 8 = 36,80 So, 458 × 8 = 3,664 .

Step 1:  Multiply ones and regroup 9 × 3 ones = 27 ones regroup 27 ones as 2 tens and 7 ones

Step 2: Multiply tens and regroup tens 9 × 2 tens = 18 tens 18 tens + 2 tens = 20 tens regroup as 2 hundreds and 0 tens

Step 3: Multiply hundreds and regroup hundreds 9 × 8 hundreds  = 72 hundreds 72 hundreds + 2 hundreds = 74 hundreds regroup as 7 thousands and 4 hundreds

Step 4: Multiply thousands and regroup thousands 9 × 8 thousands = 72 thousands 72 thousands + 7 thousand = 79 thousands

By holding all the places together we get 79,407.

And the estimated product is 79,200 because 8,823 is close to 8,800, 8,800 × 9 = 79,200 So, 8,823 × 9  = 79,407 .

Step 1:  Multiply ones and regroup 6 × 5 ones = 30 ones regroup as 3 tens and 0 ones

Step 2: Multiply tens and regroup tens 6 × 7 tens = 42 tens 42 tens + 3 tens = 45 tens regroup 45 tens  as 4 hundreds  and 5 tens

Step 3: Multiply hundreds and regroup hundreds 6 × 9 hundreds  = 54 hundreds 54 hundreds + 4 hundreds = 58 hundreds

By holding all places together we get 5,850.

And the estimated product is 5,820 because 975 is close to 970, 970 × 6 = 5,820 So, 975 × 6 = 5,850 .

Question 10. Estimate: _____ 1,762 × 3 = ______ Answer:  5,286, the estimated product is 5,100

Step 1:  Multiply ones and regroup 3 × 2 ones = 6 ones

Step 2: Multiply tens and regroup tens 3 × 6 tens = 18 tens regroup as 1 hundred and 8 tens

Step 3: Multiply hundreds and regroup hundreds 3 × 7 hundreds  = 21 hundreds 21 hundreds + 1 hundred = 22 hundreds regroup as 2 thousands and 2 hundreds

Step 4: Multiply thousands and regroup thousands 3 × 1 thousands = 3 thousands 3 thousands + 2 thousands = 5 thousands

By holding all the places together we get 5,286.

And the estimated product is 5,100 because 1,762 is close to 1,700, 1,700 × 3  = 5,100 So, 1,762 × 3  = 5,286 .

Question 11. Estimate: ______ 5 × 5,492 = ______ Answer:  27,460, the estimated product is 27,000

Step 1:  Multiply ones and regroup 5 × 2 ones = 10 ones regroup 10 ones as 1 ten and 0 ones

Step 2: Multiply tens and regroup tens 5 × 9 tens = 45 tens 45 tens + 1 ten = 46 tens regroup as 4 hundreds and 6 tens

Step 3: Multiply hundreds and regroup hundreds 5 × 4 hundreds  = 20 hundreds 20 hundreds + 4 hundreds = 24 hundreds regroup as 2 thousands and 4 hundreds

Step 4: Multiply thousands and regroup thousands 5 × 5 thousands = 25 thousands 25 thousands + 2 thousand = 27 thousands

By holding all the places together we get 27,460.

And the estimated product is 27,000 because 5,492 is close to 5,400, 5,400 × 5 = 27,000 So, 5,492  × 5  =  27,460.

Question 12. Estimate: ______ 347 × 7 = _____ Answer:   2,429, the estimated product is 2,380

Step 1:  Multiply ones and regroup 7 × 7 ones = 49 ones regroup as 4 tens and 9 ones

Step 2: Multiply tens and regroup tens 7 × 4 tens = 28 tens 28 tens + 4 tens = 32 tens regroup 32 tens  as 3 hundreds  and 2 tens

Step 3: Multiply hundreds and regroup hundreds 7 × 3 hundreds  = 21 hundreds 21 hundreds + 3 hundreds = 24 hundreds

By holding all places together we get 2,429.

And the estimated product is 2,380 because 347 is close to 340, 340 × 7 = 2,380 So, 347 × 7 = 2,429 .

Step 1:  Multiply ones and regroup 6 × 3 ones = 18 ones regroup 18 ones as 1 ten and 8 ones

Step 2: Multiply tens and regroup tens 6 × 4 tens = 24 tens 24 tens + 1 ten = 25 tens regroup as 2 hundreds and 5 tens

Step 3: Multiply hundreds and regroup hundreds 6 × 8 hundreds  = 48 hundreds 48 hundreds + 2 hundreds = 50 hundreds regroup as 5 thousands and 0 hundreds

Step 4: Multiply thousands and regroup thousands 6 × 2 thousands = 12 thousands 12 thousands + 5 thousands = 17 thousands

By holding all the places together we get 17,058 So, 2,843 × 6 = 17,058

Step 1:  Multiply ones and regroup 8 × 5 ones = 40 ones regroup 40 ones as 4 tens and 0 ones

Step 2: Multiply tens and regroup tens 8 × 4 tens = 32 tens 32 tens + 4 tens = 36 tens regroup as 3 hundreds and 6 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 6 hundreds  = 48 hundreds 48 hundreds + 3 hundreds = 51 hundreds regroup as 5 thousands and 1 hundred

Step 4: Multiply thousands and regroup thousands 8 × 1 thousand = 8 thousands 8 thousands + 5 thousands = 13 thousands

By holding all the places together we get 13,160 So, 1,645 × 8 = 13,160

Finally , 17,058  is greater than 13,160.

Step 2: Multiply tens and regroup tens 3 × 8 tens = 24 tens regroup as 2 hundreds and 4 tens

Step 3: Multiply hundreds and regroup hundreds 3 × 5 hundreds  = 15 hundreds 15 hundreds + 2 hundreds = 17 hundreds regroup as 1 thousand and 7 hundreds

Step 4: Multiply thousands and regroup thousands 3 × 6 thousands = 18 thousands 18 thousands + 1 thousand = 19 thousands

By holding all the places together we get 19,746. So, 6,582 × 3 = 19,746.

Step 1:  Multiply ones and regroup 8 × 4 ones = 32 ones regroup 32 ones as 3 tens and 2 ones

Step 2: Multiply tens and regroup tens 8 × 9 tens = 72 tens 72 tens + 3 tens = 75 tens regroup as 7 hundreds and 5 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 3 hundreds  = 24 hundreds 24 hundreds + 7 hundreds = 31 hundreds regroup as 3 thousands and 1 hundred

Step 4: Multiply thousands and regroup thousands 8 × 2 thousands = 16 thousands 16 thousands + 3 thousands = 19 thousands

By holding all the places together we get 19,152 So, 2,394 × 8 =  19,152

Finally , 19,746  is greater than 19,152.

Question 15. A roller coaster is twice as tall as a Ferris wheel that is 228 feet tall. How tall is the roller coaster? Answer:  The roller coaster is 456 feet tall.

Step 1:  Multiply ones and regroup 2 × 8 ones = 16 ones Regroup as 1 ten and 6 ones

Step 2: Multiply tens and regroup tens 2 × 2 tens = 4 tens 4 tens + 1 ten = 5 tens

Step 3: Multiply hundreds and regroup hundreds 2 × 2 hundreds  = 4 hundreds

By holding all places together we get 456 . The roller coaster is 456 feet tall.

Step 1:  Multiply ones and regroup 7 × 8 ones = 56  ones regroup 56 ones as 5 tens and 6 ones

Step 2: Multiply tens and regroup tens 7 × 4 tens = 28 tens 28 tens +  5 tens = 33 tens regroup as 3 hundreds and 3 tens

Step 3: Multiply hundreds and regroup hundreds 7 × 3 hundreds  = 21 hundreds 21 hundreds + 3 hundreds = 24 hundreds regroup as 2 thousands and 4 hundreds

Step 4: Multiply thousands and regroup thousands 7 × 8 thousand = 56 thousands 56 thousands + 2 thousands = 58 thousands

By holding all the places together we get 58,436. So, 8,348 × 7 = 58,436

Step 1:  Multiply ones and regroup 0

Step 2: Multiply tens and regroup tens 0

Step 3: Multiply hundreds and regroup hundreds 7 × 2 hundreds  = 14 hundreds regroup as 1 thousand and 4 hundreds

Step 4:  Multiply thousands and regroup 7 × 1 thousands = 7 thousands 7 thousands + 1 thousand  =  8 thousands

By holding all places together we get 8,400 .

Compare the lengths of time that each animal can hold its breath. Answer:     Penguin can hold its breath by 1,200 seconds. Elephant seal can hold its breath by 7,200 seconds. Sea turtle can hold it breath by 8,400 seconds.

The _______ can hold its breath the longest. Answer: Sea turtle can hold its breath the longest

Step 1:  Multiply ones and regroup 3 × 4 ones = 12 ones Regroup as 1 ten and 2 ones

Step 2: Multiply tens and regroup tens 3 × 8 tens = 24 tens 24 tens + 1 ten = 25 tens regroup 25 tens  as 2 hundreds and 5 ten

Step 3: Multiply hundreds and regroup hundreds 3 × 2 hundreds  = 6 hundreds 6 hundreds + 2 hundreds = 8 hundreds

By holding all places together we get 852.

