integers assignment class 7

Simply math phobia

Integers class 7 extra questions with answers and PDF Download

Integers class 7

What are Integers ?

Properties of integers: 

• Negative  integers are on the left side of 0
• Positive integers are on the right side of the zero
• 0 is neither +ve  nor -ve.
• Integers are closed under addition. It means, for any two integers a and b, a + b is an integer.
• Integers are also closed under subtraction. Thus, if a and b are two integers then a – b is also an integer.
• Addition is commutative for integers. In general, for any two integers a and b, we can say a + b = b + a

• Addition is associative for integers. In general for any integers a, b and c, we can say a + (b + c) = (a + b) + c
• For any two positive integers a and b, we can say a × (– b) = (– a) × b = – (a × b)
• Integers are closed under multiplication. In general, a × b is an integer, for all integers a and b
• Multiplication is commutative for integers. For any two integers a and b, a × b = b × a
• Distributivity of multiplication over addition is true for integers. In general, for any integers a, b and c, a × (b + c) = a × b + a × c
• Integers are not closed under division. 
• Division is not commutative for integers. 

Questions on integers for class 7 pdf

Sums on integers for class 7(Solved Examples )

Example 1: Arrange the following integers in ascending order   -102, -39, -51, -5 , 0 , -6, 35  and 7 .

Sol.  Ascending order of the given integers are  : -102 <  -51< -39 < -6< -5 < 0< 7< 35

Example 2: Find the sum of  -72 , 237 , 84 , 72, -184 , -37 .

Sol.  (-72) +237+84+72+(-184)+(-37)=(-72) +393 +(-184)+(-37)

                                                                        = -72+393-184-37

                                                                        =393-293 =100

Example 3: Write down a pair of integers whose (a) sum is –3      (b) difference is –5      (c) difference is 3     (d) sum is 0 Sol.  (a) (–1) + (–2) = –3        or       (–5) + 2 = –3     or   (-7)+(4) =-3   

         (b) (–9) – (– 4) = –5       or        (–2) – 3 = –5    or  (-7) -(-2)= -5

         (c) (–7) – (–10) = 3          or       1 – (–2) = 2     or   +7 -(+4)  =3

        (d) (–10) + 10 = 0           or          4 + (–4) = 0    or    3 +(-3) =0    (You can make more pairs.)

Example 4: Solve the following: (i) (-10) × (-5) + (-6) (ii) (-10) × [(-13) + (-10)] (iii) (-5) × [(-6) + 5] Sol.  (i) (-10) × (-5) + (-6) = 50 – 6 = 44

          (ii) (-20) × [(-13) + (-10)] = (-20) × (-23) = 460

          (iii) (-5) × [(-6) + 5]= (-5)  x  (-1)  =5

Example 5: In a class test containing 15 questions, 4 marks are given for every correct answer and (–2) marks are given for every incorrect answer. Anil attempts all questions but only 10 of her answers are correct.  What is his total score?  Sol. (i) Marks given for one correct answer = 4 So, marks given for 10 correct answers = 4 × 10 = 40 Marks given for one incorrect answer = – 2 So, marks given for 5 (= 15 – 10) incorrect answers = (–2) × 5 = –10 Therefore, Gurpreet’s total score = 40 + ( –10) = 30

Example 6:  Is  (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)?

Sol.  (–15) × [(–7) + (–1)]=   (-15) x (-8) = 120

    (–15) × (–7) + (–15) × (–1)=  105 + 15 = 120 

Hence (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)

Example 7: Find each of the following products:      (a)  (–20) × (–2) × (–5) × 7     (b) (–1) × (–5) × (– 4) × (– 6)

Sol.  (a) (–20) × (–2) × (–5) × 7 =– 20 × (–2 × –5) × 7 = [–20 × 10] × 7 = – 1400

           (b) (–1) × (–5) × (– 4) × (– 6) = [(–1) × (–5)] × [(– 4) × (– 6)] = 5 × 24 = 120 

Example 8:  A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

Example 9: Find: (a) 125 ÷ (–25)       (b) 80 ÷ (–5)        

Sol.  (a) 125 ÷ (-25) = (-125) ÷ 25 = =5 

          (b)  80 ÷ (-5) =(-80) ÷ 5 = -16 

Example  10: Find: (a) (–36) ÷ (– 4)         (b) (–201) ÷ (–3) 

Sol.  (a) (-36) ÷ (-4)= 36 ÷ 4 = 9

          (b) (-201) ÷ (-3) = 201÷ 3 = 67 

Example 11:  Solve the following :

(a) 3+2-1 x 4 ÷ 2 

 Sol. 3+2-1 x 4 ÷ 2 = 3+2-1 x 2 = 3+2-2 = 3

(b) 53 x 2 -1 x 6 

Sol. 53 x 2 -1 x 6  = 106-6 =100 

(c) 7 x 3 +8-2

Sol. 7 x 3 +8-2=  21 +8 – 2 =  29-2 = 27

(d) 12+(-3) +5 – (-2)

Sol. 12+(-3) +5 – (-2) = 12-3+5+2 =9+7 = 16 

Unsolved Examples with answers

(i) Complete the following pattern: (a) 7, 3, – 1, – 5, _____, _____, _____. (b) – 2, – 4, – 6, – 8, _____, _____, _____. (c) 15, 10, 5, 0, _____, _____, _____. (d) – 11, – 8, – 5, – 2, _____, _____, _____.

(iii) Solve the following:  (a) (-15) × 8 + (-15) × 4  (b) [32 + 2 × 17 + (-6)] ÷ 15

(iv) a × (b – c) = a × b – …………

(v) (a) For any integer a, what is (–1) × a equal to?   (b) Determine the integer whose product with (–1) is 24

(vi) Replace the blank with an integer to make it a true statement. (a) (–3) × _____ = 24          (b) 5 × _____ = –40 (c) _____ × (– 9) = –63       (d) _____ × (–12) = 132

(vii) For any integer a,   a ÷ 1 = ……………..

(viii) For any integer a,   a ÷ (- 1) =………….

(ix) Evaluate the following :  (a) (-526)-(-217)      (b) (-31) +31         (c) [(-6)  x (-8) ] x 5     (d) -13 x (7-8)      (e) (-3) x 8 x (-5)

(x) Match the following                        Column I                                                      Column II

 (a) a × 1                                                                        (i) Additive inverse of a

(b) 1                                                                               (ii) Additive identity

(c) ( – a) ÷ ( – b)                                                          (iii) Multiplicative identity

(d) a × ( – 1)                                                                  (iv) a ÷ ( – b)

(e) a × 0                                                                          (v) a ÷ b

(f) ( –a) ÷ b                                                                    (vi) a

(g) 0                                                                                (vii) – a

(h) a ÷ (–a)                                                                   (viii) 0

(i) –a                                                                               (ix) –1

Ans. (i) (a) -9, -13, -17, -21   (b) -10, -12, -14, -16    (c) -5, -10, -15, -20    (d) 1, 4, 7, 10

           (ii) (a) <    (b)  <      (c) >     (d) <      (e) >     (iii) (a) -180     (b) 4        (iv) a x c   

           (v) (a) -a    (b) -24      (vi) (a)  -8    (b)  -8   (c)  7  (d) -11    (vii) a      (viii) -a  

           (ix) (a) -309     (b) 0        (c) 240    (d) 13       (e) 120   

           (x) (a) → (vi), (b) → (iii), c → (v), d → (vii), e → (viii), f → (iv)     g → (ii), h → (ix), i → (i)

DOWNLOAD PDF          Integers class 7 worksheet

MCQ questions  for class 7 maths integers

(a) <                 (b) >               (c) =               (d) none of these

(ii) Solve  40-(-39) + (-5) 

(a) 74              (b) 64              (c) 60            (d) 0

(iii)  When the integers 12, 0, 5, – 5, – 8 are arranged in descending or ascending order, then find out which of the following integers always remains in the middle of the arrangement.

(a)   0                (b) 5                (c) – 8            (d) – 5

(iv) Next three consecutive numbers in the pattern 11, 8, 5, 2, –, –, –are (a) 0, – 3, – 6          (b) – 1, – 5, – 8        (c) – 2, – 5, – 8             (d) – 1, – 4, – 7

(v)The  ……………   is an additive identity for integers.

(a)1               (b) 0           (c)-1           (d) 2

(vi) (–1) × (–1) × (–1) × (–1) × (–1) = ………….  

(a) 1        (b) -1        (c) 0       (d) 2

(vii) …………………… is the multiplicative identity for integers.

(a) 0             (b) 1            (c) -1            (d) 2

(viii) 0 ÷ a = …………… for a ≠ 0

(a) 0          (b) 1          (c) -1           (d) not defined

(ix) any integer divided by zero is ……………………………

(a) 0           (b) meaningless         (c) 1         (d) -1

(x)  (– 85) × 43 + 43 × ( – 15)  is equal to ?

(a) -4300        (b) 4300          (c) 430         (d)  -430

Ans. (i) (a)       (ii) (a)          (iii) 0      (iv) (d)     (v) (b)        (vi)( b)         (vii)  (b)      (viii) (a)    (ix)  (b)      (x) (a) 

 Integers Class 7 Maths quiz 

Maths quiz for class 7 integers

•  Find the absolute value of  -5 .

2.  Add the integers +15,  -4 , + 8 and -6  .

3.  Write a negative integer and a positive integer whose sum is  -5 .

5. In a quiz team A scored -40 , 10 and 0 and team B scored 10 , 0 and -30 in three successive round . Which team scored more ?

6.  Subtract the sum of -1878 and 878   from 2000 .

7.  Subtract -134  from the sum of 37 and -87 .

8. If the sum of two integers is -1700 and one of them is 560 . Find the other number.

9. Determine the integer whose product with -17  is  -153 .

10. Find the value (-23){(-5) +25}

11. Anil is standing in the middle of a bridge which is 30 m above the water level of a river. If a 35 m deep river is flowing under the bridge , then the vertical distance between the foot of Anil and bottom level of  the river is?

12.  [(– 10) × (+ 9)] + ( – 10) is equal to

13.  –16 ÷ [8 ÷ (–2)] is equal to

14. (– 35) × 30 = – 30 × _______.

15. .Write a pair of integers whose product is – 36 and whose difference is 15.

Your score is

The average score is 66%

Restart quiz

Integers class 7 (extra questions  with answers) 

A. State whether the following statements are correct or incorrect. 

(i) When two positive integers are added we get a positive integer.

(ii) When two negative integers are added we get a positive integer.

(iii) When a positive integer and a negative integer are added, we always get a negative integer.

(iv) Additive inverse of an integer 8 is (– 8) and additive inverse of (– 8) is 8.

(v) For subtraction, we add the additive inverse of the integer that is being subtracted, to the other integer.

(vi) (–10) + 3 = 10 – 3

(vii) 8 + (–7) – (– 4) = 8 + 7 – 4

(viii) 25 × (–21) = (–25) × 21

(ix) –1 is a multiplicative identity of integers?

(x)  The distributivity of multiplication over addition is true for integers. 

(xi)  Is division associative for integers? 

(xii) When we change the order of integers, their sum remains the same.

(xiii) When we change the order of integers their difference remains the same.

(xiv) a ÷ b = b ÷ a

(xv)  a – b = b – a

B . Answer the following questions: 

(i) Write a pair of integers whose sum is zero (0) but difference is 8.

(ii) Write a pair of integers whose product is – 15 and whose difference is 8.

(iii) On multiplying or dividing two integers, If the signs of both the integers are  same, the sign of the answer is  ………………..

(iv) On multiplying or dividing two integers, If the signs of both the integers are different, the sign of the answer is  ………………

(v) If a, b and c are integers then a x (b+c)= ………….+…………..

(vi)  The product of three negative integers is a ……………..  integer.

(vii) The product of four negative integers is a ………………….  integer.

(viii) If the number of negative integers in a product is even, then the product is a ………………..  integer; if the number of negative

integers in a product is odd, then the product is a ………………….  integer.

(ix) What will be the sign of the product if we multiply together: (a) 8 negative integers and 3 positive integers?

(b) 5 negative integers and 4 positive integers?

(x)  (-5)  x (-10)  =………… x   (-5)

(xi) The sum of two integers is 116. If one of them is -79, find the other integers.

(xii) The product of three integers does not depend upon the grouping of integers and this is called the ……………………..  for multiplication of integers

Ans. A.  (i) True   (ii) False   (iii) False   (iv) True    (v) True    (vi) False    (viii) False   (viii) True   (ix) False  (x)  True    (xi) False  (xii) True      (xiii) False   (xiv) False     (v) False 

B. (i) 4 and -4      (ii)5,  -3 and  3 ,-5.        (iii) positive        (iv) negative       (v) (a x b)+(b x c)     (vi) negative      (vii) positive    (viii) positive, negative  (ix) (a) positive (b) negative   (x) -10    (xi) 195      (xii) associative property 

Integers class 7 extra questions word problems 

(i) A spacecraft is at 4525km above the earth’s surface.if it descends at the rate of 5km per minute. What will be its position after 9 hours.

(ii)A fruit merchant earns a profit of Rs. 66 per bag of orange sold and a loss of Rs. 44 per bag of grapes sold.

(a)Merchant sells 1800 bags of orange and 2500 bags of grapes. What is the profit or   loss?

(b) What is the number of bags of oranges to be sold to have neither profit nor loss if the number   of grapes bags are sold is 900 bags?​

(iii) Nathan ended round one of a quiz with 200 points. In round two, he scored -300 points and in the third round, he gained 200 points. What was his total score at the end of the third round?

(iv) A submarine submerges from the surface of the sea at the rate of 10 m/min. How long will it take to reach 300 m below the sea level?

(v)Roman civilization began in 509 B.C. and came to an end in 476 A.D. How long did Roman civilization last?

