problem solving involving addition and subtraction of decimals ppt

Adding and Subtracting Decimals

Decimals - numbers that are smaller than one whole.

When do you see decimals in the real world?

Decimal Models: Tenths and Hundreths

Decimal Models

1 + .25 = 1.25

Decimal Models: Hundredths and Thousandths

Place Value

Place Values change in the same ways on BOTH sides of the decimal point.

Remember: each place have a value of 10 times that of the place to its right

Move decimal point to the RIGHT

Move decimal point to the LEFT

Represent as a Decimal or a Fraction

Two ways to write one tenth are 0.1 and 1 / 10

Two ways to write one hundredth are 0.01 and

How to write a decimal 3 ways

Standard Form: 2.35

Word Form: two and thirty-five hundredths

Expanded Form: 2 x 1 + 3 x (1/10) + 5 x (1/100)

OR 2 + .3 + .05

Standard Form: 1.72

Word Form: _________________________________________________________

Expanded Form: 1 x 1 + 7 x (1/10) + 2 x (1/100)

Standard Form: ______________________________________________

Word Form: four and sixty one hundredths

Expanded Form: 4 x 1 + 6 x (1/10) + 1 x (1/100)

Standard Form: 3.614

Word Form: Three and six hundred fourteen thousandths

Expanded Form: _______________________________________________________________________

Find the value of the underlined digit

Place value: The value of the place of a digit in a number.

8 54.327 - The value of the digit 8 is 8 hundreds, or 800.

8 5 4.327 - The value of the digit 5 is 5 tens, or 50.

85 4 .327 - The value of the digit 4 is 4 ones, or 4.

854. 3 27 - The value of the digit 3 is 3 tenths, or 0.3.

854.3 2 7 - The value of the digit 2 is 2 hundredth, or 0.02.

854.32 7 - The value of the digit 7 is 7 thousandths, or 0.007.

Find the value of the underlined digit.

0.4 or four tenths

0.03 or three hundredths

0.006 or six thousandths

0.0005 or five ten thousandths

Compare Decimals

• Line up decimal points
• Fill in any place values with zero
• Begin at left and compare the digits until they are different
• Decide which digit is smaller or larger
• Use the correct symbol to show the relationship between the two numbers

0.264 _<_ 0.4 2 < 4

0.45____0.1

0.8____ 0.207

1.234___1.23

3.45 ____1.45

0.09____0.090

0.45_ > ___0.1

0.8_ > ___ 0.207

1.234_ > __1.23

3.45 __ > __1.45

0.09__ = __0.090

Ordering Decimals

Rounding Decimals

Rounding Decimals Video

If the number to the right is 5 or above, give it a shove.

If the number to the right is 4 or below, then let it go.

Round each number to the nearest tenth.

Round each number to the nearest hundredth.

Round each number to the nearest thousandth.

Adding Decimals

1. Line up decimal point to help you align the place value positions. Decimal point should be between the ones and tenths place.

** If needed, add zeros to make equivalent decimals

2. Add as you normally would. Bring down decimal point in the sum.

• 0.59 + 1.15

1.4 + 0.22 0.81 + 0.43

Subtracting Decimals

1. Line up decimal points to align place-value positions. Subtract the place value to the right.

2. Move the next place value to the left and continue subtracting. Regroup if needed.

3. Bring down the decimal point in the difference.

4. Check with quick addition.

• 0.61 - 1.08

0.84 - 0.17 1.39 - 1.14

Add or Subtract Decimals Video

Add or Subtract

1. 8.2 + 2.28 + 2.18

2. 8.22 - 4.39

3. $54.78 + $43.62

4. 6.3 + 2.98 + 7.7

5. $18 - $3.55

Change words to decimals than add or subtract

1.) seven and twenty- five hundredths added to nine and four tenths.

2.) twelve and eight hundredths added to four and thirty-five hundredths.

3.) one and eighty-two hundredths added to fifteen and eight tenths.

4.) three and seventy-two hundredths subtracted from five and eighty-one hundredths.

5.) one and six hundredths subtracted from eight and thirty-two hundredths.

