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#### Question 1:

Evaluate:

(i) 15 + (−8)
(ii) (−16) + 9
(iii) (−7) + (−23)
(iv) (−32) + 47
(v) 53 + (−26)
(vi) (−48) + (−36)

(i) 15 + (−8) = 7

(ii) (−16) + 9 = −7

(iii) (−7) + (−23) = −30

(iv) (−32) + 47 = 15

(v) 53 + (−26) = 27

(vi) (−48) + (−36) = −84

#### 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

(i) 153 + (−302) = −149

(ii)  1005 + (−277) = 728

(iii) (−2035) + 297 = −1738

(iv)  (−489) + (−324) = −813

(v)  (−1000) + 438 = −562

(vi) (−238) + 500 = 262

#### Question 3:

(i) − 83
(ii) 256
(iii) 0
(iv) − 2001

(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

#### 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

(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

#### Question 5:

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

Sum of −1032 and 878 = −1032 + 878
= -154

Subtracting the sum from −34, we get
−34 − (−154)
= (−34)+ 154
= 120

#### Question 6:

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

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

#### 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

(i) −41   (∵ Associative property)

(ii) −83   (∵ Associative property)

(iii)  53  (∵ Commutative property)

(iv)  −76  (∵ Commutative property)

(vii)  (−60) − (−59) = −1

(viii)  (−40) − (−31) = −9

#### Question 8:

Simplify:

{−13−(−27)} + {−25−(−40)}.

{−13 − (−27)} + {−25 − (−40)}
= {−13 + 27} + {−25 + 40}
=14 + 15
= 29

#### Question 9:

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

36 − (−64) = 36 + 64 = 100

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

Here, 100 $\ne$ −100

Thus, they are not equal.

#### Question 10:

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

(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]

#### Question 11:

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

Here, (a − b) = −9 − (−6) = −3

Similarly, (b − a) = −6 − (−9) = 3

∴ (a−b) ≠ (b−a)

#### Question 12:

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

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

53 + a = −16
a = −16 − 53 = −69

∴ The other integer is −69.

#### Question 13:

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

Let the other integer be a.
Then, −31 + a = 65
⇒ a = 65 − (−31) = 96

∴ The other integer is 96.

#### Question 14:

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

We have:

a − (−6) = 4
a = 4 + (−6) = −2

a = −2

#### 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.

(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.

#### 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.

(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

#### 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

(i) 16 $×$ 9 = 144
(ii) 18 $×$ (−6) = −108
(iii) 36 $×$ (−11) = −396
(iv)  (−28) $×$14 = −392
(v) (−53) $×$ 18 = −954
(vi) (−35) $×$ 0 = 0
(vii) 0 $×$ (−23) = 0
(viii) (−16) $×$ (−12) = 192
(ix) (−105) $×$ (−8) = 840
(x) (−36) $×$ (−50) = 1800
(xi) (−28) $×$ (−1) = 28
(xii)  25 $×$ (−11) = −275

#### 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

(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

#### 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

(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.
$\left(-3{\right)}^{6}$ = 729
(vi) Since the number of negative integers in the product is odd, the product will be negative.
$\left(-5{\right)}^{5}$ = −3125
(vii) Since the number of negative integers in the product is even, the product will be positive.
$\left(-1{\right)}^{200}$= 1
(viii) Since the number of negative integers in the product is odd, the product will be negative.
$\left(-1{\right)}^{171}$ = −1

#### Question 4:

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

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.

#### Question 5:

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

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.

#### 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

(i) (−8) $×$ (9 + 7)   [using the distributive law]
= (−8) $×$ 16 = −128

(ii)  9 $×$ (−13 + (−7))  [using the distributive law]
= 9 $×$ (−20) = −180

(iii)  20 $×$ (−16 + 14)    [using the distributive law]
= 20 $×$ (−2) = −40

(iv) (−16) $×$ (−15 + (−5))  [using the distributive law]
= (−16) $×$ (−20) = 320

(v) (−11) $×$ (−15 +(−25))  [using the distributive law]
= (−11) $×$ (−40)
= 440

(vi) (−12) $×$ (10 + 5)   [using the distributive law]
= (−12) $×$ 15 = −180

(vii) (−16 + (−4)) $×$ (−8)  [using the distributive law]
= (−20) $×$ (−8) = 160

(viii) (−26) $×$ (72 + 28)    [using the distributive law]
= (−26) $×$100 = −2600

#### 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

(i) (−6) × (x) = 6

Thus, x = (−1)

(ii) 1      [∵ Multiplicative identity]
(iii) (−8)      [∵ Commutative law]
(iv) 7         [∵ Commutative law]
(v) (−5)   [∵ Associative law]
(vi) 0    [∵ Property of zero]

#### 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?

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

Now, we have the following:

(i) Ravi's score = 4 $×$ 5 + 6 $×$ (−2)
= 20 + (−12) =8

(ii) Reenu's score = 5 $×$ 5 + 5 $×$ (−2)
= 25 − 10 = 15

(iii) Heena's score = 2 $×$ 5 + 5 $×$ (−2)
= 10 − 10 = 0

#### 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.

(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 $×$ (−1) = −a, which is not the multiplicative inverse of a.
(v) True. a $×$ b = b $×$ a
(vi) True. (a $×$ b) $×$ c = a $×$ (b $×$ c)
(vii) False. Every non-zero integer a has a multiplicative inverse $\frac{1}{a}$, which is not an integer.