(vi)Metal mercury is a liquid at room temperature. Its melting point is -39°C. The freezing point of alcohol is -114°C. How much warmer is the melting point of mercury than the freezing point of alcohol?

(vii)The temperature in city-X was 10°C in the morning which dropped by 15°C in the evening. What is the temperature in the evening?

(viii)Everest, the highest peak in Asia, is 29,028 feet above sea level. The Dead Sea is 1,312 feet below sea level. What is the level difference between these two places? 7.

(ix)The temperature recorded in a city on Monday is 50°. If the temperature increases by 10° on Tuesday and falls by 11° on Wednesday. Find the temperature recorded on Wednesday

(x)In an examination,3 marks are awarded for every correct answer and1mark is deducted for every incorrect answer. If a student gets 15questions correct and7questions incorrect, find the marks scored by him.

(xi)Andrew has deposited $5500 and has withdrawn $4800 two times consecutively. Find the amount in his account.

(xii) A bird is flying 1200 feet above the sea level. At a particular point, it is directly above a fish floating at 400 feet below the sea level. By how much the bird must descend its flight to be as far as from the sea level, as the fish is?

(xiii)Ryan was playing a game where catching a fish in the basket adds 10 points to his score. If he catches an octopus instead, he loses 5 points. What is his total if he catches 3 fish and 5 octopus?

(xiv)Jason is moving from his hometown to Alaska. He is expecting a big temperature change, and he is getting ready. The hottest it gets in his hometown is 32 degrees celsius. The coldest it gets in Alaska is approximately – 45 degrees celsius. What temperature change will Jason experience?

(xv)The temperature of a hot iron rod drops by 8°𝐶 every hour. If the temperature of the iron rod is 118°𝐶, find the temperature after 4 hours.

(xvi)A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?

(xvii)At Srinagar temperature was − 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

(xviii)A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?

(xix)Mohan deposits Rs 2,000 in his bank account and withdraws Rs 1,642 from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.

(xx)Rita goes 20 km towards east from a point A to the point B. From B, she moves 30 km towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A?

(xxi) A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.

(a) The company sells 3, 000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.

(xxii) An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach − 350 m.

Ans. (i) 1825 km       (ii)  (a) profit amount is rupees 8800 .   (b) 600 bags of oranges

          (iii) 300    (iv) 30 minutes      (v) 985 degrees     (vi) -75    (vii) -5      (viii) 30340 feet 

          (ix) 49 degrees    (x) 38      (xi) $ -4100     (xii)  800 feet     (xiii)     5 points      (xiv)77            

          degrees    (xv)   86 degrees celcius    (xvi) 54 minutes     (xvii) Monday = −5°C, on     

         tuesday −7°C , on Wednesday −3ºC   (xviii) 6200 m    (xix) rs. 358   (xx)  −10 km (i.e.,  

         Rita is now in west direction)   (xxi) (a) loss of Rs 1000  (b)  4000 bags of white

        cement    (xxii) 1 hour

You might also be interested in:

• Simplification questions for class 7 PDF
• Simplification questions for class 6

You might also like

Ncert-class-8-maths-chapter-1-exercise-1.1 solution, what are 5 methods of solving a quadratic equation , [pdf] integration formulas for class 12, solved examples on rational numbers, mensuration formulas for 2d and 3d shapes pdf download, leave a reply cancel reply.

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Talk to our experts

1800-120-456-456

NCERT Solutions Class 7 Maths Chapter 1 - Integers

• NCERT Solutions
• Chapter 1 Integers

NCERT Solution for Maths Class 7 Chapter 1 Integers - Free PDF Download

In NCERT Solutions for Class 7 Maths Chapter 1 , Integers, students are introduced to the world of integers, including positive and negative whole numbers. Our NCERT solutions provide step-by-step explanations and solutions for all the exercises and problems in the chapter. Our solutions cover a wide range of topics, including understanding integers, addition and subtraction of integers, properties of integers, and more. Each question is explained in a detailed yet easy-to-understand manner, ensuring that you grasp the concepts effectively.

Glance of NCERT Solutions for Class 7 Maths Chapter 1 Integers | Vedantu

In this article, delve deeper into Integers, addition and subtraction of Integers along with multiplication and division of Integers.

Learn about Properties of Integers, Properties of multiplication of Integers and Properties of Division of Integers and about Number Line and steps involved in drawing a number line.

Types of Integers:

Positive Integers : These are whole numbers greater than zero (1, 2, 3, and so on).

Negative Integers : These are whole numbers less than zero (-1, -2, -3, and so on).

Zero : Zero is a special case, considered neither positive nor negative.

We can compare integers using greater than (>) and less than (<) signs. Just like on a number line, higher numbers are to the right and considered greater.

A number line is a great tool to represent integers. Zero is placed in the middle, positive integers extend to the right, and negative integers extend to the left. The farther a number is from zero, the greater its value (positive or negative).

This article contains chapter notes, formulas, exercise links and important questions for Chapter 1 - Integers.

There are three exercises (15 fully solved questions) in Class 7th Maths Chapter 1 Integers

Access Exercise Wise NCERT Solutions for Chapter 1 Maths Class 7

Exercises under NCERT Class 7 Maths Chapter 1 - Integers

Chapter 1 of the CBSE Class 7 syllabus includes three exercises on Integers. Each exercise contains problems that aim to help students understand the concept of Integers and their practical applications in solving various word problems.

Exercise 1.1 -  This Exercise contains 4 problems, with multiple parts . These problems aim to introduce students to the fundamentals of Integers which includes addition between two negative integers, one positive and one negative integer, and two negative integers.

Exercise 1.2 -  This Exercise contains 4 problems, with multiple parts . This exercise covers several problems that involve multiplication of any two integers, distributive property and associative property.

Exercise 1.3 -   This is the final exercise that contains 7 problems with multiple parts. This exercise deals with division.

What is an Integer?

The word ‘Integer’ is derived from the Latin word intact or whole. So, integers are always the whole number, which consists of positive or negative numbers or zero, which is simply called a combination of negative and whole numbers. Integers will never be fractional or decimal numbers.  Usually, the set of integers is denoted by Z.

Eg, Z = { -5, -2, 0, 3, 9}

Addition and Subtraction of Integers

Learning the addition and subtraction of Integers is most important to make simple calculations in day-to-day life for performing simple calculations. Like calculating the pocket money spent by you in a day. Calculating average among integers. 

Multiplication of Integers

Multiplication is a simple one for many of you. But, while multiplying the integers it is important to note a sign of the numbers. This will mainly help while simplifying an equation.

Multiplication of a Positive and Negative Integer

Multiplication of a positive and negative integer will always leave the answer as a negative integer.

Multiplication of Two Negative Integers

Multiplication of two negative integers will always result in a positive integer. Should keep in the note of this topic while simplifying the quadratic equation.

Properties of Multiplication of Integers

Multiplication of two positive integers leaves a positive result

Multiplication of two negative integers leaves a positive result 

Multiplication of a positive integer and a negative integer leaves a negative result 

Multiplication of zero with any number is zero.

Division of Integers

Properties of division of integers.

Division of two positive integers leaves a positive result.

The division of two negative integers leaves a positive result. 

The division of a positive integer and a negative integer leaves a negative result. 

The division of zero by any number is zero. 

The division of any number by zero is infinite.

Access NCERT Solutions for Maths Chapter 1 – Integers

Exercise 1.1.

1. Write down a pair of integers whose:

a) sum is $-7$ 

Ans : The pair of integers whose sum is $-7$ is $\left( -4,-3 \right)$ i.e., $-4+\left( -3 \right)=-7$.

b) difference is $-10$

Ans : The pair of integers whose difference is $-10$ is $\left( -3,7 \right)$ i.e., $-3-7=-10$

c) sum is $0$

Ans : The pair of integers whose sum is $0$ is $\left( -30,30 \right)$ i.e., $-30+30=0$.

2. Find the integers in the below questions:

a) Write a pair of negative integers whose difference gives $8$.

Ans : The pair of negative integers whose difference is $8$ is $\left( -1,-9 \right)$ i.e., $-1-\left( -9 \right)=-1+9=8$

b) Write a negative integer and a positive integer whose sum is $-5$. 

Ans : The pair of negative and positive integers whose sum is $-5$ is $\left( -9,4 \right)$ i.e., $\left( -9 \right)+4=-5$.

c) Write a negative integer and a positive integer whose difference is $-3$.

Ans : The pair of negative and positive integers whose difference is $-3$ is $\left( -1,2 \right)$ i.e., $\left( -1 \right)-2=-1-2=-3$.

3. In a quiz, team A scored $-40,10,0$ and team B scores $10,0,-40$ in three successive roun ds. Which team scored more? Can we say that we can add integers in any order?

Ans : Given that the team $A$ scored $-40,10,0$. Therefore, total score of the team $A$ $=-40+10+0=-30$.

Given that the team $B$ scored $10,0,-40$.Therefore, total score of Team $B$ $=10+0+\left( -40 \right)=-30$. 

Therefore, scores of both teams are same and we can add integers in any order due to commutative property.

4. Fill in the blanks to make the following statements true:

i) $\left( -5 \right)+\left( -8 \right)=\left( -8 \right)+\left( ...... \right)$ 

Ans : Using Commutative Property we can fill the blank as $-5$. 

$\therefore $ $\left( -5 \right)+\left( -8 \right)=\left( -8 \right)+\left( -5 \right)$.

ii) $-53+\left( ...... \right)=-53$

Ans : Using Zero additive property we can fill the blank as $0$ .

$\therefore $ \[-53+0=-53\]

iii) $17+\left( ...... \right)=0$ 

Ans : Using Zero Additive identity we can fill the blank as $-17$ .

$\therefore $ $17+\left( -17 \right)=0$

iv) $\left[ 13+\left( -12 \right) \right]+\left( ...... \right)=13+\left[ \left( -12 \right)+\left( -7 \right) \right]$

Ans : Using Associative property we can fill the blank as $-7$.

$\therefore $ $\left[ 13+\left( -12 \right) \right]+\left( -7 \right)=13+\left[ \left( -12 \right)+\left( -7 \right) \right]$

v) $\left( -4 \right)+\left[ 15+\left( -3 \right) \right]=\left[ -4+15 \right]+\left( ...... \right)$

Ans : Using Associative property we can fill the blank as $-3$.

$\therefore $ $\left( -4 \right)+\left[ 15+\left( -3 \right) \right]=\left[ -4+15 \right]+\left( -3 \right)$ 

Exercise 1.2

1. Find each of the following products:

a) $3\,\,\times \,\,\left( -1 \right)$

Ans : While multiplying a negative integer and a positive integer, multiply them as whole numbers and then put a minus sign $\left( - \right)$ before the product i.e., 

$3\times \left( -1 \right)=-3$

b) $\left( -1 \right)\,\,\times \,\,225$

$\left( -1 \right)\times 225=-225$

c) $\left( -21 \right)\,\,\times \,\,\left( -30 \right)$

Ans : While multiplying two negative integers, multiply them as whole numbers and then put a plus sign $\left( + \right)$ before the product i.e.,

$\left( -21 \right)\times \left( -30 \right)=630$

d) $\left( -316 \right)\,\,\times \,\,\left( -1 \right)$

$\left( -316 \right)\times \left( -1 \right)=316$

e) $\left( -15 \right)\,\,\times \,\,0\,\,\times \,\,\left( -30 \right)$

$\left( -15 \right)\times \,0\times \left( -18 \right)=0$

f) $\left( -12 \right)\,\,\times \,\,\left( -11 \right)\,\,\times \,\,\left( 10 \right)$

Ans : While multiplying two negative integers, multiply them as whole numbers and then put a plus sign $\left( + \right)$ before the product i.e., 

$\left[ \left( -12 \right)\times \left( -11 \right) \right]\times \left( 10 \right)=132\times 10=1320$

g) $9\,\,\times \,\,\left( -3 \right)\,\,\times \,\,\left( -6 \right)$

$9\times \left[ \left( -3 \right)\times \left( -6 \right) \right]=9\times 18=162$

h) $\left( -18 \right)\,\,\times \,\,\left( -5 \right)\,\,\times \,\,\left( -4 \right)$

Ans : While multiplying two negative integers, multiply them as whole numbers and then put a plus sign $\left( + \right)$ before the product i.e., $\left[ \left( -18 \right)\times \left( -5 \right) \right]\times \left( -4 \right)=90\times \left( -4 \right)$   ….. (1)

While multiplying a negative integer and a positive integer, multiply them as whole numbers and then put a minus sign $\left( - \right)$ before the product i.e., from (1), 

$\left[ \left( -18 \right)\times \left( -5 \right) \right]\times \left( -4 \right)=-360$

i) $\left( -1 \right)\,\,\times \,\,\left( -2 \right)\,\,\times \,\,\left( -3 \right)\,\,\times \,\,4$

Ans : While multiplying two negative integers, multiply them as whole numbers and then put a plus sign $\left( + \right)$ before the product and while multiplying a negative integer and a positive integer, multiply them as whole numbers and then put a minus sign $\left( - \right)$ before the product i.e.,

$\left[ \left( -1 \right)\times \left( -2 \right) \right]\times \left[ \left( -3 \right)\times 4 \right]=2\times \left( -12 \right)=-24$

j) $\left( -3 \right)\,\,\times \,\,\left( -6 \right)\,\,\times \,\,\left( 2 \right)\,\,\times \,\,\left( -1 \right)$

$\left[ \left( -3 \right)\times \left( -6 \right) \right]\times \left[ \left( 2 \right)\times \left( -1 \right) \right]=\left( 18 \right)\times \left( -2 \right)=-36$

2. Verify the following:

a) $18\,\,\times \,\,\left[ 7+\left( -3 \right) \right]=\left[ 18\times 7 \right]+\left[ 18\times \left( -3 \right) \right]$

Ans : Given expression, $18\times \left[ 7+\left( -3 \right) \right]=\left[ 18\times 7 \right]+\left[ 18\times \left( -3 \right) \right]$.

