Chapter 5: Negative Numbers and Integers – Exercise 5.3

Negative Numbers and Integers – Exercise – 5.3 – Q.1

Ans. 

(i) Additive inverse of 52 is -52.

(ii) 176

(iii) 0

(iv) -1

Negative Numbers and Integers – Exercise – 5.3 – Q.2

Ans. 

(i) Success - or – 42 is = – 42 + (-1)

= 1- 42

= – 41

(ii) -1 + 1 = 0

(iii) 0 + 1 =1

(iv) – 200 + 1 = –199

(v) – 99 + 1 = –98.

Negative Numbers and Integers – Exercise – 5.3 – Q.3

Ans. 

(i) predecessor of 0 is ⟹ 0 -1 = -1

(ii) 1 - 1 = 0

(iii) -1 -1 = -2

(iv) -125 -1 = -126

(v) 1000 -1 = 999

 

Negative Numbers and Integers – Exercise – 5.3 – Q.4

Ans. 

(i) True

(ii) False

(iii) False

(iv) False

(v) False

 

Negative Numbers and Integers – Exercise – 5.3 – Q.5

Ans. 

Integers whose absolute values less than 5 are

– 4, – 3, – 2, – 1, 0, 1, 2, 3, 4.

 

Negative Numbers and Integers – Exercise – 5.3 – Q.6

Ans. 

(i) True

(ii) False

(iii) True

(iv) True

 

Negative Numbers and Integers – Exercise – 5.3 – Q.7

Ans. 

+	- 6	- 4	- 2	0	2	4	6
6	0	2	4	6	8	10	12
4	- 2	0	2	4	6	8	10
2	- 4	- 2	0	2	4	6	8
0	- 6	-4	- 2	4	2	4	6
- 2	- 8	-6	- 4	- 2	0	2	4
- 4	- 10	-8	- 6	- 4	- 2	0	2
- 6	- 12	-10	- 8	- 6	- 4	- 2	0

(i) (+6, -6), (4, -4), (3, -3), (2, -2), (1, -1), (0, 0)

(ii) yes by commutativity of Addition

(-4) + (-2) = (-2) + (-4)

(iii) By existence of additive identity

0 + (-6) = -6 [∵ 0 + a = a]

 

Negative Numbers and Integers – Exercise – 5.3 – Q.8

Ans. 

(i) x +1 = 0

⟹ x + 1 - 1 = 0 - 1 [subtract ∵ on both sides]

⟹ x = -1

(ii) x + 5 = 0

x + 5 - 5 = 0 - 5

x + 0 = -5

⟹ x = -5

(iii) -3 + x = 0

3 - 3 + x = 0 + 3

x = 3

(iv) x + (-8) = 0

x - 8 = 0

x - 8 + 8 = 0 + 8

x = 8

(v) 7 + x = 0

⟹ 7 + x - 7 = 0 - 7

⟹ x = - 7

(vi) x + 0 = 0

x = 0.