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

Q.1. Evaluate:
(i) 15 + (−8)
(ii) (−16) + 9
(iii) (−7) + (−23)
(iv) (−32) + 47
(v) 53 + (−26)
(vi) (−48) + (−36)
Ans. (i) 15 + (−8) = 7
(ii) (−16) + 9 = −7
(iii) (−7) + (−23) = −30
(iv) (−32) + 47 = 15
(v) 53 + (−26) = 27
(vi) (−48) + (−36) = −84

Q.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
Ans. (i) 153 + (−302) = −149
(ii)  1005 + (−277) = 728
(iii) (−2035) + 297 = −1738
(iv)  (−489) + (−324) = −813
(v)  (−1000) + 438 = −562
(vi) (−238) + 500 = 262

Q.3. Find the additive inverse of:
(i) − 83
(ii) 256
(iii) 0
(iv) − 2001
Ans. (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

Q.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
Ans. (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

Q.5. Subtract the sum of − 1032 and 878 from − 34.
Ans. Sum of −1032 and 878
= −1032 + 878
= -154
Subtracting the sum from −34, we get
−34 − (−154)
= (−34)+ 154
= 120

Q.6. Subtract − 134 from the sum of 38 and − 87.
Ans. 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

Q.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
Ans. (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

Q.8. Simplify: {−13−(−27)} + {−25−(−40)}.
Ans. {−13 − (−27)} + {−25 − (−40)}
= {−13 + 27} + {−25 + 40}
=14 + 15
= 29

Q.9. Find 36 − (−64) and (−64) − 36. Are they equal?
Ans. 36 − (−64) = 36 + 64 = 100
Now, (−64) − 36 = (−64) + (−36) = −100
Here, 100 ≠≠ −100
Thus, they are not equal.

Q.10. If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c).
Ans. (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]

Q.11. If a = − 9 and b = − 6, show that (a−b) ≠ (b−a).
Ans. Here, (a − b) = −9 − (−6) = −3
Similarly, (b − a) = −6 − (−9) = 3
∴ (a−b) ≠ (b−a)

Q.12. The sum of two integers is − 16. If one of them is 53, find the other.
Ans. Let the other integer be a. Then, we have: 53 + a = −16
⇒ a = −16 − 53 = −69
∴ The other integer is −69.

Q.13. Ths sum of two integers is 65. If one of them is − 31, find the other.
Ans. Let the other integer be a.
Then, −31 + a = 65
⇒ a = 65 − (−31) = 96
∴ The other integer is 96.

Q.14. The difference of an integer a and (−6) is 4. Find the value of a.
Ans. We have: a − (−6) = 4
⇒ a = 4 + (−6) = −2
∴ a = −2

Q.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.
Ans. (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.

Q.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.
Ans. (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