RS Aggarwal 2017 Solutions for Class 7 Math Chapter 1 Integers are provided here with simple step-by-step explanations. These solutions for Integers are extremely popular among class 7 students for Math Integers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggarwal 2017 Book of class 7 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RS Aggarwal 2017 Solutions. All RS Aggarwal 2017 Solutions for class 7 Math are prepared by experts and are 100% accurate.

#### Page No 4:

#### Question 1:

Evaluate:

(i) 15 + (−8)

(ii) (−16) + 9

(iii) (−7) + (−23)

(iv) (−32) + 47

(v) 53 + (−26)

(vi) (−48) + (−36)

#### Answer:

(i) 15 + (−8) = 7

(ii) (−16) + 9 = −7

(iii) (−7) + (−23) = −30

(iv) (−32) + 47 = 15

(v) 53 + (−26) = 27

(vi) (−48) + (−36) = −84

#### Page No 4:

#### Question 2:

Find the sum of:

(i) 153 and − 302

(ii) 1005 and − 277

(iii) − 2035 and 297

(iv) − 489 and − 324

(v) − 1000 and 438

(vi) − 238 and 500

#### Answer:

(i) 153 + (−302) = −149

(ii) 1005 + (−277) = 728

(iii) (−2035) + 297 = −1738

(iv) (−489) + (−324) = −813

(v) (−1000) + 438 = −562

(vi) (−238) + 500 = 262

#### Page No 4:

#### Question 3:

Find the additive inverse of:

(i) − 83

(ii) 256

(iii) 0

(iv) − 2001

#### Answer:

(i) Additive inverse of −83 = −(−83) = 83

(ii) Additive inverse of 256 = −(256) = −256

(iii) Additive inverse of 0 = −(0) = 0

(iv) Additive inverse of 2001 = −(−2001) = 2001

#### Page No 5:

#### Question 4:

Subtract:

(i) 28 from − 42

(ii) − 36 from 42

(iii) − 37 from − 53

(iv) − 66 from − 34

(v) 318 from 0

(vi) − 153 from − 240

(vii) − 64 from 0

(viii) − 56 from 144

#### Answer:

(i) −42 − 28 = (−42) + (−28) = −70

(ii) 42 −(−36) = 42 + 36 = 78

(iii) -53 - (-37) = (-53) - (-37) = -16

(iv) -34 - (-66) = -34 + 66 = 32

(v) 0 - 318 = -318

(vi) (-240) - (-153) = -87

(vii) 0 - (-64) = 0 + 64 = 64

(viii) 144 - (-56) = 144 + 56 = 200

#### Page No 5:

#### Question 5:

Subtract the sum of − 1032 and 878 from − 34.

#### Answer:

Sum of −1032 and 878 = −1032 + 878

= -154

Subtracting the sum from −34, we get

−34 − (−154)

= (−34)+ 154

= 120

#### Page No 5:

#### Question 6:

Subtract − 134 from the sum of 38 and − 87.

#### Answer:

First, we will calculate the sum of 38 and −87.

38 + (−87) = −49

Now, subtracting −134 from the sum, we get:

−49 − (−134)

=(−49) + 134

= 85

#### Page No 5:

#### Question 7:

Fill in the blanks:

(i) {(−13) + 27} + (−41) = (−13) + {27 + (......)}

(ii) (−26) + {(−49) + (−83)} = {(−26) + (−49)} + (......)

(iii) 53 + (−37) = (−37) + (......)

(iv) (−68) + (−76) = (......) + (−68)

(v) (−72) + (......) = −72

(vi) − (−83) = ......

(vii) (−60) − (......) = − 59

(viii) (−31) + (......) = − 40

#### Answer:

(i) −41 (∵ Associative property)

(ii) −83 (∵ Associative property)

(iii) 53 (∵ Commutative property)

(iv) −76 (∵ Commutative property)

(v) 0 (∵ Additive identity)

(vi) 83 (∵ Additive inverse)

(vii) (−60) − (−59) = −1

(viii) (−40) − (−31) = −9

#### Page No 5:

#### Question 8:

Simplify:

{−13−(−27)} + {−25−(−40)}.

#### Answer:

{−13 − (−27)} + {−25 − (−40)}

= {−13 + 27} + {−25 + 40}

=14 + 15

= 29

#### Page No 5:

#### Question 9:

Find 36 − (−64) and (−64) − 36. Are they equal?