So,852 football cards are the greatest number of cards.

Question 18. A principal has $2,000 to spend on updating some of your school’s tablets. She buys 4 tablets that each cost $299. How much money does the principal have left? Answer: $299 × 4 = $1,196 , the principal have left $804.

Step 1:  Multiply ones and regroup 4 × 9 ones = 36 ones Regroup as 3 tens and 6 ones

Step 2: Multiply tens and regroup tens 4 × 9 tens = 36 tens 36 tens + 3 tens = 39 tens regroup 39 tens  as 3 hundreds and 9 tens

Step 3: Multiply hundreds and regroup hundreds 4 × 2 hundreds  = 8 hundreds 8 hundreds + 3 hundreds = 11 hundreds regroup as 1 thousand and 1 hundred.

By holding all places together we get 1,196 So, $299 × 4 = $1,196 , the principal have left $804.

Question 19. A train ticket from New York City to Miami costs $152. A train ticket from New York City to Orlando costs $144. A group of 8 friends is in New York City. How much money can the group save by going to Orlando instead of going to Miami? Answer: They can save $64.

Step 1:  Multiply ones and regroup 8 × 2 ones = 16 ones Regroup as 1 ten and 6 ones

Step 2: Multiply tens and regroup tens 8 × 5 tens = 40 tens 40 tens + 1 ten = 41 tens regroup 41 tens  as 4 hundreds and 1 ten

Step 3: Multiply hundreds and regroup hundreds 8 × 1 hundreds  = 8 hundreds 8 hundreds + 4 hundred = 12 hundreds regroup as 1 thousand and 2 hundreds

By holding all places together we get 1,216 So, $152 × 8 = $1,216.

Step 1:  Multiply ones and regroup 8 × 4 ones = 32 ones Regroup as 3 tens and 2 ones

Step 2: Multiply tens and regroup tens 8 × 4 tens = 32 tens 32 tens + 3 tens = 35 tens regroup 35 tens  as 3 hundreds and 5 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 1 hundreds  = 8 hundreds 8 hundreds + 3 hundred = 11 hundreds regroup as 1 thousand and 1 hundred

By holding all places together we get 1,152 So, $144 × 8 = $1,152.

Finally , $1,216  – $1,152 = $ 64 They can save $64.

Multiply Three-and Four-Digit Numbers by One-Digit Numbers Homework & Practice 3.8

Step 1:  Multiply ones and regroup 9 × 4 ones = 36 ones Regroup 36 ones  as 3 tens and 6 ones

Step 2: Multiply tens and regroup tens 9 × 0 tens = 0 tens 0 tens + 3 tens = 3 tens

Step 3: Multiply hundreds and regroup hundreds 9 × 3 hundreds  = 27 hundreds Regroup 27 hundreds  as 2 thousands and 7 hundreds

By holding all places together we get 2,736 .

And the estimated product is 2,700 because 304 is close to 300, 300 × 9 = 2,700 So, 304 × 9 = 2,736 .

Step 1:  Multiply ones and regroup 8 × 7 ones = 56 ones Regroup 56 ones  as 5 tens and 6 ones

Step 2: Multiply tens and regroup tens 8 × 1 ten = 8 tens 8 tens + 5 tens = 10 tens regroup as 1 hundred and 0 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 6 hundreds  = 48 hundreds 48 hundreds + 1 hundred = 49 hundreds Regroup 49 hundreds  as 4 thousands and 9 hundreds

By holding all places together we get 4,936 .

And the estimated product is 4,880 because 617 is close to 610, 610 × 8 = 4,880 So, 617 × 8 = 4,936 .

Step 1:  Multiply ones and regroup 4 × 9 ones = 36 ones regroup 36 ones as 3 tens and 6 ones

Step 2: Multiply tens and regroup tens 4 × 3 tens = 12 tens 12 tens + 3 tens = 15 tens regroup as 1 hundred and 5 tens

Step 3: Multiply hundreds and regroup hundreds 4 × 9 hundreds  = 36 hundreds 36 hundreds + 1 hundred = 37 hundreds regroup as 3 thousands and 7 hundreds

Step 4: Multiply thousands and regroup thousands 4 × 5 thousands = 20 thousands 20 thousands + 3 thousands = 23 thousands

By holding all the places together we get 23,756.

And the estimated product is 23,760 because 5,939 is close to 5,940, 5,940 × 4 = 23,760 So, 5,939 × 4  = 23,756 .

Step 1:  Multiply ones and regroup 3 × 4 ones = 12 ones regroup 12 ones as 1 ten and 2 ones

Step 2: Multiply tens and regroup tens 3 × 5 tens = 15 tens 15 tens + 1 ten = 16 tens regroup as 1 hundred and 6 tens

Step 4: Multiply thousands and regroup thousands 3 × 2 thousands = 6 thousands 6 thousands + 2 thousands = 8 thousands

By holding all the places together we get 8,262

And the estimated product is 8,250 because 2,754 is close to 2,750, 2,750 × 3 = 8,250 So, 2,754 × 3  = 8,262 .

Step 2: Multiply tens and regroup tens 6 × 6 tens = 36 tens 36 tens + 3 tens = 39 tens regroup as 3 hundreds and 9 tens

Step 3: Multiply hundreds and regroup hundreds 6 × 4 hundreds  = 24 hundreds 24 hundreds + 3 hundreds = 27 hundreds regroup as 2 thousands and 7 hundreds

Step 4: Multiply thousands and regroup thousands 6 × 8 thousands = 48 thousands 48 thousands + 2 thousands = 50 thousands

By holding all the places together we get 50,790.

And the estimated product is 50,760, because 8,465 is close to 8,460, 8,460 × 6 = 50,760 So, 8,465 × 6  = 50,790.

Step 1:  Multiply ones and regroup 7 × 2 ones = 14 ones Regroup 14 ones  as 1 tens and 4 ones

Step 2: Multiply tens and regroup tens 7 × 2 tens = 14 tens 14 tens + 1 tens = 15 tens regroup as 1 hundred and 5 tens

Step 3: Multiply hundreds and regroup hundreds 7 × 8 hundreds  = 56 hundreds 56 hundreds + 1 hundred = 57 hundreds Regroup 57 hundreds  as 5 thousands and 7 hundreds

By holding all places together we get 5,754 .

And the estimated product is 5,740 because 822 is close to 820, 820 × 7 = 5,740 So, 822 × 7 = 5,754 .

Find the product. Check whether your answer is reasonable. Question 7. Estimate: _______ 629 × 5 = ______ Answer: 3,145 , The estimated product is 3,150

Step 1:  Multiply ones and regroup 5 × 9 ones = 45 ones Regroup 45 ones  as 4 tens and 5 ones

Step 2: Multiply tens and regroup tens 5 × 2 tens = 10 tens 10 tens + 4 tens = 14 tens regroup as 1 hundred and 4 tens

Step 3: Multiply hundreds and regroup hundreds 5 × 6 hundreds  = 30 hundreds 30 hundreds + 1 hundred = 31 hundreds Regroup 31 hundreds  as 3 thousands and 1 hundred

By holding all places together we get 3,145.

And the estimated product is 3,150. because 629 is close to 630, 630 × 5 = 3,150. So, 629 × 5 = 3,145 .

Question 8. Estimate: _______ 7 × 1,836 = ______ Answer:  12,852 , The estimated product is  12,880

Step 1:  Multiply ones and regroup 7 × 6 ones = 42 ones regroup 42 ones as 4 tens and 2 ones

Step 2: Multiply tens and regroup tens 7 × 3 tens = 21 tens 21 tens + 4 tens = 25 tens regroup as 2 hundreds and 5 tens

Step 3: Multiply hundreds and regroup hundreds 7 × 8 hundreds  = 56 hundreds 56 hundreds + 2 hundreds = 58 hundreds regroup as 5 thousands and 8 hundreds

Step 4: Multiply thousands and regroup thousands 7 × 1 thousands = 7 thousands 7 thousands + 5 thousands = 12 thousands

By holding all the places together we get 12,852

And the estimated product is 12,880 because 1,836 is close to 1,840, 1,840 × 7 = 12,880 So, 1,836 × 7  = 12,852 .

Question 9. Estimate: ______ 453 × 3 = ______ Answer: 1,359 , The estimated product is  1,350

Step 1:  Multiply ones and regroup 3 ×  ones = 9 ones

Step 2: Multiply tens and regroup tens 3 × 5 tens = 15 tens regroup as 1 hundred and 5 tens

Step 3: Multiply hundreds and regroup hundreds 3 × 4 hundreds  = 12 hundreds 12 hundreds + 1 hundred = 13 hundreds Regroup 13 hundreds  as 1 thousand and 3 hundreds

By holding all places together we get 1,359 .

And the estimated product is 1,350 because 453 is close to 450, 450 × 3 = 1,350. So, 453 × 3 = 1,359 .

