Rs Aggarwal 2018 for Class 7 Math Chapter 1 - Integers

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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 $\neq$ −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 $\div$ (−13) = $\frac{65}{- 13} =$ −5

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

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

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

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

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

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

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

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

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

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

(xii) (−8) $\div$ 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
$\Rightarrow \frac{72}{x} = - 4 \Rightarrow x = \frac{72}{- 4} = - 18$

(ii)
−36 ÷ (x) = −4
$\Rightarrow \frac{- 36}{x} = - 4 \Rightarrow x = \frac{- 36}{- 4} = 9$

(iii)
(x) ÷ (−4) = 24
$\Rightarrow \frac{x}{- 4} = 24 \Rightarrow x = 24 \times (- 4) = - 96$

(iv)
(x) ÷ 25 = 0
$\Rightarrow \frac{x}{25} = 0 \Rightarrow x = 25 \times 0 = 0$

(v)
(x) ÷ (−1) = 36
$\Rightarrow \frac{x}{- 1} = 36 \Rightarrow x = 36 \times (- 1) = - 36$

(vi)
(x) ÷ 1 = −37
$\Rightarrow \frac{x}{1} = - 37 \Rightarrow x = - 37 \times 1 = - 37$

(vii)
39 ÷ (x) = −1
$\Rightarrow \frac{39}{x} = - 1 \Rightarrow x = - 1 \times 39 = - 39$

(viii)
1 ÷ (x) = −1
$\Rightarrow \frac{1}{x} = - 1 \Rightarrow x = - 1 \times 1 = - 1$

(ix)
−1 ÷ (x) = −1
$\Rightarrow \frac{- 1}{x} = - 1 \Rightarrow x = \frac{- 1}{- 1} = 1$

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:

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:

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:

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:

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:

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:

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:

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:

Page No 14:

Question 24:

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

(a) −90
(b) 90
(c) none of these

Answer:

(b) 90

$x \div (- 18) = - 5 \Rightarrow \frac{x}{- 18} = - 5 ∴ x = - 18 \times - 5 = 90$

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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.

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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.

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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, $(- 132) \div 6$ gives the quotient −22.

∴ 144 + (−22) = 122

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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) $\div$ a = 16
⇒ a = (−240) $\div$ 16 = −15

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

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Question 5:

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

Answer:

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

$a \div (- 7) = 12$
⇒ a = $- \frac{7}{12}$

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

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

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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.

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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.

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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

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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

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Question 12:

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

(a) 250
(b) 150
(c) −250
(d) −150

Answer:

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

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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.

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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

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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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