Simplifying the given expression by first solving the square brackets.

While multiplying a negative integer and a positive integer, multiply them as whole numbers and then put a minus sign $\left( - \right)$ before the product.

$\Rightarrow \,\,18\times \left[ 4 \right]=\left[ 126 \right]+\left[ -54 \right]$

$\Rightarrow \,\,72=72$

$\Rightarrow \,\,\text{L}\text{.H}\text{.S}\text{.}=\text{R}\text{.H}\text{.S}\text{.}$

Hence verified.

b) $\left( -21 \right)\times \left[ \left( -4 \right)+\left( -6 \right) \right]=\left[ \left( -21 \right)\times \left( -4 \right) \right]+\left[ \left( -21 \right)\times \left( -6 \right) \right]$

Ans : Given expression, $\left( -21 \right)\times \left[ \left( -4 \right)+\left( -6 \right) \right]=\left[ \left( -21 \right)\times \left( -4 \right) \right]+\left[ \left( -21 \right)\times \left( -6 \right) \right]$

While multiplying two negative integers, multiply them as whole numbers and then put a plus sign $\left( + \right)$ before the product

$\Rightarrow \,\,\left( -21 \right)\times \left( -10 \right)=84+126$

$\Rightarrow \,\,210=210$

3. Solve the following:

i)  For any integer $a$, what is $\left( -1 \right)\,\,\times \,\,a$ equal to?

Ans : $\left( -1 \right)\times a=-a,\,\text{ where }a\text{ is an integer}\text{.}$

ii) Determine the integer whose product with $\left( -1 \right)$ is:

Ans : The integer whose product with $-1$ is \[-22\] is $22$ i.e., $\left( -1 \right)\times \left( 22 \right)=-22$.

b) $37$ 

Ans : The integer whose product with $-1$ is \[37\] is $-37$ i.e., $\left( -1 \right)\times \left( -37 \right)=37$.

c) $0$ 

Ans : The integer whose product with $-1$ is \[0\] is $0$ i.e., $-1\times 0=0$.

4. Starting from $\left( -1 \right)\,\,\times \,\,5$ write various products showing some patterns to show $\left( -1 \right)\,\,\times \,\,\left( -1 \right)=1$.

Ans: Consider the product, $\left( -1 \right)\times 5=-5$

Also, $\left( -1 \right)\times 4=-4$, $\left( -1 \right)\times 3=-3$, $\left( -1 \right)\times 2=-2$, $\left( -1 \right)\times 1=-1$, etc.

Thus, we can observe that the product of one negative integer and one positive integer is negative integer.

Similarly, $\left( -1 \right)\times \left( -1 \right)=1$ i.e., the product of two negative integers is a positive integer.

1. Evaluate each of the following:

a) \[\left( -30 \right)\div 10\]

Ans : While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, \[\left( -30 \right)\div \text{10}=-\dfrac{30}{10}=-3\].

b) \[50\div \left( -5 \right)\]

Ans : While dividing a positive integer by a negative integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, \[50\div \left( -5 \right)=-\dfrac{50}{5}=-10\].

c) \[\left( -36 \right)\div \left( -9 \right)\]

Ans : While dividing a positive integer by a positive integer, divide them as whole numbers and then put a plus sign $\left( + \right)$ before the quotient. Therefore, \[\left( -36 \right)\div \left( -9 \right)=\dfrac{36}{9}=4\].

d) \[\left( -49 \right)\div 49\]

Ans : While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, \[\left( -49 \right)\div 49=-\dfrac{49}{49}=-1\].

e) $13\div \left[ \left( -2 \right)+1 \right]$

Ans : Simplifying the given expression, \[13\div \left[ \left( -\text{2} \right)+1 \right]=13\div \left( -1 \right)\] ….(1)

While dividing a positive integer by a negative integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore from (1), \[13\div \left( -1 \right)=-13\].

f) $0\div \left( -12 \right)$

Ans : While dividing $0$ by any integer, the quotient is $0$. Therefore  \[0\div \left( -12 \right)=0\].

g) $\left( -31 \right)\div \left[ \left( -30 \right)\div \left( -1 \right) \right]$

Ans : While dividing a positive integer by a positive integer, divide them as whole numbers and then put a plus sign $\left( + \right)$ before the quotient. Therefore, \[\left( -30 \right)\div \left( -1 \right)=30\].  …..(1)

Hence from (1), \[\left( -31 \right)\div \left[ \left( -30 \right)\div \left( -1 \right) \right]=\left( -31 \right)\div \left( 30 \right)\] ….. (2)

While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore from (2), \[\left( -31 \right)\div \left[ \left( -30 \right)\div \left( -1 \right) \right]=-\dfrac{31}{30}\].

h) $\left[ \left( -36 \right)\div 12 \right]\div 3$

Ans : While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, $\left( -36 \right)\div 12=-\dfrac{36}{12}=-3$  …..(1)

While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore from (1), $\left[ \left( -36 \right)\div 12 \right]\div 3=\left( -3 \right)\div 3=-1$.

i) $\left[ \left( -6 \right)+5 \right]\div \left[ \left( -2 \right)+1 \right]$

Ans : Simplifying the given expression, $\left[ \left( -6 \right)+5 \right]\div \left[ \left( -2 \right)+1 \right]=\left( -1 \right)\div \left( -1 \right)$ ….(1)

While dividing a negative integer by a negative integer, divide them as whole numbers and then put a plus sign $\left( + \right)$ before the quotient. Therefore from (1), $\left[ \left( -6 \right)+5 \right]\div \left[ \left( -2 \right)+1 \right]=1$.

2. Verify that \[a\div \left( b+c \right)\ne \left( a\div b \right)+\left( a\div c \right)\]  for each of the following values of $a,b\text{ and }c.$

a) \[a=12,b=-4,c=2\]

Ans : Given, $a=12,b=-4,c=2$. We have to verify $a\div \left( b+c \right)\ne \left( a\div b \right)+\left( a\div c \right)$.

Substituting the given values of $a,b,c$ in LHS we get,

L.H.S.$=12\div \left( -4+2 \right)=12\div \left( -2 \right)$ ….. (1)

While dividing a positive integer by a negative integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore from (1), \[12\div \left( -4+2 \right)=-6\].   …..(2)

Substituting the given values of $a,b,c$ in RHS we get,

R.H.S.$=\left[ 12\div \left( -4 \right) \right]\text{+}\left( 12\div 2 \right)\text{ }$ …..(3)

While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, from (3), $\left[ 12\div \left( -4 \right) \right]\text{+}\left( 12\div 2 \right)=\left( -3 \right)\text{+}6\text{ }$

$\Rightarrow RHS=3$ …..(4)

From (2) and (4), we can conclude that $\,\text{L}\text{.H}\text{.S}\text{.}\ne \text{R}\text{.H}\text{.S}\text{.}$ Hence verified.

b) $a=\left( -10 \right),b=1,c=1$

Ans : Given, $a=-10,b=1,c=1$. We have to verify $a\div \left( b+c \right)\ne \left( a\div b \right)+\left( a\div c \right)$.

L.H.S.$=-10\div \left( 1+1 \right)=-10\div \left( 2 \right)$ ….. (1)

While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore from (1), \[-10\div \left( 1+1 \right)=-5\].   …..(2)

R.H.S.$=\left[ -10\div 1 \right]\text{+}\left( -10\div 1 \right)\text{ }$ …..(3)

While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, from (3), $\left[ -10\div 1 \right]\text{+}\left( -10\div 1 \right)\text{ }=\left( -10 \right)\text{+}\left( -10 \right)\text{ }$

$\Rightarrow RHS=-20$ …..(4)

3. Fill in the Blanks:

a) \[369\div \_\_\_\_\_=369\]

Ans : While dividing any integer by $1$, the quotient is the original integer. Therefore, \[369\div \underline{1}=369\].

b) \[\left( -75 \right)\div \_\_\_\_\_=\left( -1 \right)\]

Ans : While dividing any integer by itself, the quotient is $1$. Also, while dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, \[\left( -75 \right)\div \underline{75}=\left( -1 \right)\]

c) \[\left( -206 \right)\div \_\_\_\_\_=1\]

Ans : While dividing any integer by itself, the quotient is $1$. Also, while dividing a negative integer by a negative integer, divide them as whole numbers and then put a plus sign $\left( + \right)$ before the quotient. Therefore, $\left( -206 \right)\div \underline{\left( -206 \right)}=1$

d) \[\left( -87 \right)\div \_\_\_\_\_=87\]

Ans : While dividing any integer by $1$, the quotient is the original integer. Also, while dividing a negative integer by a negative integer, divide them as whole numbers and then put a plus sign $\left( + \right)$ before the quotient. Therefore, $\left( -87 \right)\div \underline{\left( -1 \right)}=87$.

e) $\_\_\_\_\_\div 1=-87$

Ans : While dividing any integer by $1$, the quotient is the original integer. Therefore, $\underline{\left( -87 \right)}\div 1=-87$.

f) $\_\_\_\_\_\div 48=-1$

Ans : While dividing any integer by $1$, the quotient is the original integer. Also, while dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, $\underline{\left( -48 \right)}\div 48=-1$

g) \[20\div \_\_\_\_\_=-2\]

Ans : While dividing a positive integer by a negative integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient. Therefore, $20\div \underline{\left( -10 \right)}=-2$

h) $\_\_\_\_\_\div \left( 4 \right)=-3$

Ans : While dividing a negative integer by a positive integer, divide them as whole numbers and then put a minus sign $\left( - \right)$ before the quotient.$\left( -12 \right)\div \left( 4 \right)=-3$

4. Write five pairs of integers $\left( a,b \right)$ such that $a\div b=-3$. One such pair is $ \left( 6,-2 \right)$ because $6\div \left( -2 \right)=\left( -3 \right)$.

Ans : Five pair of integers $\left( a,b \right)$ such that $a\div b=-3$ are:

i) The pair of integers $\left( -9,3 \right)$ is such that $\left( -9 \right)\div 3=-3$.

ii) The pair of integers $\left( -15,5 \right)$ is such that $\left( -15 \right)\div 5=-3$.

iii) The pair of integers $\left( 12,-4 \right)$ is such that $12\div \left( -4 \right)=-3$.

iv) The pair of integers $\left( -3,1 \right)$ is such that $\left( -3 \right)\div 1=-3$.

v) The pair of integers $\left( 21,-7 \right)$ is such that $21\div \left( -7 \right)=-3$.  

5. The temperature at noon was ${{10}^{\circ }}\text{C}$ above zero. If it decreases at the rate of ${{2}^{\circ }}\text{C}$ per hour until mid-night, at what time would the temperature be ${{8}^{\circ }}\text{C}$ below zero? What would be the temperature at mid-night?

Ans : Given that the temperature at $12$ noon is \[{{10}^{\circ }}C\] above the zero i.e., $+{{10}^{\circ }}C$. Now, the temperature decreases ${{2}^{\circ }}C$ each hour until midnight. Therefore, following number line represents the temperature path:

Temperature at $12$ noon $={{10}^{\circ }}C$.

Temperature at $1PM$ $={{\left( 10-2 \right)}^{\circ }}C={{8}^{\circ }}C$.

Temperature at $2PM$ $={{\left( 8-2 \right)}^{\circ }}C={{6}^{\circ }}C$.

Temperature at $3PM$ $={{\left( 6-2 \right)}^{\circ }}C={{4}^{\circ }}C$.

Therefore, temperature at $nPM$ $={{\left( 10-2n \right)}^{\circ }}C$.

According to the question, $\left( 10-2n \right)=-8$ ….(1)

Solving (1) by rearranging terms we get, 

$\Rightarrow n=9$ 

Therefore, at $9\,\text{pm}$ the temperature would be ${{8}^{\circ }}\text{C}\,\,\text{below}\,\,{{0}^{\circ }}\text{C}$.

6. In a class test $\left( +3 \right)$ marks are given for every correct answer and $\left( -2 \right)$ marks are given for every incorrect answer and no marks for not attempting any question.

i) Radhika scored $20$ marks. If she has got $12$ correct answers, how many questions has she attempted incorrectly?

Ans : Given that Radhika scored $20$ marks and she has got $12$ correct answers.

Let the number of incorrect answers be $x$ then, 

Marks given for one correct answer $=3$

Marks given for $12$ correct answers $=3\times 12=36$ ….. (1)

Marks given for one wrong answer $=-2$

Marks given for $x$ wrong answers $=-2x$ ….. (2)

Also, Radhika scored $20$ marks. Hence from (1) and (2),

$20=36+\left( -2x \right)$ ….. (3)

Solving (3) by rearranging terms we get, 

$\Rightarrow x=8$ 

Therefore, Radhika has attempted $8$ incorrect questions.

ii) Mohini scores $\left( -5 \right)$ marks in this test, though she has got $7$ correct Answers. How many questions has she attempted incorrectly?

Ans : Given that Mohini scored $-5$ marks and she has got $7$ correct answers.

Marks given for $7$ correct answers $=3\times 7=21$ ….. (1)

Also, Mohini scored $-5$ marks. Hence from (1) and (2),

$-5=21+\left( -2x \right)$ ….. (3)

$\Rightarrow x=13$ 

Therefore, Mohini has attempted $13$ incorrect questions.

7. An elevator descends into a mine shaft at the rate of $6\text{ m/min}$ . If the descent starts from \[10\] above the ground level, how long will it take to reach $\text{-350 m}$?

Ans: Given that the starting position of mine shaft is $10\,\,\text{m}$ above the ground.

And its destination is $350m$ below the ground.

Let us denote the distance above the ground by $+$ sign and the distance below the ground by $-$ sign. Therefore, starting from $10m$ it has to go $-350m$. 