Step 3: Multiply hundreds and regroup hundreds 3 × 7 hundreds  = 21 hundreds 21 hundreds + 2 hundreds = 23 hundreds regroup as 2 thousands and 3 hundreds

Step 4: Multiply thousands and regroup thousands 3 × 6 thousands = 18 thousands 18 thousands + 2 thousands = 20 thousands

By holding all the places together we get 20,346

Step 1:  Multiply ones and regroup 2 × 1 ones = 2 ones

Step 2: Multiply tens and regroup tens 2 × 9 tens = 18 tens regroup as 1 hundred and 8 tens

Step 3: Multiply hundreds and regroup hundreds 2 × 3 hundreds  = 6 hundreds 6 hundreds + 1 hundred = 7 hundreds

Step 4: Multiply thousands and regroup thousands 2 × 3 thousands = 6 thousands

By holding all the places together we get 6,782. So, 20,346 is greater than 6,782.

Step 1:  Multiply ones and regroup 9 × 2 ones = 18 ones regroup 18 ones as 1 tens and 8 ones

Step 2: Multiply tens and regroup tens 9 × 9 tens = 81 tens 81 tens + 1 tens = 82 tens regroup as 8 hundreds and 2 tens

Step 3: Multiply hundreds and regroup hundreds 9 × 3 hundreds  = 27 hundreds 27 hundreds + 8 hundreds = 35 hundreds regroup as 3 thousands and 5 hundreds

Step 4: Multiply thousands and regroup thousands 9 × 1 thousands = 9 thousands 9 thousands + 3 thousands = 12 thousands

By holding all the places together we get 12,528.

Step 1:  Multiply ones and regroup 4 × 3 ones = 12 ones regroup 12 ones as 1 tens and 2 ones

Step 2: Multiply tens and regroup tens 4 × 9 tens = 36 tens 36 tens + 1 tens = 37 tens regroup as 3 hundreds and 7 tens

Step 3: Multiply hundreds and regroup hundreds 4 × 4 hundreds  = 16 hundreds 16 hundreds + 3 hundreds = 19 thousands regroup as 1 thousand and 9 hundreds

Step 4: Multiply thousands and regroup thousands 4 × 2 thousands = 8 thousands 8 thousands + 1 thousand = 9 thousands

By holding all the places together we get 9,972. So, 12,528 is greater than 9,972.

Question 12. A backpacker hikes the Buckeye Trail 5 times. The trail is 1,444 miles long. How many miles has he hiked on the Buckeye Trail in all? Answer: 7,220 miles has hiked on the Buckeye Trail.

Step 1:  Multiply ones and regroup 5 × 4 ones = 20 ones regroup 20 ones as 2 tens and 0 ones

Step 2: Multiply tens and regroup tens 5 × 4 tens = 20 tens 20 tens + 2 tens = 22 tens regroup as 2 hundreds and 2 tens

Step 3: Multiply hundreds and regroup hundreds 5 × 4 hundreds  = 20 hundreds 20 hundreds + 2 hundreds = 22 hundreds regroup as 2 thousands and 2 hundreds

Step 4: Multiply thousands and regroup thousands 5 × 1 thousands = 5 thousands 5 thousands + 2 thousands  = 7 thousands

By holding all the places together we get 7,220.

Question 13. Number Sense What number is 980 more than the product of 6,029 and 8? Answer: 49,212, The product of 6,029 and 8 is 48,232

Step 1:  Multiply ones and regroup 8 × 9 ones = 72 ones regroup 72 ones as 7 tens and 2 ones

Step 2: Multiply tens and regroup tens 8 × 2 tens = 16 tens 16 tens + 7 tens = 23 tens regroup as 2 hundreds and 3 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 0 hundreds  = 0 hundreds 0 hundreds + 2 hundreds = 2 hundreds

Step 4: Multiply thousands and regroup thousands 8 × 6 thousands = 48 thousands

By holding all the places together we get  48,232.

Given, The required number is 980 more than  48,232, Then 48,232 + 980 = 49,212. Finally the wanted number is 49,212.

Question 14. YOU BE THE TEACHER Newton says that the product of a three-digit number and a one-digit number is always a three-digit number. Is Newton correct? Explain. Answer: NO

Explanation: The Assumption that the product of a three-digit number and a one-digit number is always a three-digit number is wrong because, the the factor numbers of a product might vary in places . The highest one digit number is multiplied by the highest 3 digit number will not be a 3 digit number as a output product . So, Newton is wrong about his statement.

Step 1:  Multiply ones and regroup 2 × 7 ones = 14 ones Regroup as 1 ten and 4 ones

Step 2: Multiply tens and regroup tens 2 × 6 tens = 12 tens 12 tens + 1 ten = 13 tens regroup 11 tens  as 1 hundreds and 3 tens

Step 3: Multiply hundreds and regroup hundreds 2 × 1 hundreds  = 2 hundreds 2 hundreds + 1 hundred = 3 hundreds

By holding all places together we get 334 . The songs that i downloaded are 334 Newton has 351 songs and Descartes has 167 songs and compared to all of us , Newton has more songs that is 315 songs.

So, 612 + 289 = 901 .

By subtracting 500 – 351 , we get 149 To check inverse operation : Add 315 + 149  = 500 .

So 500 – 351 = 149 .

Explanation:  7 × 25 × 4 By using commutative property of multiplication = 7 × ( 25 × 4) =7 × 100 = 700 So, 7 × 25 × 4 = 700 .

5 × 79 × 2 By using commutative property of multiplication = 79 × ( 5 × 2) =79 × 10 = 790 So, 5 × 79 × 2 = 790 .

9 × 5,001 By using Distributive property of multiplication = 9 × (5,000 + 1) = ( 9 × 5,000) + ( 9 × 1) = 45,000 + 9 = 45,009 So,  9 × 5,001 = 45,009.

9 × 4,999 By using Distributive property of multiplication = 9 × (5,000 – 1) = ( 9 × 5,000) – ( 9 × 1) = 45,000 – 9 = 44,991 So,  9 × 4,999 = 44,991.

Construct Arguments Compare your strategies with your partner’s. How are they alike? How are they different? Answer:  All the strategies are correct that are used by my friend and me. Using any method in multiplication is frequently used to find the product as fast as possible some methods are long and some of them are really fast and easy . Every method is correct unless you did not do any mistakes, so , all are alike.

Think and Grow: Use Properties to Multiply

Explanation: 8 × 250 By using associative property of multiplication =( 4 × 2 ) × 250 = 4 × ( 2 × 250) = 4 × 500 = 2,000. So, 8 × 250 = 2,000.

5 × 698 By using Distributive property of multiplication = 5 × ( 700 – 2) = (5 × 700) – ( 5 × 2) = 3,500 – 10 = 3,490 So,  5 × 698 = 3,490.

4 × 9 × 25 By using commutative property of multiplication = 9 × ( 4 × 25) = 9 × 100 = 900. So, 4 × 9 × 25 = 900.

Use properties to find the product. Explain your reasoning. Question 1. 6 × 150 Answer: 900

Explanation: By using Distributive property of multiplication = 6 × ( 100 + 50) = (6 × 100) + ( 6 × 50) = 600 + 300 = 900. So, 6 × 150 = 900.

Question 2. 3 × 494 Answer: 1,482

Explanation: By using Distributive property of multiplication = 3 × ( 500 – 6) = (3 × 500) – ( 3 × 6) = 1500 – 18 = 1,482. So, 3 × 494 = 1,482.

Question 3. 25 × 7 × 4 Answer:  700

Explanation: By using commutative property of multiplication = 7 × ( 25 × 4 ) = 7 × 100 = 700. So, 25 × 7 × 4 = 700.

Use properties to find the product. Explain your reasoning. Question 4. 7 × 798 Answer: 5,586

Explanation: By using Distributive property of multiplication = 7 × ( 800 – 2) = (7 × 800) – ( 7 × 2) = 5,600 – 14 = 5,586 So,  7 × 798 = 5,586.

Question 5. 350 × 6 Answer:  2,100

Explanation: By using Distributive property of multiplication = 6 × ( 300 + 50) = (6 × 300) + ( 6 × 50) = 1,800 + 300 = 2,100. So, 6 × 350 = 2,100.

Question 6. 106 × 5 Answer: 530

Explanation: By using Distributive property of multiplication = 5 × ( 100 + 6) = (5 × 100) + ( 5 × 6) = 500 + 30 = 530. So, 5 × 106 = 530.

Question 7. 4 × 625 Answer:  2,500

Explanation: By using Distributive property of multiplication = 4 × ( 600 + 25) = (4 × 600) + ( 4 × 25) = 2400 + 100 = 2,500. So, 4 × 625 = 2,500.

Question 8. 395 × 8 Answer: 3,160.

Explanation: By using Distributive property of multiplication = 8 × ( 400 – 5) = (8 × 400) – ( 8 × 5) = 3,200 – 40 = 3,160. So, 8 × 395 = 3,160.

Question 9. 2 × 7 × 15 Answer: 210

Explanation: By using commutative property of multiplication = 7 × ( 15 × 2 ) = 7 × 30 = 210. So, 2 × 7 × 15 = 210.