#### Answer:

36 − (−64) = 36 + 64 = 100

Now, (−64) − 36 = (−64) + (−36) = −100

Here, 100 $\ne $ −100

Thus, they are not equal.

#### Page No 5:

#### Question 10:

If *a* = − 8, *b* = − 7, *c* = 6, verify that (*a+b*) *+ c = a + *(*b+c*)*.*

#### Answer:

(a + b) + c = (−8 + (−7)) + 6 = −15 + 6 = −9

a + (b + c) = −8 + (−7 + 6) = −8 + (−1) = −9

Hence, (a + b) + c = a + (b + c) [i.e., Property of Associativity]

#### Page No 5:

#### Question 11:

If *a* = − 9 and *b* = − 6, show that (*a−b*) ≠ (*b−a*).

#### Answer:

Here, (a − b) = −9 − (−6) = −3

Similarly, (b − a) = −6 − (−9) = 3

∴ (*a−b*) ≠ (*b−a*)

#### Page No 5:

#### Question 12:

The sum of two integers is − 16. If one of them is 53, find the other.

#### Answer:

Let the other integer be *a*. Then, we have:

53 + *a* = −16

⇒ *a* = −16 − 53 = −69

∴ The other integer is −69.

#### Page No 5:

#### Question 13:

Ths sum of two integers is 65. If one of them is − 31, find the other.

#### Answer:

Let the other integer be *a*.

Then, −31 + *a* = 65

*⇒ a* = 65 − (−31) = 96

∴ The other integer is 96.

#### Page No 5:

#### Question 14:

The difference of an integer *a* and (−6) is 4. Find the value of *a*.

#### Answer:

We have:

*a* − (−6) = 4

⇒ *a* = 4 + (−6) = −2

∴ *a* = −2

#### Page No 5:

#### Question 15:

Write a pair of integers whose sum gives

(i) zero;

(ii) a negative integer;

(iii) an integer smaller than both the integers;

(iv) an integer greater than both the integers;

(v) an integer smaller than only one of the integers.

#### Answer:

(i) Consider the integers 8 and −8. Then, we have:

8 + (−8) = 0

(ii) Consider the integers 2 and (−9). Then, we have:

2 + (−9)= −7, which is a negative integer.

(iii) Consider the integers −4 and −5. Then, we have:

(−4) + (−5) = −9, which is smaller than −4 and −5.

(iv) Consider the integers 2 and 6. Then, we have:

2 + 6 = 8, which is greater than both 2 and 6.

(v) Consider the integers 7 and −4. Then, we have:

7 + (−4) = 3, which is smaller than 7 only.

#### Page No 5:

#### Question 16:

For each of the following statements, write (T) for true and (F) for false:

(i) The smallest integer is zero.

(ii) − 10 is greater than − 7

(iii) Zero is larger than every negative integer.

(iv) The sum of two negative integers is a negative integer.

(v) The sum of a negative integer and a positive integer is always a positive integer.

#### Answer:

(i) F (false). −3, −90 and −100 are also integers. We cannot determine the smallest integer, since they are infinite.

(ii) F (false). −10 is less than −7.

(iii) T (true). All negative integers are less than zero.

(iv) T (true).

(v) F (false). Example: −9 + 2 = −7

#### Page No 9:

#### Question 1:

Multiply:

(i) 16 by 9

(ii) 18 by − 6

(iii) 36 by − 11

(iv) − 28 by 14

(v) − 53 by 18

(vi) − 35 by 0

(vii) 0 by − 23

(viii) − 16 by − 12

(ix) − 105 by − 8

(x) − 36 by − 50

(xi) − 28 by − 1

(xii) 25 by − 11

#### Answer:

(i) 16 $\times $ 9 = 144

(ii) 18 $\times $ (−6) = $-(18\times 6)=$−108

(iii) 36 $\times $ (−11) = $-(36\times 11)=$−396

(iv) (−28) $\times $14 = $-(28\times 14)=$−392

(v) (−53) $\times $ 18 = $-(53\times 18)=$−954

(vi) (−35) $\times $ 0 = 0

(vii) 0 $\times $ (−23) = 0

(viii) (−16) $\times $ (−12) = 192

(ix) (−105) $\times $ (−8) = 840

(x) (−36) $\times $ (−50) = 1800

(xi) (−28) $\times $ (−1) = 28

(xii) 25 $\times $ (−11) = $-(25\times 11)=$−275

#### Page No 9:

#### Question 2:

Find each of the following products:

(i) 3 × 4 × (−5)

(ii) 2 × (−5) × (−6)

(iii) (−5) × (−8) × (−3)

(iv) (−6) × 6 × (−10)

(v) 7 × (−8) × 3

(vi) (−7) × (−3) × 4

#### Answer:

(i) 3 × 4 × (−5) = (12) × (−5) = −60

(ii) 2 × (−5) × (−6) = (−10) × (−6) = 60

(iii) (−5) × (−8) × (−3) = (−5) × (24) = −120

(iv) (−6) × 6 × (−10) = 6 × (60) = 360

(v) 7 × (−8) × 3 = 21 × (−8) = −168

(vi) (−7) × (−3) × 4 = 21 × 4 = 84

#### Page No 9:

#### Question 3:

Find each of the following products:

(i) (−4) × (−5) × (−8) × (−10)

(ii) (−6) × (−5) × (−7) × (−2) × (−3)

(iii) (−60) × (−10) × (−5) × (−1)

(iv) (−30) × (−20) × (−5)

(v) (−3) × (−3) × (−3) × ...6 times

(vi) (−5) × (−5) × (−5) × ...5 times

(vii) (−1) × (−1) × (−1) × ...200 times

(viii) (−1) × (−1) × (−1) × ...171 times

#### Answer:

(i) Since the number of negative integers in the product is even, the product will be positive.

(4) × (5) × (8) × (10) = 1600

(ii) Since the number of negative integers in the product is odd, the product will be negative.

−(6) × (5) × (7) × (2) × (3) = −1260

(iii) Since the number of negative integers in the product is even, the product will be positive.

(60) × (10) × (5) × (1) = 3000

(iv) Since the number of negative integers in the product is odd, the product will be negative.

−(30) × (20) × (5) = −3000

(v) Since the number of negative integers in the product is even, the product will be positive.

$(-3{)}^{6}$ = 729

(vi) Since the number of negative integers in the product is odd, the product will be negative.

$(-5{)}^{5}$ = −3125

(vii) Since the number of negative integers in the product is even, the product will be positive.

$(-1{)}^{200}$= 1

(viii) Since the number of negative integers in the product is odd, the product will be negative.

$(-1{)}^{171}$ = −1

#### Page No 9:

#### Question 4:

What will be the sign of the product, if we multiply 90 negative integers and 9 positive integers?

#### Answer:

Multiplying 90 negative integers will yield a positive sign as the number of integers is even.

Multiplying any two or more positive integers always gives a positive integer.

The product of both(the above two cases) the positive and negative integers is also positive.

Therefore, the final product will have a positive sign.

#### Page No 9:

#### Question 5:

What will be the sign of the product, if we multiply 103 negative integers and 65 positive integers?

#### Answer:

Multiplying 103 negative integers will yield a negative integer, whereas 65 positive integers will give a positive integer.

The product of a negative integer and a positive integer is a negative integer.

#### Page No 9:

#### Question 6:

Simplify:

(i)(−8) × 9 + (−8) × 7

(ii) 9 × (−13) + 9 × (−7)

(iii) 20 × (−16) + 20 × 14

(iv) (−16) × (−15) + (−16) × (−5)

(v) (−11) × (−15) + (−11) × (−25)

(vi) 10 × (−12) + 5 × (−12)

(vii) (−16) × (−8) + (−4) × (−8)

(viii) (−26) × 72 + (−26) × 28

#### Answer:

(i) (−8) $\times $ (9 + 7) [using the distributive law]

= (−8) $\times $ 16 = −128

(ii) 9 $\times $ (−13 + (−7)) [using the distributive law]

= 9 $\times $ (−20) = −180

(iii) 20 $\times $ (−16 + 14) [using the distributive law]

= 20 $\times $ (−2) = −40

(iv) (−16) $\times $ (−15 + (−5)) [using the distributive law]

= (−16) $\times $ (−20) = 320

(v) (−11) $\times $ (−15 +(−25)) [using the distributive law]

= (−11) $\times $ (−40)

= 440

(vi) (−12) $\times $ (10 + 5) [using the distributive law]

= (−12) $\times $ 15 = −180

(vii) (−16 + (−4)) $\times $ (−8) [using the distributive law]

= (−20) $\times $ (−8) = 160

(viii) (−26) $\times $ (72 + 28) [using the distributive law]

= (−26) $\times $100 = −2600

#### Page No 9:

#### Question 7:

Fill in the blanks:

(i) (−6) × (......) = 6

(ii) (−18) × (......) = (−18)

(iii) (−8) × (−9) = (−9) × (......)