Total distance covered by mine shaft $=10\,\text{m}-\left( -350 \right)\text{m}=10+350=360\,\text{m}$…..(1)

Now, it is given that elevator takes $1\text{ }\min $ to cover the distance of $6m$ i.e., 

Time taken to cover a distance of $6\,\text{m}$$=1$ minute.    …..(2) 

Hence from (2),

Time taken to cover a distance of $1\,\text{m}$ $=\dfrac{1}{6}$ minute.   …..(3)

Hence from (1) and (3), time taken to cover a distance of $360\,\text{m}$ 

$=\,\dfrac{1}{6}\times 360=60$ minutes $=1$ hour.

Therefore, in $1$ hour the mine shaft reaches $-350$ below the ground.

NCERT Solutions for Class 7 Chapter 1 Maths Integers – Free PDF Download

Integers : The set of natural numbers like ……., -4, -3, -2, -1, 0, 1, 2, 3, 4 ….. are called integers.

How are Integers Applicable in Our Real Life?

Integers are applied in many ways in our real-life besides math class. We can use integers for calculating the efficiency of positive and negative numbers in all fields.

In our day-to-day life, we come across many situations where integers are used:

i. Positive integers are used to determine profit, income, increase, rise, high, north, east, above depositing, climbing and so on.

ii. Negative integers are used to determine quantities like loss, expenditure, decrease, fall, low, south, west, below, withdrawing, sliding and so on.

Example : A point A is on a mountain which is 4680 m above sea level and a point B is in a mine which is 765 m below sea-level. What is the distance between A and B?

In this example, we can consider a point O at the sea level. 

Then, height OA = + 4680m;

Height OB = - 765m.

Distance between A and B  = [OA] + [OB]

            = {[ + 4680 ]  + [ -765]} m

            = (4680 + 765) m = 5445 m

Properties of Integers

The properties of integers include numbers for addition and multiplication through patterns. They also include the whole numbers as well. Integers involve expressing communicative and associative properties in a general form.

The counting numbers 1, 2, 3, 4, 5, …….. and so on are called Natural Numbers, whereas the set of natural numbers together with zero like  0, 1, 2, 3, 4, 5, ……. and so on are called whole numbers.

On a number line, we represent the negative integers by the points to the left of zero and positive integers by the points to the right of zero.

The integer 0 is an additive identity for integers by the points to the left of zero and positive integers by the points to the right of zero. 

The integer 0 is neither positive nor negative.

The absolute value of an integer is its numerical value of the integer regardless of its sign. The absolute value of an integer a is denoted by | a |.

Absolute value of 8 i.e. | 8 | = 8

Absolute value of –8 i.e. | -8 | = 8

If ‘a’ and ‘b’ are integers, then (a + b), (a - b) and (a x b) are also integers. Integers are used for addition, subtraction and multiplication. 

If ‘a’ and ‘b’ are integers then a x b = b x a and a + b = b + a. Multiplication is a commutative property for integers. 

For any three integers a, b and c, we have:

Addition is associative property for integers. a + ( b + c ) = ( a + b ) + c = c + ( b + a )

Multiplication is associative property for integers. a x ( b x c ) = ( a x b ) x c = c x ( b x a)

a x (b + c) = (a x b) + ( a x c)

a x (b-c) = (a x b) – (a x c)

1 is the multiplicative identity for integers and 0 is the identity under addition. 

Ex : a + 0 = a = 0 + a and a x 1= a =1 x a

If the integers are of like signs, their product is positive.

When we add two positive or negative integers with like signs, we add their numerical values and assign the sign of the numbers added with the sum.

Ex : 6 + 5 = 11

            - 6 + ( - 5 ) = - 6  - 5 = -11

If the integers have unlike signs, their product is negative.   a x –b = - ab

Ex :  5 x – 4 = -20

           - 5 x 4 = -20 

When we add two integers with unlike signs then we take the difference of their numerical values and assign the sign of the integer with the greater numerical value. 

Ex : 2 + ( - 8 ) = - 2

            8 + ( - 2 ) = 2

The product of an integer and 0 is always 0.

If the dividend and divisor are integers of like signs, then the quotient is a positive integer. 

If the dividend and divisor are integers of unlike signs, then the quotient is a negative integer.

Division by 0 is not possible. However, 0 divided by any integer (except 0) is equal to 0.

Important Note

0 is neither positive nor negative.

The + sign is not written before a positive number.

½  and 0.5 are not integers because they are not whole numbers. 

Negative numbers are usually placed in brackets to avoid confusion arising due to two signs in evaluations.

Ex : 4 + ( - 2 ) = -2

Number Line

A number line represents natural numbers, whole numbers, positive integers and negative integers. The identities are marked at equal intervals on a line to determine numerical operations. Number lines are important because they represent numbers that are used in our daily life.

Steps for drawing a number line

Draw a straight line of any length.

Mark points at equal intervals on the drawn line to divide it into the required number.

Mark any one of the points, marked on the line in step 2, as 0.

Starting from 0 and on the right-hand side of the line, mark the positive numbers + 1, + 2, + 3, and so on. Similarly, starting from 0 on the left side of mark the negative integers -1, -2, -3, and so on.

The arrowheads on both the sides of the drawn line indicate that the numbers continue up to infinity.

Overview of Deleted Syllabus for CBSE Class 7  Maths Chapter - Integers

Class 10 maths chapter 1: exercise breakdown.

The NCERT Solutions for Class 7 Maths Chapter 1 Integers, provided by Vedantu, are essential for understanding the basics of integers. These solutions help students grasp concepts like addition, subtraction, multiplication, and division of integers, as well as their properties. It's important to focus on solving the examples and practice problems to reinforce these concepts. The step-by-step explanations make complex topics easier to understand, which is crucial for building a strong foundation in mathematics. For best results, regularly practice the exercises and review the key concepts highlighted in these solutions.

Other Related Links for CBSE Class 7 Maths Chapter 1

Ncert solutions for class 7 maths - chapter-wise list.

Given below are the chapter-wise NCERT Solutions for Class 7 Maths. These solutions are provided by the Maths experts at Vedantu in a detailed manner. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

FAQs on NCERT Solutions Class 7 Maths Chapter 1 - Integers

1 . Write a Pair of Integers Whose Sum Gives

Negative Integer.

an Integer Smaller than Only one of the Integers.

an Integer Greater than Both the Integers.

1. (-20) and 8

sum: ( -20) + 8 = -2 ( -2 is a negative integer)

2. -15 and 15 

sum: (-15) + 15 = 0

3. ( -8 ) and ( -2 )

sum: ( -8 ) + ( -2 ) = - 10 ( - 10 is smaller than - 8 and -2 )

4. 5 and - 7

sum: 5 + ( -7) = -2 ( -2 is smaller than 5)

5. 15 and 20

sum: 15 + 20 = 35 ( 35 is greater than 15 and 20)

2. Simplify the Following, Using Suitable Properties:

( -1500 ) x ( -100 ) + ( -1500 ) x ( -50 )

(2500 x 845) – (579 x 845)

1. (-1500) x (-100) + (-1500) x (-50)

= 1500 ((-1) x (-100) + (-1) x (-50))

= 1500 (100 + 50)

= 1500(150)

2. (2500 x 845) – (579 x 845)

= 845 (2500 - 579)

= 845 (1921)

3. Choose the Correct Answers from the Given Choice and Fill in the Following Blanks.

-3, -2, -1 are __________________ Integers.  (positive/ negative)

The Greatest Negative Integer is __________________. (0/ -1)

Every Positive Integer is _________________ then Every Negative Integer. (Smaller/ Greater)

The Product of Two Integers is Always ______________________. (an Integer/ not an Integer)

1. Negative

4. An integer

4. What are the 4 rules of integers?

The four basic rules for integers are:

The sum of two positive integers is a positive integer. (Ex: 9 + 2 = 11)

The sum of two negative integers is a negative integer. (Ex: -3 + (-5) = -8)

The sum of a positive integer and a negative integer depends on their values. The integer with the larger absolute value determines the sign of the sum. (Ex: 5 + (-3) = 2, -2 + 4 = 2)

Subtraction:

Subtracting a positive integer is the same as adding a negative integer with the same absolute value. (Ex: 6 - 4 = 6 + (-4) = 2)

Subtracting a negative integer is the same as adding a positive integer with the same absolute value. (Ex: 10 - (-2) = 10 + (2) = 12)

Multiplication:

The product of two positive integers is a positive integer. (Ex: 4 x 6 = 24)

The product of two negative integers is a positive integer. (Ex: -4 x (-6) = 24)

The product of a positive integer and a negative integer is a negative integer. (Ex: 2 x (-8) = -16)

Dividing two positive integers results in a positive integer (assuming no remainder). (Ex: 10 ÷ 5 = 2)

Dividing two negative integers results in a positive integer (assuming no remainder). (Ex: -18 ÷ (-2) = 9)

Dividing a positive integer by a negative integer results in a negative integer (assuming no remainder). (Ex: 20 ÷ (-5) = -4)

Dividing a negative integer by a positive integer results in a negative integer (assuming no remainder). (Ex: -16 ÷ 4 = -4)

5. What are integers for 7th class?

Integers is the first chapter in the NCERT Class 7 Maths textbook. The set of natural numbers like -4, -3, -2, -1, 0, 1, 2, 3, 4, and so on are called integers. They have a lot of applications in real life. Both positive and negative integers play an important role in daily calculations and transactions. It is essential to master elementary topics like Integers to be able to do well in Maths in higher classes. 

6. What I found challenging in chapter integers?

Understanding negative numbers: It might be difficult to understand negative numbers and how they differ from positive numbers.It can be difficult to see them as a number line or to understand their behavior when they are operating.

Applying Signs Correctly : It might be challenging to recall the rules for positive and negative signs, particularly in operations like subtraction and multiplication. Students might struggle to determine the resulting sign (+ or -) based on the signs of the numbers being operated on.

7. What is the fraction for 7th class?

Fractions and Decimals is the 2nd chapter in the NCERT CBSE Class 7 Maths textbook. An introduction to fractions has already been provided in earlier classes. The addition and subtraction of fractions have also already been discussed previously. The chapter Fractions in class 7 mostly deals with the multiplication and division of fractions. The concept behind reciprocal fractions and mixed fractions is taught in detail and questions are set on the same. 

8. What are the formulas of integers?

You do not need any formulas for Integers as long as your concepts are clear. However, you can remember some tricks like the product of two integers of the same sign is always positive whereas the product of two integers of different signs is always negative. To add two integers of the same signs, you just need to add their absolute values while to add two integers of different signs, you need to subtract their absolute values.

9. Where can I get NCERT Solutions for Class 7th Maths Chapter 1?

The best place to get all your questions answered and find solutions for NCERT Class 7 Maths Chapter 1 is Vedantu. Now you need not worry if you get stuck on a sum or do not know the method of solving a complicated maths problem. All you need to do is click on Vedantu's NCERT Class 7 Maths Chapter 1 Solutions and get all your doubts solved instantly in a comprehensive and easy-to-understand  manner. You can download the solution free of cost in PDF format from the Vedantu website and from the Vedantu app.

10. What are the 3 types of integers?

Positive Integers: These are the counting numbers we all know, starting from 1 and going up forever (like 1, 2, 3, 4, 5...). They represent positive quantities.

Negative Integers: Imagine a number line where zero is the center. Negative integers live to the left of zero. They represent quantities less than zero, like -1, -2, -3, and so on.

Zero: Zero stands alone at the center of the number line. It's neither positive nor negative, but it's still considered an integer.

11. What is the full form of integers?

The word integer originated from the Latin word “Integer” which means whole or intact.

NCERT Solutions for Class 7 Maths

Ncert solutions for class 7.

NCERT Solutions Class 7 Maths Chapter 1 Integers

NCERT solutions for class 7 maths chapter 1 integers comprise exercises based on differentiating integers from the higher sets, their properties and operations. Integers are non-fractional numbers that can hold a positive, negative, or zero value. These numbers are significantly important in performing arithmetic operations due to their prefixed signs. NCERT solutions class 7 maths chapter 1 integer covers all the important concepts based on the properties of these numbers in detail with examples.

The first few exercises in these class 7 maths NCERT solutions chapter 1 integers explain the representation of integers on a number line along with the revision of integers concepts studied in the previous classes with suitable examples. Sample problems covered in this chapter are sufficient for students to gain an in-depth understanding of integers and their properties. You can find some of these in the exercises given below and also find some of these in the exercises given below.

• NCERT Solutions Class 7 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 7 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 7 Maths Chapter 1 Ex 1.3
• NCERT Solutions Class 7 Maths Chapter 1 Ex 1.4

NCERT Solutions for Class 7 Maths Chapter 1 PDF

NCERT solutions for class 7 maths are well-structured to provide the optimal math learning of complete math syllabus. To get the best results in exams, one can easily plan preparation and revision with these competent resources. These solutions are also available for free pdf download as given below.

☛ Download Class 7 Maths NCERT Solutions Chapter 1 Integers

NCERT Class 7 Maths Chapter 1   Download PDF

NCERT Solutions for Class 7 Maths Chapter 1 Integers

With a thorough practice of the above exercises, students will attain the right approach required for solving arithmetic operations on integers. The regular practice of these exercises will also guide the students through the types of questions and the stepwise solution to each of them. The chapter-wise detailed analysis of NCERT Solutions Class 7 Maths Chapter 1 Integers is given below.

• Class 7 Maths Chapter 1 Ex 1.1 - 10 Questions
• Class 7 Maths Chapter 1 Ex 1.2 - 4 Questions
• Class 7 Maths Chapter 1 Ex 1.3 - 9 Questions
• Class 7 Maths Chapter 1 Ex 1.4 - 7 Questions

☛ Download Class 7 Maths Chapter 1 NCERT Book

Topics Covered: Properties of integers and their arithmetic operations ( addition , subtraction , multiplication, and division ) are the most important topics. Other topics included in these class 7 maths NCERT solutions chapter 1 are the properties of commutativity, associativity under addition and multiplication , and the distributive property of multiplication of integers.