Question 10. 430 × 2 Answer:  860

Explanation: By using Distributive property of multiplication = 2 × ( 400 + 30) = (2 × 400) + ( 2 × 30) = 800 + 60 = 860. So, 2 × 430 = 860.

Question 11. 8 × 150 Answer: 1,200

Explanation: By using Distributive property of multiplication = 8 × ( 100 + 50) = (8 × 100) + ( 8 × 50) = 800 + 400 = 1,200. So, 8 × 150 = 1,200.

Question 12. 3 × 1,997 Answer: 5,991

Explanation: By using Distributive property of multiplication = 3 × ( 2000 – 3) = (3 × 2000) – ( 3 × 3) = 6000 – 9 = 5,991. So, 3 × 1,997 = 5,991.

Question 13. 25 × 9 × 2 Answer: 450

Explanation: By using commutative property of multiplication = 9 × ( 25 × 2 ) = 9 × 50 = 450. So, 25 × 9 × 2 = 450.

Question 14. 404 × 6 Answer:  2,424

Explanation: By using Distributive property of multiplication = 6 × ( 400 + 4) = (6 × 400) + ( 6 × 4) = 2400 + 24 = 2,424. So, 6 × 404 = 2,424.

Question 15. 4 × 2,004 Answer:  8,016

Explanation: By using Distributive property of multiplication = 4 × ( 2000 + 4) = (4 × 2000) + ( 4 × 4) = 8000 + 16 = 8,016. So, 4 × 2,004 = 8,016.

Question 16. Which One Doesn’t Belong? Which expression does not belong with the other three? (3 × 30) + (3 × 7), (3 × 40) – (3 × 3) 3 × (30 + 7), 3 × 3 × 7 Answer: 3 × 3 × 7

Explanation: (3 × 30) + (3 × 7) (3 × 40) – (3 × 3) 3 × (30 + 7) , These 3 expressions are related to the distributive property of multiplication. So, 3 × 3 × 7 this expression does not belong to the distributive property of multiplication.

Question 17. Number Sense Use properties to find each product 9 × 80 = 720, so 18 × 40 = _____. 5 × 70 = 350, so 5 × 72 = _____. Answer: 720, 360.

Explanation: By using associative property of multiplication =( 6 × 3 ) × 40 = 6 × ( 3 × 40) = 6 × 120 = 720. So, 18 × 40 = 720.

5 × 72 By using Distributive property of multiplication = 5 × ( 70 + 2) = (5 × 70) + ( 5 × 2) = 350 + 10 = 360. So, 5 × 72 = 360.

Explanation: 3 × 120 By using Distributive property of multiplication = 3 × ( 100 + 20) = (3 × 100) + ( 3 × 20) = 300 + 60 = 360. So, 3 × 120 = 360.

Subtract to find 31 miles per hour less _____ – 31 = _______ miles per hour Answer:  329 miles per hour

Explanation: 360 – 31 = 329 .

So, the speed of the car was ______ miles per hour. Answer: the speed of the car was 329 miles per hour.

Explanation: A theme park used 300 drones for a holiday show China used 4 times as many drones for a lantern festival. So, 4 × 300 = 1,200 Given, China used 200 fewer than 4 times as many drones for a lantern festival. So 1,200 – 200 = 1,000.

China used 1,000 drones.

Explanation: A subway train has 8 cars Each car can hold 198 passengers. So, 8 × 198 By using Distributive property of multiplication = 8 × ( 200 – 2) = (8 × 200) – ( 8 × 2) = 1600 – 16 = 1,584. So, 8 × 198 = 1,584. 1,584 passengers for a subway train For 2 subway trains , 1,584 + 1,584 = 3,168. Two subway trains can hold 3,168 passengers.

Question 20. You plant cucumbers, green beans, squash, and corn in a community garden. You plant 3 rows of each vegetable with 24 seeds in each row. How many seeds do you plant? Answer: 288 seeds

Explanation: plant 3 rows of each vegetable with 24 seeds in each row. So, 3 × 24 By using Distributive property of multiplication = 3 × ( 20 + 4) = (3 × 20) + ( 3 × 4) = 60 + 12 = 72. So, 3 × 24 = 72.

You plant cucumbers, green beans, squash, and corn in a community garden. Total 4 various vegetables are planted So, 4 × 72 By using Distributive property of multiplication = 4 × ( 70 + 2) = (4 × 70) + ( 4 × 2) = 280 + 8 = 288. So, 4 × 72 = 288.

We have to plant 288 seeds.

Use properties to find the product. Explain your reasoning. Question 1. 3 × 497 Answer: 1,491

Explanation: By using Distributive property of multiplication = 3 × ( 500 – 3) = (3 × 500) – ( 3 × 3) = 1500 – 9 = 1,491. So, 3 × 497 = 1,491.

Question 2. 36 × 9 Answer: 324

Explanation: By using Distributive property of multiplication = 9 × ( 30 + 6) = (9 × 30) + ( 9 × 6) = 270 + 54 = 324. So, 9 × 36 = 324.

Question 3. 8 × 350 Answer: 2,800

Explanation: By using Distributive property of multiplication = 8 × ( 300 + 50) = (8 × 300) + ( 8 × 50) = 2400 + 400 = 2,800. So, 8 × 350 = 2,800.

Question 4. 25 × 8 × 4 Answer: 800

Explanation: By using commutative property of multiplication = 8 × ( 25 × 4 ) = 8 × 100 = 800. So, 25 × 8 × 4 = 800.

Question 5. 999 × 5 Answer:  4,995

Explanation: By using Distributive property of multiplication = 5 × ( 1000 – 1) = (5 × 1000) – ( 5 × 1) = 5,000 –  5 = 4,995 So,  5 × 999 = 4,995.

Question 6. 9 × 402 Answer: 3,618

Explanation: By using Distributive property of multiplication = 9 × ( 400 + 2) = (9 × 400) + ( 9 × 2) = 3600 + 18 = 3,618. So, 9 × 402 = 3,618.

Question 7. 509 × 4 Answer: 2,036

Explanation: By using Distributive property of multiplication = 4 × ( 500 + 9) = (4 × 500) + ( 4 × 9) = 2000 + 36 = 2,036 . So, 4 × 509 = 2,036.

Question 8. 2 × 9 × 15 Answer: 270

Explanation: By using commutative property of multiplication = 9 × ( 15 × 2 ) = 9 × 30 = 270. So, 2 × 9 × 15 = 270.

Question 9. 3,998 × 7 Answer: 27,986

Explanation: By using Distributive property of multiplication = 7 × ( 4000 – 2) = (7 × 4000) – ( 7 × 2) = 28,000 – 14 = 27,986. So, 3,998 × 7 = 27,986.

Explanation: By using Distributive property of multiplication = 4 × ( 900 – 5) = (4 × 900) – ( 4 × 5) = 3600 – 20 = 3,620. So, 895 × 4 = 3,580.

Explanation: The height of the Great Pyramid of Giza is 2 times the height of the Luxor Hotel in Las Vegas The height of the Luxor Hotel in Las Vegas is 365 feet, So, 2 × 365 By using Distributive property of multiplication = 2 × ( 300 + 60 + 5 ) = (2 × 300) + ( 2 × 60) + ( 2 × 5 ) = 600 + 120 + 10 = 730. So, 2 × 365 = 730.

Given, The height of the Great Pyramid of Giza is 275 feet shorter than 2 times the height of the Luxor Hotel in Las Vegas. So, 730 -275 = 455

The height of the Great Pyramid of Giza is 455 feet.

Explanation: Water from their firetruck hose hits the wall 7 times where the spray from a fire extinguisher hits the wall. The spray from a fire extinguisher hits the wall at 24 feet, So, 7 × 24 By using Distributive property of multiplication = 7 × ( 20 + 4) = (7 × 20) + ( 7 × 4) = 140 + 28 = 168. So, 7 × 24 = 168. Water from their firetruck hose hits the wall 12 feet higher than 7 times where the spray from a fire extinguisher hits the wall. Then 168 + 12 = 180 feet

The wall water from the hose hit the wall is 180 feet.

Question 14. You want to learn 95 new vocabulary words. You learn 5 words the first week and an equal number of words each week for the next 9 weeks. How many words do you learn in each of the 9 weeks? Answer: 45 words.

Explanation: You learn 5 words the first week An equal number of words each week for the next 9 weeks So, 5 × 9 = 45

We learn 45 words for 9 weeks.

Explanation: Each otter eats about 16 pounds of food each day. There are 37 otters in a raft, The food eaten by a raft in a day is 37 × 16 = 592 pounds.

The food eaten by a raft in 7 days ( 1 week ) is 592 × 7 By using Distributive property of multiplication = 7 × ( 500 + 90 + 2 ) = (7 × 500) + ( 7 × 90) + ( 7 × 2 ) = 3500 + 630 + 14 = 4,144. So, 592 × 7 = 4,144.

A raft eats 4,144 pounds in 1 week.