6.) five and twenty-five thousandth subtracted from nine and fifteen thousandths.

Estimating before + or -

You can use rounding to help you estimate sums and differences.

Use rounding to estimate 1.24 + 0.82 + 3.4

Round to the nearest whole number. Then add.

You can use benchmarks to estimate.

- 0.30 - 0.25

0.78 is between 0.75 and 1. It is closer to 0.75

0.30 is between 0.25 and 0.50. It is closer to 0.25

Adding and Subtracting Decimals

Jul 28, 2014

440 likes | 958 Views

Adding and Subtracting Decimals. Lesson 1-5. The Basic Steps:. Line up the numbers by the decimal point. Fill in missing places with zeroes. Add or subtract. Addition Properties. Commutative Property of Addition: Numbers can be added in any order. Example: 5+3=3+5.

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Adding and Subtracting Decimals Lesson 1-5

The Basic Steps: • Line up the numbers by the decimal point. • Fill in missing places with zeroes. • Add or subtract.

Addition Properties Commutative Property of Addition: Numbers can be added in any order. Example: 5+3=3+5 Associative Property of Addition: Numbers can be grouped in any way. Example: (7+3) + 5 = 7 + (3+5) Identity Property of Addition: The sum of any number and zero is that number. Example: 18 + 0 = 18

Mental Math • Addition properties can be used to quickly find sums. • Example: What is 52 + 12.4 + 48? • We can use an addition property to quickly add this. • First, change the order: 52 + 48 + 12.4 ________________ property. • Then, group the first two addends together: (52 + 48) + 12.4________________ property • 100 + 12.4 = 112.4 commutative associative

Why Estimate? • Before adding your numbers, use one of the estimating strategies you learned to see what the answer should be close to. • When you add, you can see if your answer is reasonable.

Example: 28.9 + 13.31 This can estimate to 30 + 13, which is 43. (Compatible numbers) 28.9 0 + 13.31 42.21 The answer is close to the estimate.

Subtracting • The addition properties do not work for subtraction. • Estimate and subtract to find what the answer is close to. • Subtract to find the real answer.

Subtracting Across Zeroes • If you have several zeroes in a row, and you need to borrow, go to the first digit that is not zero, and borrow. • All middle zeroes become 9’s. • The final zero becomes 10.

Example: 15 – 9.372 0 1 4 9 9 10 .000 15 - 9.372 5 . 6 2 8

Classwork Use this site to play MATHFROG- ADDING AND SUBTRACTING FRACTIONS http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/addsubdec.shtml Homework Time! P. 27, 1-49 odd

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Adding and Subtracting Decimals Solve problems involving addition and subtraction of decimals.

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Mathematics 6 Quarter 1 – Module 7: Multiplying Decimals and Mixed Decimals

This module was designed and written with you in mind. It is here to help you master the skills in multiplying decimals. The scope of this module allows you to use it in many different learning situations. The language used recognizes your diverse vocabulary level. The lessons are arranged to follow the standard sequence of your course. But the order in which you read them can be changed to match with the textbook you are now using.

The module is divided into three lessons, namely:

• Lesson 1 – Multiplying Decimals with Factors Up to 2 Decimal Places
• Lesson 2 – Multiplying Mixed Decimals with Factors Up to 2 Decimal Places
• Lesson 3 – Multiplying Decimals and Mixed Decimals with Factors Up to 2 Decimal Places

After going through this module, you are expected to:

1. multiply decimals with factors up to 2 decimal places; (M6NS-Ie-111.3)

2. multiply mixed decimals with factors up to 2 decimal places; (M6NS-Ie-111.3)

3. multiply decimals and mixed decimals with factors up to 2 decimal places; (M6NS-Ie-111.3)

4. solve routine and non-routine problems involving multiplication of decimals and mixed decimals including money using appropriate problem-solving strategies; (M6NS-Ie-113.2) and

5. solve multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money using appropriate problem-solving strategies and tools. (M6NS-If-113.3)

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Decimals word problems

Adding and subtracting decimals.

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Add and subtract word problems.

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

26 December 2020

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