Total Questions: Class 7 maths chapter 1 Integers Chapter 1 consists of a total of 30 questions of which 9 are easy, 10 are moderate and11 are long answer type questions.

List of Formulas in NCERT Solutions Class 7 Maths Chapter 1

NCERT solutions class 7 maths chapter 1 covers lots of important concepts based on integers that are crucial for strengthening the math foundation. Some important concepts in NCERT solutions for class 7 maths chapter 1 are given below:

• Commutative Property: a + b = b + a
• Associative Property: a + (b + c) = (a + b) + c
• Distributive Property: a × (b – c) = a × b – a × c

Important Questions for Class 7 Maths NCERT Solutions Chapter 1

Ncert solutions for class 7 maths video chapter 1, faqs on ncert solutions class 7 maths chapter 1, what is the importance of ncert solutions class 7 maths chapter 1 integers.

NCERT Solutions Class 7 Maths Chapter 1 deals with integers and their concepts that strengthen the student’s theoretical and practical knowledge. This enables students to score well in their examinations as NCERT solutions lay a strong mathematical foundation.

Do I Need to Practice all Questions Provided in NCERT Solutions for Class 7 Maths Integers?

Most questions in the NCERT Solutions Class 7 Maths Integers are important. Questions based on addition, subtraction, multiplication, and division of integers, should be regularly practiced while studying. The associative and distributive property of multiplication is one topic that needs regular practice.

What are the Important Topics Covered in NCERT Solutions Class 7 Maths Chapter 1?

The important sub-topics covered in NCERT Solutions Class 7 Maths Chapter 1 are properties of arithmetic operations of integers. Integers Chapter 1 is very well structured to include all the important sub-topics.

How Many Questions are there in Class 7 Maths NCERT Solutions Chapter 1 Integers?

There are a total of 30 questions in NCERT class 7 maths chapter 1 integers. Out of these 30 questions, 20 are carefully paced to provide a gradual understanding of the context of the theory. These 20 questions can be further categorized into long answers, moderate level, and easy ones. Students can plan and set a practice time for each of these subcategories.

What are the Important Formulas in NCERT Solutions Class 7 Maths Chapter 1?

The important formulas covered in the NCERT Solutions Class 7 Maths Chapter 1 are based on integer’s properties of addition and multiplication like commutative, associative, or distributive, etc. These formulas are also important for students to acquire a clear understanding of applying arithmetic operators to integers.

Why Should I Practice NCERT Solutions Class 7 Maths Integers Chapter 1?

Practicing NCERT Solutions Class 7 Maths Integers Chapter 1 can help develop excellent mathematical skills and accuracy. This will help in enhancing the student’s math skills. While practicing the various arithmetic operations on integers, make sure to use all the tips that have been mentioned in NCERT solutions.

เครดิตฟรี 50 ยืนยันเบอร์ ไม่ต้องฝาก ไม่ต้องแชร์ ทดลองเล่นสล็อต แจกฟรี สล็อตเครดิตฟรี ไม่ผ่านเอเย่นต์ รับเครดิตฟรี สล็อตpg ทดลองเล่น ฟรีทุกค่าย ไม่ต้องแชร์ ทางเข้า pg แจกเครดิตฟรี

• สล็อต ทดลองฟรี แจกเครดิต ไม่เสียเงิน รับเลย สล็อตโปรโมชั่น ล่าสุด ทดลองเล่นฟรี ไม่ต้องสมัคร
• วิธีถอนเงินจากเว็บพนัน การทำรายการรวดเร็ว รับเงินไว ไม่มีขั้นต่ำ สุดคุ้ม
• เครดิตฟรีกรอกโค้ด สล็อต โบนัส ฝากถอน ทางเข้า อัพเดท ระบบ แจก ล่าสุด
• ชุด ฮาวาย ผู้หญิง สุดเซ็กซี่ แซ่บสุดใจ ลองเล่นเลย ฟรีทุกค่าย ที่นี่เท่านั้น
• คาเฟ่ หาด จอม เทียน สุดยอด คาเฟ่ บรรยากาศดี ทะเลสวย ชิวๆ พร้อมทานกาแฟหอม รับประทานขนมอร่อย และพักผ่อนสบาย ๆ ที่เอาใจคนรักคาเฟ่ และทะเล CTA มาลองกาแฟคุณภาพ และสัมผัสบรรยากาศทะเลที่น่าตื่นเต้น ที่คาเฟ่ หาด จอม เทียน ตอนนี้!
• สล็อต777 เว็บตรง แจกฟรี เล่นง่าย ได้เงินจริง ทดลองเล่น สมัครฟรี ปังสุด ไม่เด้ง
• ทดลองเล่นสล็อต10000 สุดล้ำ รับเงินจริง ไม่ต้องทำเทิร์น แจกฟรี ล่าสุด ทรูวอเลท ที่สุด 2024 ไม่ผ่านเอเย่นต์ ไม่มีขั้นต่ำ 2*suffleเล่นเลย
• เล่นเกมมาชัวเบส ได้เงินจริง ทดลองเล่นฟรี สล็อตแตกง่าย ล่าสุด ไม่มีขั้นต่ำ แจกฟรี
• เว็บสล็อต Megame369 ที่แจกโบนัสมากที่สุด สล็อตเว็บตรง ฝากถอนง่าย รับเครดิตฟรี สล็อตแตกง่าย ลุ้นรวยได้ทุกวัน
• 'เว็บพนันออนไลน์ ฝากถอนไม่มีขั้นต่ำ ส่วนลดพิเศษ รับเงินจริง ทุกยอดฝาก ล่าสุด'
• เกม jili ออนไลน์ ที่ดีที่สุด สุดเจ๋ง แจกเครดิตฟรี รับโบนัส ไม่ต้องฝาก ล่าสุด
• งานทำที่บ้าน หางานออนไลน์ ทำเงินเข้าบัญชี ทดลองงานที่บ้าน สมัครงานออนไลน์ ทำงานระยะไกล หางานทำที่บ้าน ทำงานออนไลน์ ทำเงินเข้าบัญชี
• โหลดเกมสล็อตxo สุดฮิต ทดลองเล่นฟรี ฝากถอนไว รับโบนัสมาก แจกเครดิตฟรี ลุ้นรับรางวัล ล่าสุด
• สล็อต 689 วอเลท แจกเครดิตฟรี ล่าสุด สมัครเลย ฝากถอนไว ทดลองเล่น
• สล็อต ซื้อฟรีสปิน ทดลองเล่น เว็บตรง แจกฟรี เล่นได้ไม่จำกัด 2024
• เล่นโจ๊กเกอร์สล็อต แตกง่าย รับโบนัส ฟรี ทันที ทดลองเล่น สล็อตโจ๊กเกอร์ สุดมันส์ ลุ้นรวย ลุ้นแจ็คพอต สูตรสล็อตฟรี
• สูตรสล็อต ทดลองเล่น แจกฟรี ไม่เด้ง ฝากถอน รวดเร็ว สล็อตเว็บตรง 2024 เล่นง่าย ได้เงินจริง ปังมาก
• เว็บตรง 123 โจ๊กเกอร์ สมัครเล่น แจกโบนัส ฟรีเครดิต ทดลองเล่น สล็อตออนไลน์
• เว็บสล็อต เล่นง่าย แจกเครดิต ฝากถอนไว สล็อตเว็บตรง แตกง่าย รับโบนัส สล็อตpg ทดลองเล่น สมัครฟรี
• เครดิตฟรี uea8 สล็อต แจกฟรี เว็บตรง ทดลองเล่น สมัครวันนี้ ไม่ต้องฝาก แตกง่าย
• เครดิตฟรี สมัครเล่นเลย ทดลองเล่นเกมสล็อต ฝากถอนไว สล็อตเว็บตรง แจกเครดิตฟรี สล็อตออนไลน์ ที่สุดของปี2024
• เว็บสล็อต pbet168 ทดลองเล่น แจกฟรี ล่าสุด ไม่เด้ง ฝากถอน 24 ชม.
• เกมสล็อต neko pg ทดลองเล่น สนุกสุดเหนือ รับโบนัสสุดพิเศษ ลุ้นรางวัลใหญ่
• เว็บสล็อตที่ใหญ่ที่สุดที่ไม่เป็นเอเย่นต์ที่ทำให้เข้าเล่นสล็อต 460 เว็บตรงที่แตกง่าย
• เว็บสล็อตpg vip แจกเครดิตฟรี ทดลองเล่น สมัครเว็บตรง ฝากถอนไว ไม่มีขั้นต่ำ
• สล็อตทดลองฟรี แจกเครดิต ไม่มีเงื่อนไข ลองเล่นเสี่ยงทาย ฟรีเล่นได้ไม่จำกัด
• เว็บสล็อตpg ที่แจกโบนัสมากที่สุด ลุ้นรับเงินสด สมัครเล่นได้ที่นี่
• เว็บไม่ผ่านเอเย่น สล็อตแตกง่าย ทดลองเล่นฟรี สมัครเลย ฝากถอนไว
• เว็บไซต์ Lava168 เล่นสนุก รับเงินจริง สล็อต ฝากถอน ไม่เสียเวลา ทดลองเล่นฟรี สูตรเล่นเกม แจกฟรี
• สล็อตเว็บทดลอง ซื้อฟรีสปิน แจกฟรี ไม่จำกัดเวลา ลุ้นรับเงิน เล่นง่าย ได้เงินจริง
• สล็อตp6 เว็บตรง โบนัส จริง แจกฟรี ล่าสุด ทุกค่าย ทดลองเล่น ฝากถอน ไม่มีขั้นต่ำ สุดปัง
• สร้อยทอง100บาท ซื้อง่าย ไม่ต้องรอ โปรโมชั่นเด็ด รับเลย ส่งฟรี แค่คลิก
• PG SLOT 1688 เว็บตรง สล็อตออนไลน์ ทดลองเล่นฟรี แจกเครดิต เล่นง่าย ได้เงินจริง ไม่ต้องแชร์
• เว็บสล็อตทดลอง สุดฮิต ปั่นเกมสล็อต ทดลองฟรี แจกเครดิต ไม่ต้องฝาก ลุ้นรับเงินจริง
• เว็บตรง สล็อต ฝากถอน ไม่มีขั้นต่ำ 1 บาท แจกโบนัส สุดพิเศษ สมัครเลย
• เว็บสล็อต999 แจ็คพอตแตกง่าย โบนัสมาก สล็อตออนไลน์ เล่นง่าย รับเงินจริง ทดลองเล่นสล็อตฟรี
• สล็อตพีจี777 เว็บตรง แจกเครดิตฟรี ไม่เด้ง ลุ้นรับโบนัส ที่สุดในปี 2024 ปังสุด สมัครเลย
• ทดลองเล่นสล็อตวอเลท แจกฟรี ไม่เสียเงิน สล็อตเว็บตรง ล่าสุด รับเงินจริง ที่สุดในปีนี้ ลองเล่นได้ทุกเกม สล็อตแตกง่าย 2*suffle ฝากถอนไว ไม่ต้องแชร์ ทดลองเล่นฟรี
• เกมสล็อต คุณค่าอย่างไร ทดลองเล่น สล็อตออนไลน์ ฟรี เล่นง่าย รับเครดิตฟรี
• เข้าแอพกสิกรไม่ได้ แจ้งเตือนเข้าสู่ระบบไม่ทำงาน สอบถามช่องทางแก้ไข ที่สามารถใช้งานได้
• ไอ โฟน 14 พลัส ล่าสุด ราคาพิเศษ ซื้อเลย ส่งฟรี พร้อมส่วนลด สุดคุ้ม
• เว็บบาคาร่า888เว็บตรง สุดหรู ทดลองเล่นฟรี แจกเครดิตฟรี ฝากถอนรวดเร็ว ไม่ผ่านเอเย่นต์ รับเงินจริง
• เสื้อชีฟองสวย ๆ ทรูวอเลท แฟชั่นเว็บตรง ล่าสุด สุดปัง ไม่ต้องแชร์ แจกฟรี ทดลองเล่นเลย
• ทางเข้าpg168 สุดเร้าใช้ง่าย รับเครดิตฟรี แจกโบนัส มาแรงที่สุด ลุ้นรวยได้เลย
• เว็บสล็อต 168 ฝากถอน true wallet แจกโบนัส สุดพิเศษ ลุ้นรับเงินรางวัล ทันที
• สล็อต betflik แจกโบนัส ฟรีเครดิต สมัครเลย ทดลองเล่น สล็อต โปรโมชั่น สุดคุ้ม
• เว็บสล็อต 888 เล่นได้ไม่จำกัด ทุกค่าย แจกโบนัส ฝากถอนรวดเร็ว สล็อตเว็บตรง ทดลองเล่นฟรี
• เว็บตรง g2g แจกโบนัส สล็อต แตกง่าย ฝากถอน ไม่มีขั้นต่ำ ลุ้นรับเงินเยอะ ล่าสุด
• G2Gเว็บตรง วอเลท แจกเครดิตฟรี ล่าสุด ไม่ต้องแชร์ รับเงินจริง ทดลองเล่นสล็อต สมัครฟรี
• ราคา คอม โปรโมชั่น ลด สุดพิเศษ ส่วนลด มากที่สุด ซื้อเลย สินค้า คุณภาพ รับประกัน
• เว็บไซต์พนันออนไลน์ เล่นง่าย แจกเครดิตฟรี รวยได้เร็ว ลุ้นรับโบนัส ฝากถอนไว ไม่ผ่านเอเย่นต์
• สล็อตเว็บตรง betflik แจกโบนัส ไม่เอเย่นต์ ลุ้นรับเงินสด ที่นี่เท่านั้น
• สมาชิกใหม่ สล็อตออนไลน์ เว็บตรง ฝากถอน ไม่มีขั้นต่ำ ทดลองเล่นฟรี แจกเครดิต สล็อตแตกง่าย
• ทดลองเล่นสล็อต pp megaways สุดเร้าใจ แจกโบนัส ฟรีเครดิต รับเงินจริง ลุ้นรวยทุกวัน ไม่ต้องแชร์ ลองเล่นเดี๋ยวนี้
• สล็อตเว็บตรงxo โปรโมชั่นเด็ด รับเครดิตฟรี ลุ้นรางวัลใหญ่ สมัครเลย ที่นี่
• ทดลองเล่น roma เว็บตรง สุดเร้าใจ รองรับทุกอุปกรณ์ แจกโบนัสเยอะ รับเงินไวที่นี่
• หมู่บ้าน โก ล เด้ น ทาวน์ เล่นสนุก รับโปรโมชั่น ไม่เสียเงิน ทดลองเล่น สล็อต เว็บตรง สมัครเลย ฟรีเครดิต
• เทคนิคเจาะลึกเห็ดชิลิน โปรแกรมเสริมสร้างแรงบันดาลใจ สูตรพิชิตชิลินอย่างมืออาชีพ วิธีเร่งเสถียรภาพชิลิน จุดเด่นเหดชิลินที่ไม่ควรพลาด
• สล็อต เครดิต ฟรี ใหม่ ล่าสุด 2024 แจกเยอะ ไม่มีเงื่อนไข สล็อตออนไลน์ สมัครฟรี ทดลองเล่น
• เว็บตรง bk8 สล็อตออนไลน์ แจกเครดิตฟรี ล่าสุด ฝากถอนไว ไม่ต้องแชร์ รับเงินจริง
• สล็อต ทดลองฟรี
• pg neko wallet
• สล็อตแตกง่าย fafa212
• แอ พ ธนาคาร ธ ก ส เข้า ไม่ ได้
• รับสมัครแอดมินเว็บพนัน
• สล็อตเว็บตรงไม่ผ่านเอเย่นต์ ไม่มี ขั้น ต่ํา วอ เลท
• siam99เครดิตฟรี
• slot vip 168
• คาเฟ่ หาด จอม เทียน
• เว็บพนันออนไลน์ ฝากถอน ไม่มี ขั้นต่ำ
• โจ๊กเกอร์ สล็อต
• ทดลองเล่นสล็อต10000
• เครดิตฟรีกรอกโค้ด
• กสิกร ไทย โทร
• สล็อตเว็บทดลอง ซื้อฟรีสปิน
• ขุดบิทคอยน์ฟรี ถอนได้ โดย ไม่มีขั้นต่ำ
• เล่นสล็อตทดลอง ฟรี
• วิธี ถอนเงิน จากเว็บพนัน
• เว็บสล็อตล่าสุด
• บ้าน มี สวน คาเฟ่ สุดหรู ที่สุด ไม่เด้ง รับประกัน แน่นอน ลองเล่น ฟรี ทุกค่าย
• เครดิตฟรี กดรับเอง ที่หน้าเว็บล่าสุด ปังมาก ไม่ต้องแชร์ รับเครดิตฟรี ฝากถอนไว สล็อตเว็บตรง แจกเครดิตฟรี
• งานครู หางาน สอนพิเศษ ทำงานออนไลน์ สอนเด็ก เรียนออนไลน์ สอนภาษา สอนเสริมทักษะ สอนเพลง
• เปอร์เซ็นต์การแตก สล็อต pg แจกโบนัส ล่าสุด ฟรีเครดิต ทดลองเล่น สมัครเลย ไม่ผ่านเอเย่นต์
• เว็บสล็อตยอดนิยม สล็อตเว็บตรง ทดลองเล่น ฝากถอน ไม่มีขั้นต่ำ แจกเครดิตฟรี ล่าสุด สมัครฟรี ทุกค่าย
• PG ซุปเปอร์ซากะ ฟุตบอล แห่งชาติ ทดลองเล่น ฟรี โปรโมชั่น สุดพิเศษ สล็อต ฟุตบอล สุดมันส์ ระบบออโต้
• pg slot ออโต้ แจกโบนัส ฟรีเครดิต ล่าสุด ทดลองเล่น สล็อตเว็บตรง เล่นง่าย ไม่มีขั้นต่ำ
• นิ ว โน เบิ ล แจ้งวัฒนะ สุดเจ๋ง สล็อตออนไลน์ เว็บตรง แจกเครดิตฟรี ไม่มีขั้นต่ำ ทดลองเล่น แล้วรวยเร็ว
• ufa356 ทางเข้า สุดเร้าใจ ลองเล่นเดี่ยว ฟรีเครดิต รับเงินจริง สล็อตแจกฟรี
• pgsoft โค้ดเครดิตฟรี แจกฟรี รับทันที สล็อต ฟรี เล่นได้ไม่จำกัด รับโบนัสสุดพิเศษ
• ทางเข้า PG168 เล่นสล็อตแท้ ฝากถอนไว ไม่มีขั้นต่ำ
• เล่นสล็อต Betflik ที่ดีที่สุด รับโบนัสมากมาย
• เว็บสล็อต 44 ล่าสุด! เล่นได้ไม่จำกัด แตกง่าย ฝากถอนไว
• สาวถ้า เว็บสล็อตแท้ อันดับ 1 ที่ไม่มีขั้นต่ำ ล่าสุดและเกมแตกง่าย
• เกมสล็อต ความสนุกสุดเหนือ ทุกความต้องการ
• moo555 ทางเข้า เว็บสล็อตแท้ ฝากถอนไว ไม่ต้องฝาก รับเครดิตฟรี
• สร้อยทอง100บาท รับฟรีเครดิต ทดลองเล่นสล็อต เล่นได้ไม่จำกัด
• สุดยอดหมู่บ้าน โก ล เด้ น ทาวน์ สล็อตเว็บตรง อันดับ 1 ที่ไม่มีขั้นต่ำ
• สล็อตพีจี777 เกมใหม่ล่าสุด ระบบออโต้ แตกง่าย ลิขสิทธ์แท้
• เว็บสล็อต ฝากถอนไม่มีขั้นต่ํา เล่นได้ไม่จำกัด รับเครดิตฟรี
• สล็อตเว็บตรง แตกง่าย ฝากถอนไว ไม่มีขั้นต่ำ วอลเล็ท
• ปั่นสล็อตเว็บทดลอง ลุ้นเงินแจ๋ว ไม่ต้องฝาก ฟรีเครดิต
• สปินหรี เล่นสล็อตฟรี รับโบนัสสปินฟรี ลุ้นรางวัลใหญ่
• เคล็ดลับการเล่นเกม Qilin เทคนิคที่ทำให้คุณชนะในเกมสล็อต
• เกมสล็อตออนไลน์ bkkslot ที่มั่นคง และมีเกมใหม่ล่าสุด
• PG SLOT 1688 เว็บสล็อตแท้ อันดับ 1 เล่นได้ไม่จำกัด
• King77 สล็อต เว็บตรง อันดับ 1 ฝากถอนไว ไม่มีขั้นต่ำ เล่นได้ไม่จำกัด
• สมาชิกใหม่ สล็อตเว็บตรง ล่าสุด ทดลองเล่น ฝากถอน ไม่จำกัด
• เกมสล็อต68 ล่าสุด โบนัสมาก สนุกสุดๆ เล่นได้ทั้งวัน
• สล็อต P6 เกมใหม่ แจกโบนัส รับเงินง่าย
• เว็บสล็อต 999 ทดลองเล่นเกมใหม่ แจกโบนัส สุดคุ้ม
• ทดลองเล่นสล็อตวอเลท ล่าสุด! รับเครดิตฟรี สนุกได้ไม่จำกัด
• ทดลองเล่นเกมสล็อต ลุ้นรับโบนัส แตกง่าย สูตรฟรี
• PG Slot1688 ทางเข้า สุดยอดเกมสล็อตออนไลน์ แจกโบนัส ทดลองเล่นฟรี
• เจอคอนโดสุดพิเศษ ที่ให้บริการเหนือระดับ ไม่ควรพลาด
• เล่นคาสิโนออนไลน์ ทุกเกม ทุกค่าย สุดเร้าใจ ไม่เสียเรท ที่เดียว
• สล็อตเครดิตฟรี ล่าสุด! เล่นฟรี ไม่ต้องฝาก รับโบนัสพิเศษ
• เล่นบาคาร่า 888 เว็บตรง ทดลองเล่นฟรี แจ็คพอตแตกง่าย
• ทดลองเล่นบาคาร่า สุดปัง ได้เงินจริง ไม่ผ่านเอเย่นต์
• เว็บตรง BK8 ล่าสุด ทดลองเล่น สมัครฟรี
• ลิงค์มิตรภาพ