(iv) 7 × (−3) = (−3) × (......)

(v) {(−5)×3} × (−6) = (......) × {3×(−6)}

(vi) (−5) × (......) = 0

#### Answer:

(i) (−6) × (*x*) = 6

$x=\frac{6}{-6}=\frac{-6}{6}=-1$

Thus, x = (−1)

(ii) 1 [∵ Multiplicative identity]

(iii) (−8) [∵ Commutative law]

(iv) 7 [∵ Commutative law]

(v) (−5) [∵ Associative law]

(vi) 0 [∵ Property of zero]

#### Page No 9:

#### Question 8:

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (−2) marks are awarded for every incorrect answer and 0 for each question not attempted.

(i) Ravi gets 4 correct and 6 incorrect answers. What is his score?

(ii) Reenu gets 5 correct and 5 incorrect answers. What is her score?

(iii) Heena gets 2 correct and 5 incorrect answers. What is her score?

#### Answer:

We have 5 marks for correct answer and (−2) marks for an incorrect answer.

Now, we have the following:

(i) Ravi's score = 4 $\times $ 5 + 6 $\times $ (−2)

= 20 + (−12) =8

(ii) Reenu's score = 5 $\times $ 5 + 5 $\times $ (−2)

= 25 − 10 = 15

(iii) Heena's score = 2 $\times $ 5 + 5 $\times $ (−2)

= 10 − 10 = 0

#### Page No 9:

#### Question 9:

Which of the following statements are true and which are false?

(i) The product of a positive and a negative integer is negative.

(ii) The product of two negative integers is a negative integer.

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

(iv) Every integer when multiplied with −1 gives its multiplicative inverse.

(v) Multiplication on integers is commutative.

(vi) Multiplication on integers is associative.

(vii) Every nonzero integer has a multiplicative inverse as an integer.

#### Answer:

(i) True.

(ii) False. Since the number of negative signs is even, the product will be a positive integer.

(iii) True. The number of negative signs is odd.

(iv) False. *a* $\times $ (−1) = −*a*, which is not the multiplicative inverse of *a*.

(v) True. *a* $\times $ *b* = *b* $\times $ *a*

(vi) True. (*a* $\times $ *b*) $\times $ *c* = *a* $\times $ (*b* $\times $ *c*)

(vii) False. Every non-zero integer *a* has a multiplicative inverse $\frac{1}{a}$, which is not an integer.

#### Page No 12:

#### Question 1:

Divide:

(i) 65 by −13

(ii) −84 by 12

(iii) −76 by 19

(iv) −132 by 12

(v) −150 by 25

(vi) −72 by −18

(vii) −105 by −21

(viii) −36 by −1

(ix) 0 by −31

(x) −63 by 63

(xi) −23 by −23

(xii) −8 by 1

#### Answer:

(i) 65 $\xf7$ (−13) = $\frac{65}{-13}=$−5

(ii) (−84) $\xf7$ 12 = $\frac{-84}{12}=$ −7

(iii) (−76) $\xf7$ 19 = $\frac{-76}{19}=$−4

(iv) (−132) $\xf7$ 12 = $\frac{-132}{12}=$−11

(v) (−150) $\xf7$ 25 = $\frac{-150}{25}=$−6

(vi) (−72) $\xf7$ (−18) = $\frac{-72}{-18}=4$

(vii) (−105) $\xf7$ (−21) = $\frac{-105}{-21}=$5

(viii) (−36) $\xf7$ (−1) = $\frac{-36}{-1}=$36

(ix) 0 $\xf7$ (−31) = $\frac{0}{-31}=$0

(x) (−63) $\xf7$ 63 = $\frac{-63}{63}=$−1

(xi) (−23) $\xf7$ (−23) = $\frac{-23}{-23}=$1

(xii) (−8) $\xf7$ 1 = $\frac{-8}{1}=$−8

#### Page No 12:

#### Question 2:

Fill in the blanks

(i) 72 ÷ (......) = −4

(ii) −36 ÷ (......) = −4

(iii) (......) ÷ (−4) = 24

(iv) (......) ÷ 25 = 0

(v) (......) ÷ (−1) = 36

(vi) (......) ÷ 1 = −37

(vii) 39 ÷ (......) = −1

(viii) 1 ÷ (......) = −1

(ix) −1 ÷ (......) = −1

#### Answer:

(i)

