Chapter 6 Integers Ex 6.2
Question 1.
Using the number line write the integer which is:
(a) 3 more than 5
(b) 5 more than -5
(c) 6 less than 2
Solution:
(a) 3 more than 5
Moving right 3 steps from 5, we reach at 8. Hence, 3 more than 5 = 8.
(b) 5 more than -5
Moving right 5 steps from -5 we reach at 0. Hence, 5 more than -5 = 0
(c) 6 less than 2
Moving left 6 steps from 2, we reach at -4. Hence, 6 less than 2 = -4
(d) 3 less than -2
Moving left 3 steps from -2, we reach at -5.
Question 2.
Use number line and add the following integers:
(a) 9 + (-6)
(b) 5 + (-11)
(c) (-1) + (-7)
(d) (- 5) + 10
(e) (-1) + (-2) + (-3)
Solution:
(a) 9 + (- 6)
Question 3.
Add without using number line:
(а) 11 + (-7)
(b) (-13) + (+18)
(c) (-10) + (+19)
(d) (-250) + (+150)
(e) (-380) + (-270)
(f) (-217) + (-100).
Solution:
(a) 11 + (-7) = 4 + (+7) + (-7)
[∵ (+7) + (-7) = 0]
= 4 + 0 = 4
Hence, 11 + (-7) = 4.
(b) (-13) + (+18) = (-13) + (+13) + (+5)
[∵ (-13) + (+13) = 0]
= 0 + (+ 5) = 5
Hence, (- 13) + (+ 18) = 5.
(c) (-10) + (+19) = (-10) + (+10) + (+9)
[∵ (-10) + (10) = 0] = 0 + (+9) = 9
Hence, (-10) + (19) = 9.
(d) (-250) + (+150) = (-100) + (-150) + (+150)
= (-100) + 0 = -100 [∵(-150) + (+150) = 0]
Hence, (-250) + (+150) = – 100.
(e) (-380) + (-270) = – [380 + 270] = (-650)
Hence, (-380) + (-270) = (-650).
(f) (-217) + (-100) = – [217 + 100] = -317
Question 4.
Find the sum of:
(a) 137 and -354
(b) -52 and 52 .
(d) -312, 39 and 192
(d) -50, -200 and 300
Solution:
(a) 137 and -354
(137) + ( -354) = (137) + (-137) + (-217) [∵ (137) + (-137) = 0]
= 0 + (-217) = (-217)
(b) -52 and 52
(-52) + (+52) = 0 [ ∵ (-a) + (+ a) = 0]
(c) -312, 39 and 192
(-312) + (+ 39) + (+192)
= (-231) + (- 81) + (+39) + (+192)
= (-231) + (-81) + (+ 231)
= (-231) + (+ 231) + (-81)
[∵ (-a) + (a) = 0]
= 0 + (- 81) = – 81
(d) – 50, -200 and 300
(-50) + (-200) + (+ 300)
= (-50) + (-200) + (+200) + (+100)
= (-50) + 0 + (+100)[∵ (-a) + (+ a) = 0]
= (-50) + (+100)
= (-50) + (+50) + (+ 50)
= 0 + (+ 50) = 50 [ ∵ (-a) + (+ a) = 0]
Question 5.
Find the sum of:
(a) (- 7) + (-9) + 4 + 16
(b) (37) + (-2) + (-65) + (-18)
Solution:
(a) (- 7) + (-9) + 4 + 16
= (-7) + (-9) + 4 + (+ 7) + (+ 9)
= (-7) + (+7) + (-9) + (+9) + 4
= 0 + 0 + 4 = 4 [∵ (-a) + (a) = 0]
(b) (37) + (-2) + (-65) + (-8)
= (+37) + (-75)
= (+37) + (-37) + (-38)
= 0 + (-38) = (-38) [∵ (-a) + (+a) = 0]