© Copyright：ncertbooksolutions.com

NCERT curriculum (for CBSE/ICSE) Class 7 - Integers

Unlimited worksheets.

Every time you click the New Worksheet button, you will get a brand new printable PDF worksheet on Integers . You can choose to include answers and step-by-step solutions.

Unlimited Online Practice

Unlimited adaptive online practice on Integers . Practice that feels like play! Get shields, trophies, certificates and scores. Master Integers as you play.

Unlimited Online Tests

Take unlimited online tests on Integers . Get instant scores and step-by-step solutions on submission. Make sure you always get your answers right in Integers .

Contents: Integers

Integers - 7th standard integers

LetsPlayMaths.Com

Class vii math, class 7 integers, introduction to integers, natural numbers, whole numbers, properties of addition of integers, closure property of addition, commutative law of addition, associative law of addition.

• Additive identity

Additive inverse

Properties of subtraction of integers, closure properties of subtraction, subtraction of integers is not commutative, subtraction of integers is not associative, multiplication of integers, multiplication of two positive integers, multiplication of positive and negative integers, multiplication of two negative integers, multiplication by zero, properties of multiplication of integers, closure property of multiplication, commutative law of multiplication, associative law of multiplication, distributive law of multiplication over addition, multiplicative identity, multiplicative inverse, property of zero, division of integers having like signs, division of integers having unlike signs, properties of division of integers.

Integers Test

Integers Worksheet

Answer Sheet

In class 6, we learn about integers and various operations on them. Here we will learn various properties satisfied by various operations on integers.

Till now we have covered Natural numbers, Whole numbers, and integers.

Counting numbers are known as natural numbers. 1, 2, 3, 4, 5, 6, ... are all natural numbers.

All natural numbers together with zero are known as whole numbers. 0, 1, 2, 3, 4, 5, 6, ... are whole numbers.

All natural numbers, zero and negative counting numbers are known as integers. ..., -5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ... are all integers. Here 1, 2, 3, 4, 5, ... are all Positive Integers . −1, −2, −3, −4, −5 are all Negative Integers . Zero is an integer which is neither positive nor negative.

The sum of two integers is always an integer. Let's see some examples.

Example 1. 3 + 2 = 5, here number 5 is a positive integer.

Example 2. 5 + (−9) = −4, is a negative integer

Example 3. −4 + (−5) = −9, is a negative integer

Example 4. 12 + (−7) = 5, is a positive integer

Example 5. −5 + 5 = 0, is an integer

If 'a' and 'b' are any two integers, then a + b = b + a. Let's see some examples.

Example 1. −3 + 7 = 4 and 7 + (−3) = 4 Hence, −3 + 7 = 7 + (−3).

Example 2. (−5) + (−7) = −12 and (−7) + (−5) = −12 Hence, (−5) + (−7) = (−7) + (−5).

If a, b, c are any three integers, then (a + b) + c = a + (b + c). Let's see some examples.

Example 1. Consider three integers 4, −5, −7. {4 + (−5)} + (−7) = (4 − 5) −7 = −1 −7 = −8 And, 4 + {(−5) + (−7)} = 4 + (−12) = −8

Additive Identity

For any integer 'p', we have: p + 0 = 0 + p = p. 0 is called the additive identity for integers. Let's see some examples.

Example 1. 8 + 0 = 0 + 8 = 8.

Example 2. (−5) + 0 = 0 + (−5) = −5

For any integer 'p', we have: p + (−p) = (−p) + p = 0. The opposite of an integer 'p' is (−p). The sum of an integer and it's opposite is 0. Additive inverse of p is (−p). Similarly, additive inverse of (−p) is p. Let's see some examples.

Example 1. 4 + (−4) = (−4) + 4 = 0 So, the additive inverse of 4 is (−4). Additive inverse of (−4) is 4.

• Closure properties of subtraction
• Subtraction of integers is not commutative
• Subtraction of integers is not associative

If 'a' and 'b' are any two integers, then (a − b) is always an integer. Let's see some examples.

Example 1. 5 − 4 = 5 + (−4) = 1, which is an integer.

Example 2. − 3 − 6 = (−3) + (−6) = −9, which is an integer.

Example 3. − 5 − (−7) = −5 + 7 = 2, which is an integer.

Example 4. 4 − (−8) = 4 + 8 = 12, which is an integer.

If 'a' and 'b' are any two integers, then a − b ≠ b − a. Let's see some examples.

Examples 1. Consider two integers 4 and 9. 4 − 9 = 4 + (−9) = −5 9 − 4 = 9 + (−4) = 5 Hence, 4 − 9 ≠ 9 − 4

Example 2. Consider two integers −3 and 6. (−3) − 6 = (−3) + (−6) = −9 6 − (−3) = 6 + 3 = 9 Hence, (−3) − 6 ≠ 6 − (−3)

If a, b, c are any three integers, then (a − b) − c ≠ a − (b − c). Let's see some examples.