Critique Reasoning Compare your plan to your partner’s. How are your plans alike? How are they different? Answer: All the strategies are correct that are used by my friend and me. Using any method in multiplication is frequently used to find the product as fast as possible some methods are long and some of them are really fast and easy . Every method is correct unless you did not do any mistakes, so , all are alike. in obtaining the correct answer.

Think and Grow: Problem Solving: Multiplication

Example A coach buys 6 cases of sports drinks and spends $60. Each case has 28 bottles. A team drinks 85 bottles at a tournament. How many bottles are left? Understand the Problem What do you know? • The coach buys 6 cases. • The coach spends $60. • Each case has 28 bottles. • The team drinks 85 bottles.

What do you need to find? • You need to find how many bottles are left.

Make a Plan

How will you solve? • Multiply 28 by6 to find the total number of bottles in 6 cases. • Then subtract 85 bottles from the product to find how many bottles are left. • The amount of money the coach spends is unnecessary information.

Question 1. Explain how you can check whether your answer above is reasonable. Answer: Calculate the given information to get the result.

Explanation: The coach buys 6 cases. Each case has 28 bottles. The team drinks 85 bottles We need to find how many bottles are left.

So, by calculating these we obtain the result.

By understanding the problem We know that, A zookeeper has 4 boxes. There are137 grams of leaves in each box. A koala eats 483 grams of leaves in 1 day

We need to find, how many grams of leaves are left.

Explanation: A zookeeper has 4 boxes. There are137 grams of leaves in each box. So, 137 × 4 By using Distributive property of multiplication = 4 × ( 100 + 30 + 7 ) = (4 × 100) + ( 4 × 30) + ( 4 × 7 ) = 400 + 120 + 28 = 548. So, 137 × 4 = 548.

A koala eats 483 grams of leaves in 1 day The zookeeper wants to know how many grams of leaves are left. Then 548 – 483 = 65 There are 65 leaves left.

By understanding the problem We know that, A beekeeper has 2 hives. Hive A produces 14 pounds of honey. Hive B produces 4 times as much honey as Hive A.

We should know , The beekeeper wants to know how many pounds of honey are produced in all.

Explanation: Hive A produces 14 pounds of honey. Hive B produces 4 times as much honey as Hive A. So, 4 × 14 By using Distributive property of multiplication = 4 × ( 10 + 4) = (4 × 10) + ( 4 × 4) = 40 + 16 = 56. So, 4 × 14 = 56. Hive B produces 56 pounds of honey

The honey produced by the 2 hives is 14  + 56 = 70  pounds.

Understand the problem. Then make a plan. How will you solve? Explain. Question 4. A runner completes 12 races each year. He improves his time by 10 seconds each year. Each race is 5 kilometers long. The runner wants to know how many kilometers he runs in races in 3 years. Answer: 180 kilometers.

Explanation: By understanding the problem we know that, A runner completes 12 races each year. Each race is 5 kilometers long.

We should know that, how many kilometers he runs in races in 3 years.

Then, he completes 12 races each year. The races in 3 years. are 12  × 3 = 36 , 36 races in 3 years .

Each race is 5 kilometers long. Then for 36 races , we get 36 × 5 = 180 km.

So, The runner completes 180 km in 3 years.

Question 5. A volunteer bikes 4 miles in all to travel from her home to a shelter and back. At the shelter, she walks a dog 1 mile. The volunteer wants to know how many miles she travels doing these tasks for 28 days. Answer: 140 miles

Explanation: By understanding the problem we know that, A volunteer bikes 4 miles in all to travel from her home to a shelter and back. At the shelter, she walks a dog 1 mile.

We should know that, how many miles she travels doing these tasks for 28 days.

A volunteer bikes 4 miles in all to travel from her home to a shelter and back. For 28 days, we get 4 × 28 = 112, she bikes for 112 miles. At the shelter, she walks a dog 1 mile. for 28 days, we get 1 × 28 = 28, she walks dog for 28 miles .

she travels doing these tasks for 28 days by covering  a total of 140 miles.

Explanation: By understanding the problem we know that, Cats have 32 muscles in each ear. Humans have 12 ear muscles in all.

We should know that, How many more muscles do cats have in both ears than humans have in both ears

Cats have 32 muscles in each ear, For 2 ears we get 32 +32 = 64 muscles Humans have 12 ear muscles in all. Then 64 – 12 = 52 .

Cats have 52 more muscles than humans have in both the ears.

Question 7. A school has 5 hallways. Each hallway has 124 lockers. 310 lockers are red. 586 lockers are in use. How many lockers not are in use? Answer: 34 lockers are not in use.

Explanation: By understanding the problem we know that, A school has 5 hallways. Each hallway has 124 lockers 586 lockers are in use.

We should know that, How many lockers not are in use.

Each hallway has 124 lockers , then for 5 hallways , we get 124 × 5 = 620. 620 lockers in the whole school 586 lockers are in use, to get the number of lockers that are not in use are 620 – 586 = 34.

34 lockers are not in use.

Totally scientists have $1,160 left.

Question 8. City A has 3,296 fourth graders. City B has 3 times as many fourth graders as City A. City C has 5 times as many fourth graders as City B. How many fourth graders are in all three cities? Answer: Totally There are 62,624 fourth graders in all the three cities.

Explanation: City A has 3,296 fourth graders,

Fourth graders in all the three cities are 62,624.

Understand the problem. Then make a plan. How will you solve? Explain. Question 1. Raku is a Japanese-inspired art form. fires An artist, or bakes, a raku pot at1,409 degrees Fahrenheit. The artist fires a porcelain pot at 266 degrees Fahrenheit less than 2 times the temperature at which the raku pot is fired. You want to find the temperature at which the porcelain pot is fired. Answer: The porcelain pot is fired at the temperature of 2,552 degrees Fahrenheit.

Explanation: By understanding the problem we know that, Raku is a Japanese-inspired art form bakes, a raku pot at1,409 degrees Fahrenheit. The artist fires a porcelain pot at 266 degrees Fahrenheit less than 2 times the temperature at which, the raku pot is fired.

We should know that, find the temperature at which the porcelain pot is fired.

Let us say porcelain pot as p and raku pot as r , Now, The artist fires a porcelain pot at 266 degrees Fahrenheit less than 2 times the temperature at which, the raku pot is fired. we have  p =  2r  – 266 degrees Fahrenheit 2r = 2 × 1,409 = 2,818. Then  p = 2,818 – 266 = 2,552  degrees Fahrenheit

The temperature at which the porcelain pot is fired is  2,552  degrees Fahrenheit.

Question 2. You practice basketball 6 times each week. Each basketball practice is 55 minutes long. You practice dance for 225 minutes altogether each week. You want to find how many minutes you practice basketball and dance in all each week. Answer: you practice basketball and dance  in all  for 555 minutes each week.

Explanation: By understanding the problem we know that, practice basketball 6 times each week. Each basketball practice is 55 minutes long. practice dance for 225 minutes altogether each week.

We should know that, find how many minutes you practice basketball and dance in all each week.

So, practice basketball 6 times each week. Each basketball practice is 55 minutes long. we have 6 × 55 = 330, Basketball practice for a week is for 330 min. Dance practice for a week is for 225 minutes. Then 330 + 225 = 555.

The basketball and dance practice for a whole week is for 555 minutes.

Question 3. You buy 7 books of stamps. There are 35 stamps in each book. You give some away and have124 stamps left. How many stamps did you give away? Answer: 121 stamps have left.

Explanation: By understanding the problem we know that, You buy 7 books of stamps There are 35 stamps in each book. You give some away and have124 stamps left.

We should know that, How many stamps did you give away?

So, You buy 7 books of stamps There are 35 stamps in each book. we have 35 × 7 = 245 stamps. 245 stamps are gave away.

You give some away and have124 stamps left. we get , 245 – 124 = 121.

So, Totally 121 stamps have left.

Question 4. Your neighbor fills his car’s gasoline tank with 9 gallons of gasoline. Each gallon of gasoline allows him to drive 23 miles. Can he drive for 210 miles without filling his gasoline tank? Explain. Answer: No , He can only drive for 207 miles without filling his gasoline.

Explanation: By understanding the problem we know that, Neighbor fills his car’s gasoline tank with 9 gallons of gasoline. Each gallon of gasoline allows him to drive 23 miles.

We should know that, Can he drive for 210 miles without filling his gasoline tank?

So, Neighbor fills his car’s gasoline tank with 9 gallons of gasoline. Each gallon of gasoline allows him to drive 23 miles. we have 9 × 23 = 207. He can travel for 207 miles for 9 gallons of gasoline.

So, he cannot drive for 210 miles without filling any extra gasoline.

Question 5. Writing Write and solve a two-step word problem that can be solved using multiplication as one step. Answer:  David has 20 oranges.

Explanation: Problem- Newton has 10 apples and David  has oranges 2 times as many as Newton’s apples. How many oranges does David have? Solution:  Newton has 10 apples , David  has oranges 2 times as many as Newton’s apples, then we have 2 × 10 = 20 . So, David has 20 oranges.