72 ÷ (*x*) = −4

$\Rightarrow \frac{72}{x}=-4\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{72}{-4}=-18$

(ii)

−36 ÷ (*x*) = −4

$\Rightarrow \frac{-36}{x}=-4\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{-36}{-4}=9$

(iii)

(*x*) ÷ (−4) = 24

$\Rightarrow \frac{x}{-4}=24\phantom{\rule{0ex}{0ex}}\Rightarrow x=24\times (-4)=-96$

(iv)

(*x*) ÷ 25 = 0

$\Rightarrow \frac{x}{25}=0\phantom{\rule{0ex}{0ex}}\Rightarrow x=25\times 0=0$

(v)

(*x*) ÷ (−1) = 36

$\Rightarrow \frac{x}{-1}=36\phantom{\rule{0ex}{0ex}}\Rightarrow x=36\times (-1)=-36$

(vi)

(*x*) ÷ 1 = −37

$\Rightarrow \frac{x}{1}=-37\phantom{\rule{0ex}{0ex}}\Rightarrow x=-37\times 1=-37$

(vii)

39 ÷ (*x*) = −1

$\Rightarrow \frac{39}{x}=-1\phantom{\rule{0ex}{0ex}}\Rightarrow x=-1\times 39=-39$

(viii)

1 ÷ (*x*) = −1

$\Rightarrow \frac{1}{x}=-1\phantom{\rule{0ex}{0ex}}\Rightarrow x=-1\times 1=-1$

(ix)

−1 ÷ (*x*) = −1

$\Rightarrow \frac{-1}{x}=-1\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{-1}{-1}=1$

#### Page No 12:

#### Question 3:

Write (T) for true and (F) for false for each of the following statements.

(i) 0 ÷ (−4) = 0

(ii) (−6) ÷ 0 = 0

(iii) (−5) ÷ (−1) = −5

(iv) (−8) ÷ 1 = −8

(v) (−1) ÷ (−1) = −1

(vi) (−9) ÷ (−1) = 9

#### Answer:

(i) True (T). Dividing zero by any integer gives zero.

(ii) False (F). Division by zero gives an indefinite number.

(iii) False (F). $\frac{-5}{-1}=5$

(iv) True (T). $\frac{-8}{1}=-8$

(v) False (F). $\frac{-1}{-1}=1$

(vi) True (T). $\frac{-9}{-1}=9$

#### Page No 12:

#### Question 1:

**Mark (✓) against the correct answer**

6 − (−8) = ?

(a) −2

(b) 2

(c) 14

(d) none of these

#### Answer:

(c) 14

Given:

6 − (−8)

= 6 + 8

= 14

#### Page No 12:

#### Question 2:

**Mark (✓) against the correct answer**

−9 − (−6) = ?

(a) −15

(b) −3

(c) 3

(d) none of these

#### Answer:

(b) −3

Given:

−9 − (−6)

= −9 + 6

= −3

#### Page No 13:

#### Question 3:

**Mark (✓) against the correct answer**

By how much does 2 exceed −3?

(a) −1

(b) 1

(c) −5

(d) 5

#### Answer:

(d) 5

We can see that

−3 + 5 = 2

Hence, 2 exceeds −3 by 5.

#### Page No 13:

#### Question 4:

**Mark (✓) against the correct answer**

What must be subtracted from −1 to get −6?

(a) 5

(b) −5

(c) 7

(d) −7

#### Answer:

(a) 5

Let the number to be subtracted be x.

To find the number, we have:

−1 − *x* = −6

∴ *x *= −1 + 6 = 5

#### Page No 13:

#### Question 5:

**Mark (✓) against the correct answer**

How much less than −2 is −6?

(a) 4

(b) −4

(c) 8

(d) −8

#### Answer:

(c) 4

We can see that

(−2) − (−6) = (−2) + 6 = 4

Hence, −6 is four (4) less than −2.