Example 1. Consider three integers as 5, 7, and −2. (5 − 7) − (−2) = −2 + 2 = 0 And 5 − {7 − (−2)} = 5 − (7 + 2) = 5 − 9 = −4 Hence, (5 − 7) − (−2) ≠ 5 − {7 − (−2)}

Example 2. Consider three integers as −10, 8, and −5. {(−10) − 8} − (−5) = (−18) + 5 = −13 And (−10) − {8 − (−5)} = (−10) − (8 + 5) = (−10) − 13 = −23 Hence, {(−10) − 8} − (−5) ≠ (−10) − {8 − (−5)}

• Multiplication of two positive integers
• Multiplication of positive and negative integers
• Multiplication of two negative integers
• Multiplication by zero

To multiply two positive integers, multiply them as natural numbers and the product is a positive integer. Let's see some examples.

Example 1. Multiply 5 and 6. 5 x 6 = 30, which is a positive integer.

Example 2. Multiply 6 and 10. 6 x 10 = 60, which is a positive integer.

To multiply a positive integer and negative integer, we multiply them as natural numbers and put the minus sign before the result. So, we get a negative integer. Let's see some examples.

Example 1. Multiply 5 and (-8). 5 x (−8) = −40, which is a negative integer.

Example 2. Multiply (−8) and 10. (−8) x 10 = −80, which is a negative integer.

To multiply two negative integers, we multiply them as natural numbers and put the positive sign before the result. Let's see some examples.

Example 1. Multiply (−4) and (−5). (−4) x (−5) = 20

Example 2. Multiply (−5) and (−8). (−5) x (−8) = 40

If any integer multiplied by zero, then the result will be zero.

Example 2. Multiply (−9) by 0. (−9) x 0 = 0

• Closure property of multiplication
• Commutative law of multiplication
• Associative law of multiplication
• Distributive law of multiplication over addition
• Multiplicative identity
• Multiplicative inverse

The product of two integers is always an integer.

Example 1. Multiply 4 and 5. 4 x 5 = 20, which is an integer.

Example 2. Multiply (−6) and 9 (−6) x 9 = −54, which is an integer.

Example 3. Multiply 3 and (−8) 3 x (−8) = −24, which is an integer.

Example 4. Multiply (−5) and (−6) (−5) x (−6) = 30, which is an integer.

For any two integers 'a' and 'b', (a x b) = (b x a)

Example 1. Consider 2 and 5 as two integers. 2 x 5 = 10 and 5 x 2 = 10 Hence, 2 x 5 = 5 x 2.

Example 2. Consider (−4) and 8 as two integers. (−4) x 8 = −32 and 8 x (−4) = −32 Hence, (−4) x 8 = 8 x (−4)

For any three integers 'a', 'b', 'c', (a x b) x c = a x (b x c)

Example 1. Consider three integers 4, (−5), and 6. {4 x (−5)} x 6 = (−20) x 6 = −120 4 x {(−5) x 6} = 4 x (−30) = −120 Hence, {4 x (−5)} x 6 = 4 x {(−5) x 6}

Example 2. Consider three integers (−3), (−4) and (−5). {(−3) x (−4)} x (−5) = 12 x (−5) = −60 (−3) x {(−4) x (−5)} = (−3) x 20 = 60 Hence, {(−3) x (−4)} x (−5) = (−3) x {(−4) x (−5)}

For any three integers a, b, c, a x (b + c) = (a x b) + (a x c).

Example 1. Consider three integers 2, (−3) and (−5). 2 x {(−3) + (−5)} = 2 x (−8) = −16 {2 x (−3)} + {2 x (−5)} = (−6) + (−10) = −16 Hence, 2 x {(−3) + (−5)} = {2 x (−3)} + {2 x (−5)}

For every integer 'a', we have (a x 1) = (1 x a) = a 1 is called multiplicative identity for integers.

Multiplicative inverse of a nonzero integer 'a' is the number 1 ⁄ a . a x 1 ⁄ a = 1 ⁄ a x a = 1

Example 1. Multiplicative inverse of 5 is 1 ⁄ 5 .

Example 2. Multiplicative inverse of −8 is - 1 ⁄ 8 .

If any integer multiplied by zero then the result will be zero. (a x 0) = (0 x a) = 0

For dividing one integer by the other having like signs, we divide their values and give a plus sign to the quotient. Let's see some examples.

Example 1. Divide 95 by 5. 95 ÷ 5 = 95 ⁄ 5 = 19

Example 2. Divide (−64) by (−8). (−64) ÷ (−8) = -64 ⁄ -8 = 8

For dividing two integers having unlike signs, we divide their values and give a minus sign to the quotient. Let's see some examples.

Example 1. Divide (−150) by 15. (−150) ÷ 15 = -150 ⁄ 15 = −10

Example 2. Divide 75 by (−15). 75 ÷ (−15) = 75 ⁄ -15 = −5

1. If 'a' and 'b' are integers then a ÷ b is not always an integer. Let's consider two integers as 15 and 6, but (15 ÷ 6) is not an integer. 2. If 'a' is an integer, then (a ÷ 1) is equal to 'a'. For example, 5 ÷ 1 = 5. 3. If 'a' is an integer and a ≠ 0, then a ÷ a = 1. For example, 11 ÷ 11 = 1. 4. If 'a' is an integer and a ≠ 0, then (0 ÷ a) = 0 but (a ÷ 0) has no value. For example, 0 ÷ 5 = 0, but 5 ÷ 0 has no value. 5. If 'a', 'b', 'c' are three integers, then (a ÷ b) ÷ c ≠ a ÷ (b ÷ c), unless c =1. For example, a = 15, b= 5 and c = −3. (15 ÷ 5) ÷ (−3) = 3 ÷ (−3) = −1 15 ÷ {5 ÷ (−3)} = 15 ÷ 5 ⁄ -3 = 15 x -3 ⁄ 5 = −9 Hence, (15 ÷ 5) ÷ (−3) ≠ 15 ÷ {5 ÷ (−3)}

Class-7 Integers Test

Integers Test - 1

Integers Test - 2

Class-7 Integers Worksheet

Integers Worksheet - 1

Integers Worksheet - 2

Integers Worksheet - 3

Integers Worksheet - 4

Integers-Answer Download the pdf

Copyright © 2024 LetsPlayMaths.com. All Rights Reserved. Email: [email protected]

• RD Sharma Solutions
• Chapter 1 Integers

RD Sharma Solutions for Class 7 Maths Chapter - 1 Integers

RD Sharma Solutions for Class 7 Chapter 1 Integers PDF is provided here. Students can download the PDF of these solutions from the given links. Class 7 is a stage where several important topics are introduced. These crucial topics are discussed here in a particular way. The solutions are provided in accordance with the latest syllabus of CBSE , which, in turn, helps the students to build a strong foundation and secure excellent marks in the final exam. Therefore, we, at BYJU’S, provide answers to all questions uniquely and briefly. The solutions to all questions in RD Sharma books are given here in a step-by-step way to help the students understand effectively. In this chapter, students will learn about the multiplication and division of integers and the various properties of these operations on integers.

• RD Sharma Solutions Class 7 Maths Chapter 1 Integers
• RD Sharma Solutions Class 7 Maths Chapter 2 Fractions
• RD Sharma Solutions Class 7 Maths Chapter 3 Decimals
• RD Sharma Solutions Class 7 Maths Chapter 4 Rational Numbers
• RD Sharma Solutions Class 7 Maths Chapter 5 Operations on Rational Numbers
• RD Sharma Solutions Class 7 Maths Chapter 6 Exponents
• RD Sharma Solutions Class 7 Maths Chapter 7 Algebraic Expressions
• RD Sharma Solutions Class 7 Maths Chapter 8 Linear Equations in One Variable
• RD Sharma Solutions Class 7 Maths Chapter 9 Ratio and Proportion
• RD Sharma Solutions Class 7 Maths Chapter 10 Unitary Method
• RD Sharma Solutions Class 7 Maths Chapter 11 Percentage
• RD Sharma Solutions Class 7 Maths Chapter 12 Profit and Loss
• RD Sharma Solutions Class 7 Maths Chapter 13 Simple Interest
• RD Sharma Solutions Class 7 Maths Chapter 14 Lines and Angles
• RD Sharma Solutions Class 7 Maths Chapter 15 Properties of Triangles
• RD Sharma Solutions Class 7 Maths Chapter 16 Congruence
• RD Sharma Solutions Class 7 Maths Chapter 17 Constructions
• RD Sharma Solutions Class 7 Maths Chapter 18 Symmetry
• RD Sharma Solutions Class 7 Maths Chapter 19 Visualising Solid Shapes
• RD Sharma Solutions Class 7 Maths Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures)
• RD Sharma Solutions Class 7 Maths Chapter 21 Mensuration II (Area of Circle)
• RD Sharma Solutions Class 7 Maths Chapter 22 Data Handling I (Collection and Organisation of Data)
• RD Sharma Solutions Class 7 Maths Chapter 23 Data Handling II (Central Values)
• RD Sharma Solutions Class 7 Maths Chapter 24 Data Handling III (Constructions of Bar Graphs)
• RD Sharma Solutions Class 7 Maths Chapter 25 Data Handling IV (Probability)
• Exercise 1.1 Chapter 1 Integers
• Exercise 1.2 Chapter 1 Integers
• Exercise 1.3 Chapter 1 Integers
• Exercise 1.4 Chapter 1 Integers

RD Sharma for Class 7 Maths Chapter 1 Integers

carouselExampleControls111

Previous Next

Access answers to Maths RD Sharma Solutions for Class 7 Chapter 1 – Integers

Exercise 1.1 Page No: 1.5

1. Determine each of the following products:

(i) 12 × 7

(ii) (-15) × 8

(iii) (-25) × (-9)

(iv) 125 × (-8)

(i) Given 12 × 7

Here we have to find the products of given numbers

12 ×7 = 84

Because the product of two integers of like signs is equal to the product of their absolute values.

(ii) Given (-15) × 8

(-15) ×8 = -120

Because the product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values.

(iii) Given (-25) × (-9)

(-25) × (-9) = + (25 ×9) = +225

(iv) Given 125 × (-8)

125 × (-8) = -1000

2. Find each of the following products:

(i) 3 × (-8) × 5

(ii) 9 × (-3) × (-6)

(iii) (-2) × 36 × (-5)

(iv) (-2) × (-4) × (-6) × (-8)

(i) Given 3 × (-8) ×5

Here we have to find the product of given number.

3 × (-8) × 5 = 3 × (-8 × 5)

=3 × -40 = -120

Since the product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values.

(ii) Given 9 × (-3) × (-6)

9 × (-3) × (-6) = 9 × (-3 × -6) [∵ the product of two integers of like signs is equal to

the product of their absolute values.]

=9 × +18 = +162

(iii) Given (-2) × 36 × (-5)

(-2) × 36 × (-5) = (-2 × 36) × -5 [∵ the product of two integers of like signs is equal to

=-72 × -5 = +360

(iv) Given (-2) × (-4) × (-6) × (-8)

(-2) × (-4) × (-6) × (-8) = (-2 × -4) × (-6 × -8) [∵ the product of two integers of like signs is

equal to the product of their absolute values.]

=-8 × -48 = +384

3. Find the value of:

(i) 1487 × 327 + (-487) × 327

(ii) 28945 × 99 – (-28945)

(i) Given 1487 × 327 + (-487) × 327

By using the rule of multiplication of integers, we have

1487 × 327 + (-487) × 327 = 486249 – 159249

(ii) Given 28945 × 99 – (-28945)

28945 × 99 – (-28945) = 2865555 + 28945

Since the product of two integers of like signs is equal to the product of their absolute values.

4. Complete the following multiplication table:

Second number

Is the multiplication table symmetrical about the diagonal joining the upper left corner to the lower right corner?

From the table it is clear that, the table is symmetrical about the diagonal joining the upper left corner to the lower right corner.

5. Determine the integer whose product with ‘-1’ is

(i) Given 58

Here we have to find the integer which is multiplied by -1

We get, 58 × -1 = -58

(ii) Given 0

We get, 0 × -1 = 0 [because anything multiplied with 0 we get 0 as their result]

(iii) Given -225

We get, -225 × -1 = 225

Exercise 1.2 Page No: 1.8

(i) 102 by 17

(ii) -85 by 5

(iii) -161 by -23

(iv) 76 by -19

(v) 17654 by -17654

(vi) (-729) by (-27)

(vii) 21590 by -10

(viii) 0 by -135

(i) Given 102 by 17

We can write given question as 102 ÷ 17

102 ÷ 17 = |102/17| = |102|/|17| [by applying the mod]

= 102/17 = 6

(ii) Given -85 by 5

We can write given question as -85 ÷ 5

-85 ÷ 5 = |-85/5| = |-85|/|5| [by applying the mod]

= -85/5 = -17

(iii) Given -161 by -23

We can write given question as -161 ÷ -23

-161 ÷ -23 = |-161/-23| = |-161|/|-23| [by applying the mod]

= 161/23 = 7

(iv) Given 76 by -19

We can write given question as 76 ÷ -19

76 ÷ -19 = |76/-19| = |76|/|-19| [by applying the mod]

= 76/-19 = -4

(v) Given 17654 by -17654

We can write given question as 17654 ÷ -17654

17654 ÷ -17654 = |17654/-17654| = |17654|/|-17654| [by applying the mod]

= 17654/-17654 = -1

(vi) Given (-729) by (-27)

We can write given question as (-729) ÷ (-27)

(-729) ÷ (-27) = |-729/-27| = |-729|/|-27| [by applying the mod]

= 729/27 = 27

(vii) Given 21590 by -10

We can write given question as 21590 ÷ -10

21590 ÷ -10 = |21590/-10| = |21590|/|-10| [by applying the mod]

= 21590/-10 = -2159

(viii) Given 0 by -135

We can write given question as 0 ÷ -135

0 ÷ -135 = 0 [because anything divided by 0 we get the result as 0]

Exercise 1.3 Page No: 1.9

Find the value of

1. 36 ÷ 6 + 3

Given 36 ÷ 6 + 3

According to BODMAS rule we have to operate division first then we have to do addition

Therefore 36 ÷ 6 + 3 = 6 + 3 = 9

2. 24 + 15 ÷ 3

Given 24 + 15 ÷ 3

Therefore 24 + 15 ÷ 3 = 24 + 5 = 29

3. 120 – 20 ÷ 4

Given 120 – 20 ÷ 4

According to BODMAS rule we have to operate division first then we have to do subtraction

Therefore 120 – 20 ÷ 4 = 120 – 5 = 115

4. 32 – (3 × 5) + 4

Given 32 – (3 × 5) + 4

According to BODMAS rule we have to operate in brackets first then move to addition and subtraction.