Explanation: By understanding the problem we know that, There are 1,203 pictures taken for a yearbook. There are 124 student pictures for each of the 6 grades. There are also 7 pictures for each of the 23 school clubs.

We should know that, How many teacher or candid pictures are there?

So, There are 124 student pictures for each of the 6 grades. , we have 6 × 124 = 744 . There are 744 pictures from all 6 grades students. There are also 7 pictures for each of the 23 school clubs. we have, 7 × 23 = 161 .There are 161 pictures from 23 school club students. Total number of students we calculated are 744 + 161 = 905. Totally a  number of 1,203 pictures taken for a yearbook. Then 1,203 – 905 = 298.

Finally, There are 298 pictures of teacher or candid pictures.

Question 7. Modeling Real Life A construction worker earns $19 each hour she works. A supervisor earns $35 each hour she works. How much money do the construction worker and supervisor earn in all after 8 hours of work? Answer: $432 are earned by the construction worker and supervisor earn in all after 8 hours of work.

Explanation: By understanding the problem we know that, A construction worker earns $19 each hour she works. A supervisor earns $35 each hour she works.

We should know that, How much money do the construction worker and supervisor earn in all after 8 hours of work.

So, A construction worker earns $19 each hour she works. Then for 8 hours we get , $19 × 8 = $152. Also A supervisor earns $35 each hour she works. Then for 8 hours we get , $35 × 8 = $280. Total pay of both worker and supervisor is $152 + $280 = $432.

So,$432 are earned by the construction worker and supervisor earn in all after 8 hours of work.

Question 8. Modeling Real Life A family of 8 has $1,934 to spend on a vacation that is 1,305 miles away. They buy a $217 plane ticket and an $8 shirt for each person. How much money does the family have left? Answer: The Family  have $134 left.

Explanation: By understanding the problem we know that, A family of 8 has $1,934 to spend. They buy a $217 plane ticket and an $8 shirt for each person.

We should know that, How much money does the family have left.

So, They buy a $217 plane ticket for each person, Then for 8 members , we have , $217 × 8 = $1,736. They buy an $8 shirt for each person ,Then for 8 members , we have , $8 × 8 = $64. Total cost for plane tickets and shirts are $1,736 + $64 = $1,800. The money they left is $1,934 – $1,800 = $134.

So, The Family  have $134 left.

Explanation: As sound waves travel 1,125 feet per second through air. A flash of lightning 5 seconds before you hear the thunder, at a distance of 5625 feet.

Question 2. Sound waves travel 22,572 feet per second faster through iron than through diamond. The speed of sound through the diamond is 39,370 feet per second. a. Estimate the speed of sound through iron in feet per second. b. What is the actual speed of sound through iron in feet per second? c. Is your estimate close to the exact speed of sound through iron? Explain. Answer: a. 61,9412 feet per second b. 61,9412 feet per second c. yes

Explanation: Sound waves travel 22,572 feet per second faster through iron than through diamond. The speed of sound through the diamond is 39,370 feet per second. speed of iron is 22,572 + 39,370  = 61,9412. So, we have the same answer for both of the questions because  estimated speed is the actual speed of sound through iron .

Explanation: a. speed of sound is 1,125 feet per second And sound travels 4 times faster in water than in air So, 1,125 × 4 =  4,500. b. We know that, time = distance / speed , Given distance is 9,000 feet and speed is 1,125 feet per second. so time = 9,000 / 1,125 = 8 seconds. So, Diver can hear the Horn sound from 8 seconds away.

Question 4. Do sound waves travel the fastest through solids, liquids, or gases? Explain. Answer: Yes

Explanation: As the density of the materials high, sound waves travel faster. That is the reason for high speed in solids then liquids compare to gases.

3.1 Understand Multiplicative Comparisons

Write two comparison sentences for the equation. Question 1. 72 = 8 × 9 Answer:  72 is 8 times as many as 9. or 72 is 9 times as many as 8.

Explanation: we should multiply the numbers 8 and 9 , to get the multiplication result as 72.

Question 2. 60 = 10 × 6 Answer: 60 is 10 times as many as 6. or 60 is 6 times as many as 10.

Explanation: we should multiply the numbers 10 and 6 , to get the multiplication result as 60.

Write an equation for the comparison sentence. Question 3. 28 is 4 times as many as 7. Answer:  28 = 4 × 7

Explanation:  we should multiply the numbers 4 and 7, to get the multiplication result as 28.

Question 4. 40 is 8 times as many as 5. Answer:  40 = 8 × 5

Explanation: we should multiply the numbers 8 and 5, to get the multiplication result as 40.

Question 5. Newton saves $40. Descartes saves $25 more than Newton. How much money does Descartes save? Answer: Descartes saves $65.

Explanation: Newton saves $40. Descartes saves $25 more than Newton., So, $40 + $25 = $65.

Question 6. Your friend is 10 years old. Your neighbor is 4 times as old as your friend. How old is your neighbor? Answer: 40 years old.

Explanation: Your friend is 10 years old. Your neighbor is 4 times as old as your friend. So, 10 × 4 = 40.

3.2 Multiply Tens, Hundreds, and Thousands

Find the product Question 7. 6 × 90 = _____ Answer:  540

Explanation: Using the Place-value method, 6 × 90 = 6 × 9 tens = 54 tens = 540 So, 6 × 90 = 540.

Question 8. 3,000 × 1 = _____ Answer: 3000

Explanation: Using the Place-value method, 1 × 3,000 = 1 × 3 thousands = 3 thousands = 3,000 So, 1 × 3,000 = 3,000.

Question 9. 4 × 200 = _____ Answer: 800

Explanation: Using the Place-value method, 4 × 200 = 4 × 2 hundreds = 8 hundreds = 800 So, 4 × 200 = 800.

Question 10. 4,000 × 4 = _____ Answer: 16000

Explanation: Using the Place-value method, 4 × 4,000 = 4 × 4 thousands = 16 thousands = 16,000 So, 4 × 4,000 = 16,000.

Question 11. 8 × 700 = _____ Answer: 5,600

Explanation: Using the Place-value method, 8 × 700 = 8 × 7 hundreds = 56 hundreds = 5600 So, 8 × 700 = 5,600.

Question 12. 2 × 60 = _____ Answer: 120

Explanation: Using the Place-value method, 2 × 60 = 2 × 6 tens = 12 tens = 120 So, 2 × 60 = 120.

Find the missing factor. Question 13. ____ × 200 = 1,000 Answer: 5

Explanation :Let the missing number be X So, X × 200 = 1,000 X = 1,000 / 200 = 5 Hence, the value of X is: 5.

Question 14. 5 × _____ = 450 Answer: 90

Explanation :Let the missing number be X So, 5 × X  = 450 X = 450 / 5 = 90 Hence, the value of X is: 90.

Question 15. _____ × 800 = 6,400 Answer: 8

Explanation :Let the missing number be X So, X × 800 = 6,400 X = 6,400 / 800 = 8 Hence, the value of X is: 8.

3.3 Estimate Products by Rounding

Estimate the product Question 16. 5 × 65 Answer: 350.

Explanation: Round to the nearest tens. 65 is close to 70; 5 x 70 = 350

Question 17. 2 × 903 Answer: 1,800

Explanation: Round to the nearest tens. 903 is close to 900; 2 x 900 = 1,800.

Question 18. 7 × 3,592 Answer:  25,130.

Explanation: Round to the nearest tens. 3,592 is close to 3,590; 7 x 3,590 = 25,130.

Find two estimates that the product is between. Question 19. 8 × 32 Answer: The product is in between 240 and 320.

Explanation: Round to the nearest tens. 32 is close to 30; 8 × 30 = 240 and Explanation: Round to the nearest tens. 32 is close to 40; 8 × 40 = 320 The product is in between 240 and 320.

Question 20. 4 × 284 Answer:

Question 21. 6 × 5,945 Answer:  The product is in between 35,640 and 35,700.

Explanation: Round to the nearest tens. 5,945 is close to 5,940; 6 × 5,940 = 35,640 and Explanation: Round to the nearest tens. 5,945 is close to 5,950; 6 × 5,950 = 35,700 The product is in between 35,640 and 35,700.

Question 22. A charity organizer raises $9,154 each month for 6 months. To determine whether the charity raises $50,000, can you use an estimate, or is an exact answer required? Explain. Answer: estimated raise is $54,900, The charity can raise above $50,000.

Explanation:  organizer raises $9,154 each month for 6 months. $9,154 is close to $9,150; So, $9,150 × 6 = $54,900. The charity can raise above $50,000.

