Exercise 1A
Page-4Question 1:
Evaluate:
(i) 15 + (−8)
(ii) (−16) + 9
(iii) (−7) + (−23)
(iv) (−32) + 47
(v) 53 + (−26)
(vi) (−48) + (−36)
Answer 1:
(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
Answer 2:
(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:
Find the additive inverse of:
(i) − 83
(ii) 256
(iii) 0
(iv) − 2001
Answer 3:
(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
Answer 4:
(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.
Answer 5:
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.
Answer 6:
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
Answer 7:
(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
Question 8:
Simplify:
{−13−(−27)} + {−25−(−40)}.
Answer 8:
{−13 − (−27)} + {−25 − (−40)}
= {−13 + 27} + {−25 + 40}
=14 + 15
= 29
Question 9:
Find 36 − (−64) and (−64) − 36. Are they equal?
Answer 9:
36 − (−64) = 36 + 64 = 100
Now, (−64) − 36 = (−64) + (−36) = −100
Here, 100 −100
Thus, they are not equal.
Question 10:
If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c).
Answer 10:
(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).
Answer 11:
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.
Answer 12:
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.
Answer 13:
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.
Answer 14:
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.
Answer 15:
(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.
Answer 16:
(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
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