#### 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

(i) 65 $÷$ (−13) = −5

(ii) (−84) $÷$ 12 =  −7

(iii) (−76) $÷$ 19 = −4

(iv) (−132) $÷$ 12 = −11

(v) (−150) $÷$ 25 = −6

(vi) (−72) $÷$ (−18) =

(vii)  (−105) $÷$ (−21) = 5

(viii) (−36) $÷$ (−1) = 36

(ix) 0 $÷$ (−31) =  0

(x)  (−63) $÷$ 63 = −1

(xi)  (−23) $÷$ (−23) = 1

(xii) (−8) $÷$ 1 =  −8

#### 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

(i)
72 ÷ (x) = −4

(ii)
−36 ÷ (x) = −4

(iii)
(x) ÷ (−4) = 24

(iv)
(x) ÷ 25 = 0

(v)
(x) ÷ (−1) = 36

(vi)
(x) ÷ 1 = −37

(vii)
39 ÷ (x) = −1

(viii)
1 ÷ (x) = −1

(ix)
−1 ÷ (x) = −1

#### 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

(i) True (T). Dividing zero by any integer gives zero.
(ii) False (F). Division by zero gives an indefinite number.

(iii) False (F).

(iv)  True (T).

(v)  False (F).

(vi) True (T).

#### Question 1:

Mark (✓) against the correct answer

6 − (−8) = ?

(a) −2
(b) 2
(c) 14
(d) none of these

(c) 14
Given:
6 − (−8)
= 6 + 8
= 14

#### Question 2:

Mark (✓) against the correct answer
−9 − (−6) = ?

(a) −15
(b) −3
(c) 3
(d) none of these

(b) −3
Given:
−9 − (−6)
= −9 + 6
= −3

#### Question 3:

Mark (✓) against the correct answer
By how much does 2 exceed −3?

(a) −1
(b) 1
(c) −5
(d) 5

(d) 5
We can see that

−3 + 5 = 2

Hence, 2 exceeds −3 by 5.

#### Question 4:

Mark (✓) against the correct answer
What must be subtracted from −1 to get −6?

(a) 5
(b) −5
(c) 7
(d) −7

(a)  5
Let the number to be subtracted be x.
To find the number, we have:
−1 − x = −6
x = −1 + 6 = 5

#### Question 5:

Mark (✓) against the correct answer
How much less than −2 is −6?

(a) 4
(b) −4
(c) 8
(d) −8

(c) 4
We can see that
(−2) − (−6) = (−2) + 6 = 4

Hence, −6 is four (4) less than −2.

#### Question 6:

Mark (✓) against the correct answer
On subtracting 4 from −4, we get

(a) 8
(b) −8
(c) 0
(d) none of these

(b) −8
Subtracting 4 from −4, we get:
(−4) − 4 = −8

#### Question 7:

Mark (✓) against the correct answer
By how much does −3 exceed −5?

(a) −2
(b) 2
(c) 8
(d) −8

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

#### Question 8:

Mark (✓) against the correct answer
What must be subtracted from −3 to get −9?

(a) −6
(b) 12
(c) 6
(d) −12

(c) 6
(−3) − x = −9
∴ x = (−3) + 9 = 6
Hence, 6 must be subtracted from −3 to get −9.

#### Question 9:

Mark (✓) against the correct answer
On subtracting 6 from −5, we get

(a) 1
(b) 11
(c) −11
(d) none of these

(c) −11
Subtracting 6 from −5, we get:
(−5) − 6 = −11

#### Question 10:

Mark (✓) against the correct answer
On subtracting −13 from −8, we get

(a) −21
(b) 21
(c) 5
(d) −5

(c) 5
Subtracting −13 from −8, we get:
(−8) − (−13)
= −8 + 13
= 5

#### Question 11:

Mark (✓) against the correct answer
(−36) ÷ (−9) = ?

(a) 4
(b) −4
(c) none of these

(a) 4
(−36) ÷ (−9) = 4

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

#### Question 12:

Mark (✓) against the correct answer
0 ÷ (−5) = ?

(a) −5
(b) 0
(c) not defined

(b) 0
Dividing zero by any integer gives zero as the result.

#### Question 13:

Mark (✓) against the correct answer
(−8) ÷ 0 = ?