3.4 Use Distributive Property to Multiply

Find the product. Question 23. 3 × 14 = _____ Answer: 42

Explanation: by using distributive property 3 × 14 = 3× (10 + 4) = (3 × 10) + (3 × 4) = 30 + 12 = 42

Question 24. 18 × 9 = _____ Answer: 162

Explanation: by using distributive property 9 × 18 = 9× (10 + 8) = (9 × 10) + (9 × 8) = 90 + 72 = 162

Question 25. 36 × 5 = _____ Answer:  180

Explanation: by using distributive property 5 × 36 = 5 × (30 + 6) = (5 × 30) + (5 × 6) = 150 + 30 = 180

Question 26. 8 × 56 = _____ Answer: 448

Explanation: by using distributive property 8 × 56 = 8 × (50 + 6) = (8 × 50) + (8 × 6) = 400 + 48 = 448

Question 27. 6 × 67 = ______ Answer: 402

Explanation: by using distributive property 6 × 67 = 6 × (60 + 7) = (6 × 60) + (6 × 7) = 360 + 42 = 402

Question 28. 83 × 2 = _____ Answer:  166

Explanation: by using distributive property 2 × 83 = 2 × (80 + 3) = (2 × 80) + (2 × 3) = 160 + 6 = 166

Explanation: by using distributive property 4 × 23 = 4× (20 + 3) = (4 × 20) + (4 × 3) = 80 + 12 = 92

3.5 Use Expanded Form to Multiply

Find the product Question 30. 487 × 3 = _____ Answer: 1,461

Explanation: 3 × 487, by expanding we get = 3 × (400 + 80 + 7), by using distributive property, we get = (3 × 400) + ( 3 × 80) + ( 3 × 7) = 1,200 + 240 + 21 Area model = 1,200 + 240 + 21 so the result of the partial products is 1,461

Question 31. 5 × 7,402 Answer:  37,010

Explanation: 5 × 7,402 , by expanding we get = 5 × (7,000 + 400 + 2), by using distributive property, we get = (5 × 7,000) + ( 5 × 400) + ( 5 × 2) = 3,500 + 2,000 + 10 Area model = 3,500 + 2,000 + 10 so the result of the partial products is 37,010.

Question 32. 8,395 × 7 = _____ Answer: 58,765

Explanation :  7 × 8,395 = 7 × (8,000 + 300 + 90 + 5 ) = (7 × 8,000 ) + (7 × 300 ) + ( 7 × 90) + (7 × 5)   by using Expanded form we get = 56,000 + 2,100 + 630 + 35 Area model = 56,000 + 2,100 + 630 + 35 so the result of the partial products is 58,765

3.6 Use Partial Products of Multiply

So, 1,000 , 20 , 16 are the partial products .

3.7 Multiply Two-Digit Numbers by One-Digit Numbers

6 × 9 ones = 54 ones regrouping 54 ones as 5 tens and 4 ones 6 × 1 tens = 6 tens 6 tens + 5 tens = 11 tens  or  1 hundreds and 1 tens ,Then we get 114

And the estimated product is 120 because 19 is close to 20,then 20 × 6 = 120 So, 19 × 6 = 114.

7 × 3 ones = 21 ones regrouping 21 ones as 2 tens and 1 ones 7 × 7 tens = 49 tens 49 tens + 2 tens = 51 tens  or  5 hundreds and 1 tens ,Then we get 511

And the estimated product is 490 because 73 is close to 70,then 70 × 7 = 490 So, 73 × 7 = 511.

5 × 8 ones = 40 ones regrouping 40 ones as 4 tens and 0 ones 5 × 5 tens = 25 tens 25 tens + 4 tens = 29 tens  or  2 hundreds and 9 tens ,Then we get 290.

And the estimated product is 300 because 58 is close to 70,then 60 × 7 = 300 So, 58 × 5 = 290.

3.8 Multiply Three – and Four-Digit Numbers by One-Digit Numbers

Find the product. Check whether your answer is reasonable Question 40. Estimate: _____ 402 × 3 = _____ Answer: 1,206, And the estimated product is 1,200

Step 2: Multiply tens and regroup tens 3 × 0 tens = 0 tens

Step 3: Multiply hundreds and regroup hundreds 3 × 4 hundreds  = 12 hundreds or 1 thousands and 2 hundreds

By holding all places together we get 1,206 .

And the estimated product is 1,200 because 402 is close to 400, 400 × 3 = 1,200 So, 402 × 3 =  1,206.

Question 41. Estimate: _____ 8 × 3,861 = _____ Answer: 30,888, And the estimated product is 30,880

Step 1:  Multiply ones and regroup 8 × 1 ones = 8 ones

Step 2: Multiply tens and regroup tens 8 × 6 tens = 48 tens or 4 hundreds and 8 tens

Step 3: Multiply hundreds and regroup hundreds 8 × 8 hundreds  = 64 hundreds 64 hundreds + 4 hundreds = 68 hundreds regroup as 6 thousands and 8 hundreds

Step 4: Multiply thousands and regroup thousands 8 × 3 thousands = 24 thousands 24 thousands + 6 thousands = 30 thousands

By holding all the places together we get 30,888.

And the estimated product is 30,880 because 3,861 is close to 3,860, 3,860 × 8 = 30,880 So, 3,861 × 8  = 30,888 .

Question 42. Estimate: ______ 977 × 2 = ______ Answer: 1,954 ,And the estimated product is 1,960

Step 1:  Multiply ones and regroup 2 × 7 ones = 14 ones Regroup 14 ones  as 1 tens and 4 ones

Step 2: Multiply tens and regroup tens 2 × 7 tens = 14 tens 14 tens + 1 tens = 15 tens regroup as 1 hundred and 5 tens

Step 3: Multiply hundreds and regroup hundreds 2 × 9 hundreds  = 18 hundreds 18 hundreds  + 1 hundreds = 19 hundreds Regroup  as 1 thousands and 9 hundreds

By holding all places together we get 1,954 .

And the estimated product is 1,960 because 977 is close to 980, 980 × 2 = 1,960 So, 977 × 2 = 1,954 .

Step 1:  Multiply ones and regroup 6 × 8 ones = 48 ones Regroup 48 ones  as 4 tens and 8 ones

Step 2: Multiply tens and regroup tens 6 × 0 tens = 0 tens 0 tens + 4 tens = 4 tens

Step 3: Multiply hundreds and regroup hundreds 6 × 3 hundreds  = 18 hundreds

By holding all places together we get 1,848 .

Step 1:  Multiply ones and regroup 5 × 8 ones = 40 ones Regroup 40 ones  as 4 tens and 0 ones

Step 2: Multiply tens and regroup tens 5 × 0 tens = 0 tens 0 tens + 4 tens = 4 tens

Step 3: Multiply hundreds and regroup hundreds 5 × 4 hundreds  = 20 hundreds

By holding all places together we get 2,040 .

So, 306 × 6 = 1,848 is less than 408 × 5 = 2,040.

Step 1:  Multiply ones and regroup 6 × 9 ones = 54 ones regroup 54 ones as 5 tens and 4 ones

Step 2: Multiply tens and regroup tens 6 × 8 tens = 48 tens 48 tens + 5 tens = 53 tens or regroup as 5 hundreds and 3 tens

Step 3: Multiply hundreds and regroup hundreds 6 × 7 hundreds  = 42 hundreds 42 hundreds + 5 hundreds = 47 hundreds regroup as 4 thousands and 7 hundreds

By holding all the places together we get 4,734.

Step 1:  Multiply ones and regroup 2 × 7 ones = 14 ones regroup 14 ones as 1 tens and 4 ones

Step 2: Multiply tens and regroup tens 2 × 6 tens = 12 tens 12 tens + 1 tens = 13 tens regroup as 1 hundred and 3 tens

Step 3: Multiply hundreds and regroup hundreds 2 × 3 hundreds  = 6 hundreds 6 hundreds + 1 hundred =  7 hundreds

Step 4: Multiply thousands and regroup thousands 2 × 2 thousands = 4 thousands

By holding all the places together we get 4,734. So, 6 × 789 = 4,734 is equal to 2 × 2,367 = 4,734.

Step 1:  Multiply ones and regroup 3 × 4 ones = 12 ones regroup as 1 tens and 2 ones

Step 2: Multiply tens and regroup tens 3 × 5 tens = 15 tens 15 tens + 1 tens = 16 tens regroup 16 tens  as 1 hundreds  and 6 tens

Step 3: Multiply hundreds and regroup hundreds 3 × 4 hundreds  = 12 hundreds 12 hundreds + 1 hundreds = 13 hundreds

By holding all places together we get 1,362.

Step 1:  Multiply ones and regroup 4 × 3 ones = 12 ones regroup as 1 tens and 2 ones

Step 2: Multiply tens and regroup tens 4 × 1 tens = 4 tens 4 tens + 1 tens = 5 tens

Step 3: Multiply hundreds and regroup hundreds 3 × 4 hundreds  = 12 hundreds

By holding all places together we get 1,252.

So, 454 × 3 = 1,362 is grater than 313 × 4 = 1,252.

3.9 Use Properties to Multiply

Use properties to find the product. Explain your reasoning. Question 46. 25 × 9 × 4 Answer: 900

Explanation: By using commutative property of multiplication = 9 × ( 25 × 4) =9 × 100 = 900 So,  25 × 9 × 4 = 900 .

Question 47. 8 × 250 Answer:  2,000.

Explanation: By using Distributive property of multiplication = 8 × ( 200 + 50) = (8 × 200) + ( 8 × 50) = 1,600 + 400 = 2,000. So, 8 × 250 = 2,000.