#### Page No 13:

#### Question 6:

**Mark (✓) against the correct answer**

On subtracting 4 from −4, we get

(a) 8

(b) −8

(c) 0

(d) none of these

#### Answer:

(b) −8

Subtracting 4 from −4, we get:

(−4) − 4 = −8

#### Page No 13:

#### Question 7:

**Mark (✓) against the correct answer**

By how much does −3 exceed −5?

(a) −2

(b) 2

(c) 8

(d) −8

#### Answer:

(b) 2

Required number = (−3) − (−5) = 5 − 3 = 2

#### Page No 13:

#### Question 8:

**Mark (✓) against the correct answer**

What must be subtracted from −3 to get −9?

(a) −6

(b) 12

(c) 6

(d) −12

#### Answer:

(c) 6

(−3) − x = −9

*∴ x* = (−3) + 9 = 6

Hence, 6 must be subtracted from −3 to get −9.

#### Page No 13:

#### Question 9:

**Mark (✓) against the correct answer**

On subtracting 6 from −5, we get

(a) 1

(b) 11

(c) −11

(d) none of these

#### Answer:

(c) −11

Subtracting 6 from −5, we get:

(−5) − 6 = −11

#### Page No 13:

#### Question 10:

**Mark (✓) against the correct answer**

On subtracting −13 from −8, we get

(a) −21

(b) 21

(c) 5

(d) −5

#### Answer:

(c) 5

Subtracting −13 from −8, we get:

(−8) − (−13)

= −8 + 13

= 5

#### Page No 13:

#### Question 11:

**Mark (✓) against the correct answer**

(−36) ÷ (−9) = ?

(a) 4

(b) −4

(c) none of these

#### Answer:

(a) 4

(−36) ÷ (−9) = 4

Here, the negative signs in both the numerator and denominator got cancelled with each other.

#### Page No 13:

#### Question 12:

**Mark (✓) against the correct answer**

0 ÷ (−5) = ?

(a) −5

(b) 0

(c) not defined

#### Answer:

(b) 0

Dividing zero by any integer gives zero as the result.

#### Page No 13:

#### Question 13:

**Mark (✓) against the correct answer**

(−8) ÷ 0 = ?

(a) −8

(b) 0

(c) not defined

#### Answer:

(c) not defined

Dividing any integer by zero is not defined.

#### Page No 13:

#### Question 14:

**Mark (✓) against the correct answer**

Which of the following is a true statement?

(a) −11 > −8

(b) −11 < −8

(c) −11 and −8 cannot be compared

#### Answer:

(b) −11 < −8

Negative integers decrease with increasing magnitudes.

#### Page No 13:

#### Question 15:

**Mark (✓) against the correct answer**

The sum of two integers is 6. If one of them is −3, then the other is

(a) −9

(b) 9

(c) 3

(d) −3

#### Answer:

(b) 9

Let the other integer be *a*. Then, we have:

−3 + *a *= 6

*∴ a* = 6 − (−3) = 9

#### Page No 13:

#### Question 16:

**Mark (✓) against the correct answer**

The sum of two integers is −4. If one of them is 6, then the other is

(a) −10

(b) 10

(c) 2

(d) −2

#### Answer:

(a) −10

Let the other integer be* a.* Then, we have:

6 + *a* = −4

*∴ a* = −4 − 6 = −10

Hence, the other integer is −10.

#### Page No 13:

#### Question 17:

*Mark (✓) against the correct answer*

The sum of two integers is 14. If one of them is −8, then the other is

(a) 22

(b) −22

(c) 6

(d) −6

#### Answer:

(a) 22

Let the other integer be *a*. Then, we have:

−8 + *a* = 14

∴ *a* = 14 + 8 = 22

Hence, the other integer is 22.

#### Page No 13:

#### Question 18:

**Mark (✓) against the correct answer**

The additive inverse of −6 is

(a) $\frac{1}{6}$

(b) $-\frac{1}{6}$

(c) 6

(d) 5

#### Answer:

(c) 6

The additive inverse of any integer *a* is −*a**.*

Thus, the additive inverse of −6 is 6.

#### Page No 14:

#### Question 19:

*Mark (✓) against the correct answer*

(−15) × 8 + (−15) × 2 = ?

(a) 150

(b) −150

(c) 90

(d) −90

#### Answer:

(b) −150

We have (−15) × 8 + (−15) × 2

= (−15) × (8 + 2) [Associative property]

= −150

#### Page No 14:

#### Question 20:

*Mark (✓) against the correct answer*

(−12) × 6 −(−12) × 4 = ?

