RS Aggarwal Solutions: Integers (Exercise 1D) | Mathematics (Maths) Class 7 PDF Download

Q.1. 6 − (−8) = ?
(a) −2
(b) 2
(c) 14
(d) none of these
Ans. (c) 14
Given: 6 − (−8)
= 6 + 8
= 14

Q.2. −9 − (−6) = ?
(a) −15
(b) −3
(c) 3
(d) none of these
Ans. (b) −3
Given: −9 − (−6)
= −9 + 6
= −3

Q.3. By how much does 2 exceed −3?
(a) −1
(b) 1
(c) −5
(d) 5
Ans. (d) 5
We can see that
−3 + 5 = 2
Hence, 2 exceeds −3 by 5.

Q.4. What must be subtracted from −1 to get −6?
(a) 5
(b) −5
(c) 7
(d) −7
Ans. (a)  5
Let the number to be subtracted be x.
To find the number, we have:
−1 − x = −6
∴ x = −1 + 6 = 5

Q.5. How much less than −2 is −6?
(a) 4
(b) −4
(c) 8
(d) −8
Ans. (c) 4
We can see that
(−2) − (−6) = (−2) + 6 = 4
Hence, −6 is four (4) less than −2.

Q.6. On subtracting 4 from −4, we get
(a) 8
(b) −8
(c) 0
(d) none of these
Ans. (b) −8
Subtracting 4 from −4, we get:
(−4) − 4 = −8

Q.7. By how much does −3 exceed −5?
(a) −2
(b) 2
(c) 8
(d) −8
Ans. (b) 2
Required number = (−3) − (−5) = 5 − 3 = 2

Q.8. What must be subtracted from −3 to get −9?
(a) −6
(b) 12
(c) 6
(d) −12
Ans. (c) 6
(−3) − x = −9
∴ x = (−3) + 9 = 6
Hence, 6 must be subtracted from −3 to get −9.

Q.9. On subtracting 6 from −5, we get
(a) 1
(b) 11
(c) −11
(d) none of these
Ans. (c) −11
Subtracting 6 from −5, we get: (−5) − 6 = −11

Q.10. On subtracting −13 from −8, we get
(a) −21
(b) 21
(c) 5
(d) −5
Ans. (c) 5
Subtracting −13 from −8, we get:
(−8) − (−13)
= −8 + 13
= 5

Q.11. (−36) ÷ (−9) = ?
(a) 4
(b) −4
(c) none of these
Ans. (a) 4
(−36) ÷ (−9) = 4
Here, the negative signs in both the numerator and denominator got cancelled with each other.

Q.12. 0 ÷ (−5) = ?
(a) −5
(b) 0
(c) not defined
Ans. (b) 0
Dividing zero by any integer gives zero as the result.

Q.13. (−8) ÷ 0 = ?
(a) −8
(b) 0
(c) not defined
Ans. (c) not defined
Dividing any integer by zero is not defined.

Q.14. Which of the following is a true statement?
(a) −11 > −8
(b) −11 < −8
(c) −11 and −8 cannot be compared
Ans. (b) −11 < −8
Negative integers decrease with increasing magnitudes.

Q.15. 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
Ans. (b) 9
Let the other integer be a. Then, we have:
−3 + a = 6
∴ a = 6 − (−3) = 9

Q.16. 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
Ans. (a) −10
Let the other integer be a. Then, we have:
6 + a = −4
∴ a = −4 − 6 = −10
Hence, the other integer is −10.

Q.17. 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
Ans. (a) 22
Let the other integer be a. Then, we have:
−8 + a = 14
∴ a = 14 + 8 = 22
Hence, the other integer is 22.

Q.18. The additive inverse of −6 is
(a) 1/6
(b) −1/6
(c) 6
(d) 5
Ans. (c) 6
The additive inverse of any integer a is −a.
Thus, the additive inverse of −6 is 6.

Q.19. (−15) × 8 + (−15) × 2 = ?
(a) 150
(b) −150
(c)  90
(d)  −90
Ans. (b) −150
We have (−15) × 8 + (−15) × 2
= (−15) × (8 + 2)    [Associative property]
= −150

Q.20. (−12) × 6 −(−12) × 4 = ?
(a) 24
(b) −24
(c) 120
(d) −120
Ans. (b) −24
We have (−12) × 6 − (−12) × 4
= (−12) × (6 − 4) [Associative property]
= −24

Q.21. (−27) × (−16) + (−27) × (−14) = ?
(a) −810
(b) 810
(c) −54
(d) 54
Ans. (b) 810
(−27) × (−16) + (−27) × (−14)
= (−27) × (−16 + (−14)) [Associative property]
=(−27) × (−30)
= 810

Q.22. 30 × (−23) + 30 × 14 = ?
(a) −270
(b) 270
(c) 1110
(d) −1110
Ans. (a)  −270
30 × (−23) + 30 × 14
= 30 × (−23 + 14) [Associative property]
=  30 × (−9)
= −270

Q.23. 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
Ans. (c) 152
Let the other integer be a. Then, we have:
−59 + a = 93
∴ a = 93 + 59 = 152

Q.24. (?) ÷ (−18) = −5
(a) −90
(b) 90
(c) none of these
Ans. (b) 90
x ÷ (−18) = −5
⇒x/−18 = −5
∴ x = −18 ×−5 = 90