Therefore 32 – (3 × 5) + 4 = 32 – 15 + 4

= 32 – 11 = 21

5. 3 – (5 – 6 ÷ 3)

Given 3 – (5 – 6 ÷ 3)

According to BODMAS rule we have to operate in brackets first then we have move to subtraction.

Therefore 3 – (5 – 6 ÷ 3) = 3 – (5 – 2)

= 3 –3 = 0

6. 21 – 12 ÷ 3 × 2

Given 21 – 12 ÷ 3 × 2

According to BODMAS rule we have to perform division first then move to multiplication and subtraction.

Therefore, 21 – 12 ÷ 3 × 2 = 21 – 4 × 2

= 21 – 8 = 13

7. 16 + 8 ÷ 4 – 2 × 3

Given 16 + 8 ÷ 4 – 2 × 3

According to BODMAS rule we have to perform division first followed by multiplication, addition and subtraction.

Therefore, 16 + 8 ÷ 4 – 2 × 3 = 16 + 2 – 2 × 3

= 16 + 2 – 6

8. 28 – 5 × 6 + 2

Given 28 – 5 × 6 + 2

According to BODMAS rule we have to perform multiplication first followed by addition and subtraction.

Therefore, 28 – 5 × 6 + 2 = 28 – 30 +2

= 28 – 28 = 0

9. (-20) × (-1) + (-28) ÷ 7

Given (-20) × (-1) + (-28) ÷ 7

Therefore, (-20) × (-1) + (-28) ÷ 7 = (-20) × (-1) – 4

= 20 – 4 = 16

10. (-2) + (-8) ÷ (-4)

Given (-2) + (-8) ÷ (-4)

According to BODMAS rule we have to perform division first followed by addition and subtraction.

Therefore, (-2) + (-8) ÷ (-4) = (-2) + 2

11. (-15) + 4 ÷ (5 – 3)

Given (-15) + 4 ÷ (5 – 3)

Therefore, (-15) + 4 ÷ (5 – 3) = (-15) + 4 ÷ 2

12. (-40) × (-1) + (-28) ÷ 7

Given (-40) × (-1) + (-28) ÷ 7

(-40) × (-1) + (-28) ÷ 7 = (-40) × (-1) – 4

= 40 – 4

13. (-3) + (-8) ÷ (-4) -2 × (-2)

Given (-3) + (-8) ÷ (-4) -2 × (-2)

(-3) + (-8) ÷ (-4) -2 × (-2) = -3 + 2 -2 × (-2)

= -3 + 2 + 4

= 6 – 3

14. (-3) × (-4) ÷ (-2) + (-1)

Given (-3) × (-4) ÷ (-2) + (-1)

(-3) × (-4) ÷ (-2) + (-1) = -3 × 2 -1

= – 6 – 1

Exercise 1.4 Page No: 1.12

Simplify each of the following:

1. 3 – (5 – 6 ÷ 3)

According to removal of bracket rule firstly remove inner most bracket

We get 3 – (5 – 6 ÷ 3) = 3 – (5 – 2)

= 3 – 3

2. -25 + 14 ÷ (5 – 3)

Given -25 + 14 ÷ (5 – 3)

We get -25 + 14 ÷ (5 – 3) = -25 + 14 ÷ 2

According to removal of bracket rule first we have to remove vinculum we get

= 25 – ½ {5 + 4 – (5 – 4)}

Now by removing the innermost bracket we get

= 25 – ½ {5 + 4 – 1}

By removing the parentheses we get

= 25 – ½ (8)

Now simplifying we get

= 25 – 4

= 27 – [38 – {46 – (15 – 11)}]

Now by removing inner most bracket we get

= 27 – [38 – {46 – 4}]

= 27 – [38 – 42]

Now by removing braces we get

= 27 – (-4)

By removing innermost bracket we get

= 36 – [18 – {14 – (11 ÷ 2 × 2)}]

= 36 – [18 – {14 – 11}]

Now by removing the parentheses we get

= 36 – [18 – 3]

Now remove the braces we get

= 36 – 15

6. 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]

Given 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]

First remove the inner most brackets

= 45 – [38 – {20 – (6 – 3) ÷ 3}]

= 45 – [38 – {20 – 3 ÷ 3}]

Now remove the parentheses we get

= 45 – [38 – 19]

= 45 – 19

Now first remove the vinculum we get

= 23 – [23 – {23 – (23 – 0)}]

Now remove the innermost bracket we get,

= 23 – [23 – {23 – 23}]

By removing the parentheses we get,

= 23 – [23 -0]

Now we have to remove the braces and on simplifying we get,

= 23 – 23

First we have to remove the vinculum from the given equation we get,

= 2550 – [510 – {270 – (90 – 150)}]

= 2550 – [510 – {270 – (-60)}]

= 2550 – [510 – {270 + 60}]

Now remove the parentheses we get,

= 2550 – [510 – 330]

Now we have to remove braces

= 2550 – 180

First we have to remove vinculum from the given equation,

= 4 + 1/5 [{-10 × (25 – 10)} ÷ (-5)]

Now remove the innermost bracket, we get

= 4 + 1/5 [{-10 × 15} ÷ -5]

Now by removing the parentheses we get,

= 4 + 1/5 [-150 ÷ -5]

By removing the braces we get,

= 4 + 1/5 (30)

On simplifying we get,

Now we have to remove innermost bracket

= 22 – ¼ {-5 – (- 48 ÷ – 16)}

After removing innermost bracket

= 22 – ¼ {-5 – 3}

= 22 – ¼ (-8)

First we have to remove vinculum from the given equation then we get,

= 63 – [(-3) {-2 – 5}] ÷ [3 {5 + 2}]

Now remove the parentheses from the above equation

= 63 – [(-3) (-7)] ÷ [3 (7)]

= 63 – [21] ÷ [21]

= 63 – 1

First we have to remove the innermost brackets then we get,

= [29 – (-2) {6 – 4}] ÷ [3 × {5 + 6}]

Now remove the parentheses in the above equation,

= [29 + 2 (2)] ÷ [3 × 11]

Now remove all braces present in the above equation,

= 33 ÷ 33

13. Using brackets, write a mathematical expression for each of the following:

(i) Nine multiplied by the sum of two and five.

(ii) Twelve divided by the sum of one and three.

(iii) Twenty divided by the difference of seven and two.

(iv) Eight subtracted from the product of two and three.

(v) Forty divided by one more than the sum of nine and ten.

(vi) Two multiplied by one less than the difference of nineteen and six.

(i) 9 (2 + 5)

(ii) 12 ÷ (1 + 3)

(iii) 20 ÷ (7 – 2)

(iv) 2 × 3 -8

(v) 40 ÷ [1 + (9 + 10)]

(vi) 2 × [(19 -6) -1]

RD Sharma Solutions for Class 7 Maths Chapter 1 – Integers

Chapter 1 Integers contains four exercises. RD Sharma Solutions are given here, which include the answers to all the questions present in these exercises. Let us have a look at some of the concepts that are being discussed in this chapter.

• Multiplication of integers
• Properties of multiplication
• Division of integers
• Properties of division
• Operator precedence
• Use of brackets
• Removal of brackets

Chapter Brief of RD Sharma Solutions for Class 7 Maths Chapter 1 – Integers

Chapter 1 – Integers primarily covers three topics, which are  multiplication and division of integers and operator precedence. It also explains how to use and remove the brackets. Integers can be defined as a “number that can be written without a fractional component”. Here, the students will be thorough with the precedence of fundamental operations of addition, subtraction, multiplication and division.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 7 Mathematics Assignments

We have provided below free printable Class 7 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 7 Mathematics . These Assignments for Grade 7 Mathematics cover all important topics which can come in your standard 7 tests and examinations. Free printable Assignments for CBSE Class 7 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 7 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 7 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 7. Students can click on the links below and download all Pdf Assignments for Mathematics class 7 for free. All latest Kendriya Vidyalaya Class 7 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 7 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 7 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 7th. Our expert faculty have covered Class 7 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 7 Mathematics and CBSE Assignments for Mathematics Class 7 will be really helpful for standard 7th students to prepare for the class tests and school examinations. Class 7th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 7 Mathematics Download in Pdf

More assignments for class 7 mathematics.

Advantages of Class 7 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 7, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 7 .
• All Mathematics assignments for Class 7 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 7 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 7 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 7 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 7 which you can download in Pdf

We provide here Standard 7 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 7, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 7 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 7 for all subjects. You can download them all and use them offline without the internet.

Related Posts

Class 7 Mathematics Algebraic Expressions Assignments

Class 7 Mathematics Symmetry Assignments

Class 7 Assignments Download Pdf

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Class 7 (Old)

Unit 1: integers, unit 2: fractions and decimals, unit 3: data handling, unit 4: simple equations, unit 5: lines and angles, unit 6: the triangle and its properties, unit 7: comparing quantities, unit 8: rational numbers, unit 9: perimeter and area, unit 10: algebraic expressions, unit 11: exponents and powers, unit 12: congruence of triangles.

AssignmentsBag.com

Assignments For Class 7 Mathematics Integers

Assignments for Class 7 Mathematics Integers have been developed for Standard 7 students based on the latest syllabus and textbooks applicable in CBSE, NCERT and KVS schools. Parents and students can download the full collection of class assignments for class 7 Mathematics Integers from our website as we have provided all topic wise assignments free in PDF format which can be downloaded easily. Students are recommended to do these assignments daily by taking printouts and going through the questions and answers for Grade 7 Mathematics Integers. You should try to do these test assignments on a daily basis so that you are able to understand the concepts and details of each chapter in your Mathematics Integers book and get good marks in class 7 exams.

Assignments for Class 7 Mathematics Integers as per CBSE NCERT pattern

All students studying in Grade 7 Mathematics Integers should download the assignments provided here and use them for their daily routine practice. This will help them to get better grades in Mathematics Integers exam for standard 7. We have made sure that all topics given in your textbook for Mathematics Integers which is suggested in Class 7 have been covered ad we have made assignments and test papers for all topics which your teacher has been teaching in your class. All chapter wise assignments have been made by our teachers after full research of each important topic in the textbooks so that you have enough questions and their solutions to help them practice so that they are able to get full practice and understanding of all important topics. Our teachers at https://www.assignmentsbag.com have made sure that all test papers have been designed as per CBSE, NCERT and KVS syllabus and examination pattern. These question banks have been recommended in various schools and have supported many students to practice and further enhance their scores in school and have also assisted them to appear in other school level tests and examinations. Its easy to take print of thee assignments as all are available in PDF format.

Some advantages of Free Assignments for Class 7 Mathematics Integers

• Solving Assignments for Mathematics Integers Class 7 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignments given in your class by Mathematics Integers teacher for class 7 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics Integers class test
• You will be able to revise all topics given in the ebook for Class 7 Mathematics Integers as all questions have been provided in the question banks
• NCERT Class 7 Mathematics Integers Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 7 Mathematics Integers teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 7 Mathematics Integers Assignments PDF.

You can download free assignments for class 7 Mathematics Integers from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 7 Mathematics Integers from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 7, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Integers Class 7 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

Related Posts

Assignments For Class 9 Mathematics Areas of Parallelogram and Triangle

Assignments For Class 8 Social Science Geography

Assignments For Class 5 Telegu

• SI SWIMSUIT
• SI SPORTSBOOK

Meeting the Dallas Cowboys 2024 draft class: Nathan Thomas

Tyler reed | 0 minutes ago.

The Dallas Cowboys understood the assignment when it came to bulking up the offensive line in the 2024 NFL Draft. The team jumped out of the gates, selecting offensive tackle Tyler Guyton with their first pick and then guard Cooper Beebe in the third round.

However, the Cowboys' offensive line selections weren't over. With their first of two picks in the seventh round, the Cowboys went back to the offensive line one more time.

Rd. 7: 233 Nathan Thomas OT, Louisiana Lafayette

#Cowboys clearly wanted to upgrade their OL, and they stole one in OT/OG Nathan Thomas from ULL. At 330+, he smooth, stout and effective with his punch, and keeps his kick slide controlled in space Should add depth at both guard and tackle spots for Dallas #ShrineBowlWhosNext https://t.co/b1wYQnempM pic.twitter.com/HxX2XxBK6A — Eric Galko (@EricGalko) April 27, 2024

Cowboys fans are hoping Louisiana Laffeyette's Nathan Thomas could be the next talked about late-round steal of the NFL Draft. Thomas stands at 6-foot-5 and weighs over 300 pounds. The perfect prototype build for this generation of offensive linemen that must block against hybrid creates the likes of T.J. Watt and Myles Garrett.

Dallas has a lot of work to do when filling out the offensive line.

Currently, the Cowboys team website doesn't even have a center listed on the depth chart, but Cooper Beebe is expected to compete for the job

One has to think that Guyton has a lot of work to do at the left tackle position. However, there is plenty of room for Thomas to learn the position and have the opportunity to fill in on the left or right side of the line with added depth.