(a) 24

(b) −24

(c) 120

(d) −120

#### Answer:

(b) −24

We have (−12) × 6 − (−12) × 4

= (−12) × (6 − 4) [Associative property]

= −24

#### Page No 14:

#### Question 21:

*Mark (✓) against the correct answer*

(−27) × (−16) + (−27) × (−14) = ?

(a) −810

(b) 810

(c) −54

(d) 54

#### Answer:

(b) 810

(−27) × (−16) + (−27) × (−14)

= (−27) × (−16 + (−14)) [Associative property]

=(−27) × (−30)

= 810

#### Page No 14:

#### Question 22:

**Mark (✓) against the correct answer**

30 × (−23) + 30 × 14 = ?

(a) −270

(b) 270

(c) 1110

(d) −1110

#### Answer:

(a) −270

30 × (−23) + 30 × 14

= 30 × (−23 + 14) [Associative property]

= 30 × (−9)

= −270

#### Page No 14:

#### Question 23:

**Mark (✓) against the correct answer**

The sum of two integers is 93. If one of them is −59, the other one is

(a) 34

(b) −34

(c) 152

(d) −152

#### Answer:

(c) 152

Let the other integer be *a. *Then, we have:

−59 +* a* = 93

*∴ a* = 93 + 59 = 152

#### Page No 14:

#### Question 24:

**Mark (✓) against the correct answer**

(?) ÷ (−18) = −5

(a) −90

(b) 90

(c) none of these

#### Answer:

(b) 90

$x\xf7(-18)=-5\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{-18}=-5\phantom{\rule{0ex}{0ex}}\therefore x=-18\times -5=90$

#### Page No 15:

#### Question 1:

The sum of two integers is −12. If one of them is 43, find the other.

#### Answer:

Let the other integer be *a*. Then, we have:

*a* + (−12) = 43

⇒* a* = 43 − (−12) = 55

Hence, the other integer is 55.

#### Page No 15:

#### Question 2:

The difference of an integer *p* and −8 is 3. Find the value of *p*.

#### Answer:

Given:

*p* − (−8)= 3

⇒ *p* = 3 + (−8)

⇒ *p *= −5

Hence, the value of *p* is −5.

#### Page No 15:

#### Question 3:

Add the product of (−16) and (−9) to the quotient if (−132) by 6.

#### Answer:

Product of (−16) and (−9) = $(-16)\times (-9)$ = 144

Now, $(-132)\xf76$ gives the quotient −22.

∴ 144 + (−22) = 122

#### Page No 15:

#### Question 4:

By what number should (−240) be divided to obtain 16?

#### Answer:

Suppose that *a* divides −240 to obtain 16. Then, we have:

(−240) $\xf7$ *a* = 16

⇒ *a* = (−240) $\xf7$ 16 = −15

Hence, −15 should divide −240 to obtain 16.

#### Page No 15:

#### Question 5:

What should be divided by (−7) to obtain 12?

#### Answer:

Let *a* be divided by (−7) to obtain 12. Then, we have:

$a\xf7(-7)=12$

⇒ *a* = $-\frac{7}{12}$

Hence, $-\frac{7}{12}$ should be divided by −7 to obtain 12.

#### Page No 15:

#### Question 6:

Evaluate:

(i) (−6) × (−15) × (−5)

(ii) (−8) × (−5) × 9

(iii) 9 × (−12) × 10

(iv) (−75) × 8

(v) (−5) × (−5) × (−5) ...... taken 5 times

(vi) (−1) × (−1) × (−1) ×...... taken 25 times

#### Answer:

(i) −450

(ii) 360

(iii) −1080

(iv) −600

(v) $(-5{)}^{5}=-3125$

(vi) $(-1{)}^{25}=-1$

#### Page No 15:

#### Question 7:

Evaluate

(i) (−16) × 12 + (−16) × 8

(ii) 25 × (−33) + 25 × (−17)

(iii) (−19) × (−25) + (−19) × (−15)

(iv) (−47) × 68 − (−47) × 38

(v) (−105) ÷ 21

(vi) (−168) ÷ (−14)

(vii) 0 ÷ (−34)

