Chapter 6 Integers Ex 6.3
Question 1.
Find:
(a) 35 – (20)
(b) 72 – (90)
(c) (-15) – (-18)
(d) (- 20) – (13)
(e) 23 – (-12)
(f) (-32) – (-40)
Solution:
(a) 35 – (20) = 15 + (20) – (20)
= 15 + 0 = 15 [(+a) + (-a) = 0]
(b) 72 – 90
72 – (72 + 18) = 72 – 72 – 18
= 0 – 18 = – 18 [a + (- a) = 0]
(c) (- 15) – (- 18)
= (- 15) + (additive inverse of – 18)
= (-15) + (18) = 3
(d) (- 20) – (13)
(- 20) – (13) = – [20 + 13] = – 33
(e) 23 – (- 12)
23 – (- 12) = 23 + (additive inverse of – 12)
= 23 + 12 = 35
(f) (- 32) – (- 40)
(- 32) + (additive inverse of – 40)
= (- 32) + 40 = 8
Question 2.
Fill in the blanks with >, < or = sign.
(a) (-3) + (-6) (-3) – (-6)
(b) (-21) – (-10) (- 31) + (-11)
(c) 45 – (-11) 57 + (-4)
(d) (-25) – (-42) (-42) – (-25)
Solution:
(a) (-3) + (-6) = – [3 + 6] = – 9 and (-3) – (-6) = (-3) + 6 = 3
Here, – 9 < 3
∴ (- 3) + (- 6) < (- 3) – (- 6)
(b) (-21) – (-10) = (-21) + 10 = -11 and (-31) + (-11) = – (31 + 11) = – 42
Here, -42 < -11 or -11 > -42 ∴ (-21) , -(-10) >(-31)+ (-11)
(c) 45 – (-11) = 45 + 11 = 56 and 57 + (-4) = 57 -4 = 53
Here, 56 >53
∴ 45 – (-11) > 57 + ( -4)
(d) (-25) – (-42) = -25 + 42 = 17
and (-42) – (-25) = -42 + 25 = -17
Here, 17 > -17
∴ (-25) – (-42) > (-42) – (-25).
Question 3.
Fill in the blanks.
(a) (-8) + …. = 0
(b) 13 + …. = 0
(c) 12 + (-12) = ….
(d) (-4) + …. = – 12
(e) …. -15 = – 10.
Solution:
(a) (-8) + (additive inverse of -8) = 0
= (-8) + (8) = 0
∴ Value of blank is 8
(b) 13 + (additive inverse of 13) = 0
= 13 + (-13) = 0
∴ Value of blank is – 13
(c) 12 + (-12) = 0 [∵ -12 is additive inverse of 12]
∴ The Value of blank is 0
(d) (-4) + (-8) = -[4 + 8] = -12
∴ Value of blank is -8.
(e) (+5) – 15 = -10
∴ Value of blank is +5.
Question 4.
Find :
(a) (-7) – 8 – (-25)
(b) (-13) + 32 – 8 – 1
(c) (-7) + (-8) + (-90)
(d) 50 – (-40) – (-2)
Solution:
(a) (-7) – 8 – (-25)
= (-7) – 8 + 25
[ ∵ Additive inverse of – 25 is 25]
= -7 + 17 = -7 + 7 +10
[∵ (-a) + (+a) = 0]
= 0 + 10 = 10.
(b) (-13) + 32 – 8 – 1
= (-13) + (13) + 19 – (8 + 1)
= 0 + 19 – 9
= 19 – 9 [∵ (-13) + (13) = 0]
= 10 + 9 – 9 = 10 + 0 = 10.
[(+9) – (+9) = 0]
(c) (-7) + (-8) + (-90) = – (7 + 8) + (-90)
= -15 + (-90)
= -(15 + 90)
= -105.
(d) 50 – (-40) – (-2)
= 50 – [- 40 – 2]
= 50 – (-42)
= 50 + 42
= 92.