Question 48. 3 × 497 Answer: 1,491

Explanation: By using Distributive property of multiplication = 3 × ( 400 + 90 + 7 ) = (3 × 400) + ( 3 × 90) + (3 × 7) = 1,200 + 270 + 21 = 1,491. So, 3 × 497 = 1,491.

Question 49. 2 × 8 × 15 Answer: 240

Explanation: By using commutative property of multiplication = 8 × ( 15 × 2) = 8 × 30 = 240 So,  2 × 8 × 15 = 240 .

Question 50. 699 × 9 Answer: 6,291.

Explanation: By using Distributive property of multiplication = 9 × ( 600 + 90 + 9 ) = (9 × 600) + ( 9 × 90) + (9 × 9) = 5,400 + 810 + 81 = 6,291 . So, 9 × 699 = 6,291.

Question 51. 1,003 × 6 Answer: 6,018.

Explanation: By using Distributive property of multiplication = 6 × ( 1000 + 3) = (6 × 1000) + (6 × 3) = 6000 + 18 = 6,018 So, 1,003 × 6 = 6,018.

3.10 Problem Solving: Multiplication

Explanation: By understanding the problem we know that, A musical cast sells 1,761 tickets for a big show. The cast needs to complete 36 days of rehearsal. Each rehearsal is 8 hours long. The cast has rehearsed for 102 hours so far.

We should know that, How many hours does the cast have left to rehearse

The total number of hours to practice are 36 × 8 = 288 hours They practiced for 102 hours so far then , to get the remaining hours 288 – 102 = 186 hours.

So, the cast has 186 hours left to rehearse .

Question 1. Which number is greater than 884,592? A. 89,621 B. 884,592 C. 805,592 D. 894,592 Answer: D. 894,592

Explanation: of all the given options , D is the greatest number .

Explanation : To fin the difference between two numbers, we should subtract the lowest number from the largest number, Then, 30,501 – 6,874 = 23,627.

Explanation: Because this number is the closest number to the 37,000 from the given options. so, 36,834 could be the exact number.

Question 4. What is the product of 4,582 and 6? A. 27,492 B. 24,082 C. 27,432 D. 42,117 Answer: 27,492.

Explanation: by using distributive property we get 6 × 4,582 = 6 × ( 4,000 + 500 + 80 + 2) = (6 × 4,000) + ( 6 × 500)+ ( 6 × 80 ) + ( 6 × 2) = 24,000 + 3,000 + 480 + 12 = 27,492. So, 6 × 4,582 = 27,492.

Question 5. Which expression is equal to 246,951 + 73,084? A. 246,951 + 70,000 + 3,000 + 800 + 40 B. 246,951 + 7,000 + 300 + 80 + 4 C. 246,951 + 70,000 + 3,000 + 80 + 4 D. 246,951 + 70,000 + 3,000 + 800 + 4 Answer: C

Explanation:    246,951 + 73,084, 73,084 can be written as, 246,951 + 70,000 + 3,000 + 80 + 4.

Question 6. Newton reads the number ”four hundred six thousand, twenty-nine” in a book. What is this number written in standard form? A. 4,629 B. 406,029 C. 460,029 D. 406,290 Answer: B

Explanation: 406,029 can be written as four hundred six thousand, twenty-nine.

Explanation: all the above expressions give the product of 225, 9 × 25  = 225 75 × 3  = 225 5 × 45  = 225.

Explanation: from the give numbers 6 ,1,8,4,2 , place the numbers in the descending order we get 86,421.

Question 9. What is the sum of 62,671 and 48,396? A. 111,067 B. 11,067 C. 100,967 D. 100,067 Answer:  A.1,11,067.

Explanation: Sum means Addition we should add the two numbers in order to get the result, 62,671  +  48,396 = 1,11,067.

Explanation: He drinks 8 glasses of water each day so for 1 year that is for 365 days , we get 365 × 8 = 2,920. So, He drinks 2, 920 glasses for 1 year , so it is in between 2,400 and 3,200.

Question 11. Which statement about the number 420,933 is true? A. The value of the 2 is 2,000. B. The 4 is in the ten thousands place. C. The value of the 3 in the tens place is ten times the value of the 3 in the ones place. D. There are 9 tens. Answer: C

Explanation: The number 420,933  has the value of the 3 in the tens place is ten times the value of the 3 in the ones place.

Explanation: Because the number 360,000 should be in between the same range of the given numbers that is, 480,012 – 127,465.

Question 13. There are 8 students in a book club. There are 5 times as many students in a drama club as the book club. How many students are in the drama club? A. 13 students B. 45 students C. 3 students D. 40 students Answer: D . 40 students

Explanation: There are 8 students in a book club. There are 5 times as many students in a drama club as the book club. Then, 8 × 5 = 40. So, There are 40 students in the drama club.

Question 14. The force required to shatter concrete is 3 times the amount of force required to shatter plexiglass. The force required to shatter plexiglass is 72 pounds per square foot. What is the force required to shatter concrete? A. 216 pounds per square foot B. 69 pounds per square foot C. 75 pounds per square foot D. 2,106 pounds per square foot Answer: A.216 pounds per square foot

Explanation: The force required to shatter plexiglass is 72 pounds per square foot. The force required to shatter concrete is 3 times the amount of force required to shatter plexiglass. Then, 72 × 3 = 216.

So, the force required to shatter concrete is 216 pounds per square foot.

Question 15. Which number, when rounded to the nearest hundred thousand, is equal to 100,000? A. 9,802 B. 83,016 C. 152,853 D. 46,921 Answer: B. 83,016

Explanation: it is  only number in the options which is close to 100,000 , All the other options are too far to roundoff .

Explanation: To use distributive property we have to organize the largest number in the expression in equal distributions respectively. so,  5,193 × 8 = 8 × (5,000 + 100 + 90 +3).

Explanation: Part A: By rounding the money from the table , we have 90 – minute jump pass = $20 water bottle = $10 and T-shirt = $20 ,That total amount will be $50 For five friends we get, 5 × $50 = $250. for all of them.

Part B : An Ultimate Package costs $40 and includes all of the items listed in the table. if each of the 5 members buys the package then , $40  × 5 = $200. So, from Part A and Part B we get to know that they would have save $50 if they bought the package , that is $250 – $200 = $50.

Question 18. A pair of walruses weigh 4,710 pounds together. The female weighs1,942 pounds. How much more does the male weigh than the female? A. 826 pounds B. 6,652 pounds C. 2,768 pounds D. 2,710 pounds Answer: C. 2,768 pounds

Explanation: A pair of walruses weigh 4,710 pounds together. The female weighs1,942 pounds. Then , to get the male walrus weight , we have , 4,710 – 1,942 = 2,768

So, The weight of male walrus is 2,768 pounds.

Multiply by One-Digit Numbers STEAM Performance Task

Explanation: a. Given , in picture the whole roadway and walk way is 90 feet long in total Considering 2 walkways and assuming walkway as W and roadway as R  we get R + 2W = 90 feet and The roadway is 8 times as wide as the width of both walkways combined. can say as R = 8(2W) then we have 8(2W) + 2W  = 90 16W + 2W = 90 18W = 90 W = 90 /8 W = 5 , so, each walk way is 5 feet long.

b. the length of the bridge that is suspended above the water is from the picture we have 1,125 + 4,200 + 1,125 = 6,450. feet

c. the length of the bridge that is not  suspended above the water is From the picture we have 8,981 – 6,450 = 2,531 feet.

a. 44 ft is the height of the boat as per the picture.so the distance between the water and the  bridge is 5 times the height of the ferry boat ,answer is 44 ft multiplied by 5 times i.e.220 ft. so 44 × 5 = 220 ft.

b. As per the teachers estimation height of tower is 3 times the distance between the bridge and the water, so 220ft is multiplied by 3, i.e.  660 ft.  so  220 × 3 = 660

c. learn the exact height of the tower is 86 feet taller than the teacher’s estimate.so 660 + 86 = 746 feet.

a. 11,834 steps on Wednesday b.  12,260 steps on Thursday c. 10,050 steps on Friday d.  15,978 steps on Saturday

Explanation: a. He walks 1,122 more steps on Wednesday than on Monday = 10,712 + 1,122 = 11,834 steps. b. He walks 118 steps less on Thursday than on Sunday =  12,378 – 118 = 12,260 steps. c. He walks 10,050 steps on Friday d. He walks 2 times as many steps on Saturday than on Tuesday = 2 × 7,989 = 15,978 steps.

Explanation: a. He walks 11,500 steps each day , Then for 1 Week we have 7 days , so 7 × 11,500 = 80,500 steps for a week b. By rounding the nearest numbers of all the steps he walked from Sunday to Saturday , we have, 12,380 + 10,710 + 7,990 + 11,830 + 12,260 + 10,050 + 15,980 = 81,200 steps. 81,200 steps are estimated. He reached his goal for the week. c. 1 mile = 2,000 steps. The teacher estimates that he walks 3 miles from one end of the Golden Gate Bridge to the other and back again. So, 3 × 2,000  = 6,000 steps. He walked 6,000 steps.

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