(viii) 37 ÷ 0

#### Answer:

(i) (−16) × 12 + (−16) × 8

= (−16) × (12 + 8) [Associative property]

= (−16) × 20

= −320

(ii) 25 × (−33) + 25 × (−17)

= 25 × ((−33) + (−17)) [Associative property]

= 25 × (−50) = −1250

(iii) (−19) × (−25) + (−19) × (−15)

= (−19) × ((−25) + (−15)) [Associative property]

= (−19) × (−40) = 760

(iv) (−47) × 68 − (−47) × 38

= (−47) × (68 − 38) [Associative property]

= (−47) × 30 = −1410

(v) (−105) ÷ 21 = −5

(vi) 12

(vii) 0 (zero). Dividing 0 by any integer gives 0.

(vii) Not defined. Dividing any integer by zero is not defined.

#### Page No 15:

#### Question 8:

**Mark (✓) against the correct answer**

The sum of two integers is −6. If one of them is 2, then the other is

(a) −4

(b) 4

(c) 8

(d) −8

#### Answer:

(d) −8

Let the other integer be *a*. Then, we have:

2 + *a* = −6

⇒ *a* = −6 − 2 = −8

∴ The other integer is −8.

#### Page No 15:

#### Question 9:

**Mark (✓) against the correct answer**

What must be subtracted from −7 to obtain −15?

(a) −8

(b) 8

(c) −22

(d) 22

#### Answer:

(b) 8

Suppose that *a* is subtracted from −7. Then, we have:

−7 − *a* = −15

*a* = −7 + 15 = 8

∴ 8 must be subtracted from −7 to obtain −15.

#### Page No 15:

#### Question 10:

**Mark (✓) against the correct answer**

(?) ÷ (−18) = −6

(a) −108

(b) 108

(c) 3

(d) none of these

#### Answer:

(b)108

(108) ÷ (−18) = −6

#### Page No 15:

#### Question 11:

**Mark (✓) against the correct answer**

(−37) × (−7) + (−37) × (−3) = ?

(a) 370

(b) −370

(c) 148

(d) −148

#### Answer:

(a) 370

We have:

(−37) × (−7) + (−37) × (−3)

= (−37) × {(−7) + (−3)} [Associative property]

= (−37) × (−10)

= 370

#### Page No 15:

#### Question 12:

**Mark (✓) against the correct answer**

(−25) × 8 + (−25) × 2 = ?

(a) 250

(b) 150

(c) −250

(d) −150

#### Answer:

(c) −250

(−25) × 8 + (−25) × 2

= (−25) × (8 + 2) [Associative property]

= −250

#### Page No 15:

#### Question 13:

**Mark (✓) against the correct answer**

(−9) − (−6) = ?

(a) −15

(b) −3

(c) 3

(d) 15

#### Answer:

(b) −3

(−9) − (−6)

= (−9) + 6

= −3

#### Page No 15:

#### Question 14:

**Mark (✓) against the correct answer**

How much less than −2 is −8?

(a) 6

(b) −6

(c) 10

(d) −10

#### Answer:

(b) −6

−8 − (−6) = 2

Hence, −8 is −6 less than −2.

#### Page No 15:

#### Question 15:

**Fill in the blanks.**

(i) (−35) × ... = 35

(ii) (−53) × (...) = −53

(iii) (−14) × (...) = (−16) × (−14)

(iv) (−21) × (...) = 0

(v) (−119) ÷ 17 = (...)

(vi) (−247) ÷ (...) = 13

(vii) (...) ÷ 31 = 0

(viii) (...) ÷ (−19) = −8

#### Answer:

(i) −1

(ii) 1

(iii) (−16) [Commutative property]

(iv) 0 [Property of zero]

(v) −7

(vi) −19

(vii) 0

(viii) 152

#### Page No 15:

#### Question 16:

**Write 'T' for true and 'F' for false for each of the following:**

(i) 0 ÷ (−16) = 0

(ii) (−8) ÷ 0 = 0

(iii) (−1) ÷ (−1) = −1

(iv) (−36) ÷ (−1) = 36

(v) (−52) ÷ 13 = −4

(vi) 68 ÷ (−17) = 4

#### Answer:

(i) True (T).

(ii) False (F). Dividing any integer by zero is not defined.

(iii) False (F). (−1) ÷ (−1) = 1

(iv) True (T).

(v) True (T).

(vi) False (T). 68 ÷ (−17) = −4

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