(a) −8
(b) 0
(c) not defined

(c) not defined

Dividing any integer by zero is not defined.

#### 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

(b) −11 < −8

Negative integers decrease with increasing magnitudes.

#### 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

(b) 9

Let the other integer be a. Then, we have:
−3 + a = 6
∴ a = 6 − (−3) = 9

#### 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

(a) −10
Let the other integer be a. Then, we have:
6 + a = −4
∴ a = −4 − 6 = −10

Hence, the other integer is −10.

#### 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

(a) 22
Let the other integer be a. Then, we have:
−8 + a = 14
a = 14 + 8 = 22

Hence, the other integer is 22.

#### 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

(c) 6

The additive inverse of any integer a is −a.
Thus, the additive inverse of −6 is 6.

#### Question 19:

Mark (✓) against the correct answer
(−15) × 8 + (−15) × 2 = ?

(a) 150
(b) −150
(c)  90
(d)  −90

(b) −150
We have (−15) × 8 + (−15) × 2
= (−15) × (8 + 2)    [Associative property]
= −150

#### Question 20:

Mark (✓) against the correct answer
(−12) × 6 −(−12) × 4 = ?

(a) 24
(b) −24
(c) 120
(d) −120

(b) −24
We have (−12) × 6 − (−12) × 4
= (−12) × (6 − 4)       [Associative property]
= −24

#### Question 21:

Mark (✓) against the correct answer
(−27) × (−16) + (−27) × (−14) = ?

(a) −810
(b) 810
(c) −54
(d) 54

(b) 810
(−27) × (−16) + (−27) × (−14)
= (−27) × (−16 + (−14))    [Associative property]
=(−27) × (−30)
= 810

#### Question 22:

Mark (✓) against the correct answer
30 × (−23) + 30 × 14 = ?

(a) −270
(b) 270
(c) 1110
(d) −1110

(a)  −270
30 × (−23) + 30 × 14
= 30 × (−23 + 14)     [Associative property]
=  30 × (−9)
= −270

#### 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

(c) 152
Let the other integer be a. Then, we have:
−59 + a = 93
∴ a = 93 + 59 = 152

#### Question 24:

Mark (✓) against the correct answer
(?) ÷ (−18) = −5

(a) −90
(b) 90
(c) none of these

(b) 90

#### Question 1:

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

Let the other integer be a. Then, we have:
a + (−12) = 43
a = 43 − (−12) = 55

Hence, the other integer is 55.

#### Question 2:

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

Given:
p − (−8)= 3
p = 3 + (−8)
p = −5

Hence, the value of p is −5.

#### Question 3:

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

Product of (−16) and (−9) = = 144
Now, gives the quotient −22.

∴ 144 + (−22) = 122

#### Question 4:

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

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

(−240) $÷$ a = 16
a = (−240) $÷$ 16 = −15

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

#### Question 5:

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

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

$a÷\left(-7\right)=12$
a = $-\frac{7}{12}$

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

#### 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

(i) −450
(ii)  360
(iii) −1080
(iv)  −600
(v)

(vi)

#### 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

(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.

#### 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

(d) −8
Let the other integer be a. Then, we have:
2 + a = −6
a = −6 − 2 = −8

∴ The other integer is −8.

#### Question 9:

Mark (✓) against the correct answer
What must be subtracted from −7 to obtain −15?

(a) −8
(b) 8
(c) −22
(d) 22

(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.

#### Question 10:

Mark (✓) against the correct answer
(?) ÷ (−18) = −6

(a) −108
(b) 108
(c) 3
(d) none of these

(b)108

(108) ÷ (−18) = −6

#### Question 11:

Mark (✓) against the correct answer
(−37) × (−7) + (−37) × (−3) = ?

(a) 370
(b) −370
(c) 148
(d) −148

(a) 370
We have:

(−37) × (−7) + (−37) × (−3)
= (−37) × {(−7) + (−3)}  [Associative property]
= (−37) × (−10)
= 370

#### Question 12:

Mark (✓) against the correct answer
(−25) × 8 + (−25) × 2 = ?

(a) 250
(b) 150
(c) −250
(d) −150

(c) −250

(−25) × 8 + (−25) × 2
= (−25) × (8 + 2)  [Associative property]
= −250

#### Question 13:

Mark (✓) against the correct answer
(−9) − (−6) = ?

(a) −15
(b) −3
(c) 3
(d) 15

(b) −3

(−9) − (−6)
= (−9) + 6
= −3

#### Question 14:

Mark (✓) against the correct answer
How much less than −2 is −8?

(a) 6
(b) −6
(c) 10
(d) −10

(b) −6

−8 − (−6) = 2

Hence, −8 is −6 less than −2.

#### 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

(i)  −1
(ii)  1
(iii) (−16)   [Commutative property]
(iv) 0   [Property of zero]
(v)  −7
(vi)  −19
(vii)  0
(viii) 152

#### 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