Ex 1.1 Chapter 1 INTEGERS
Question 1: Write down a pair of integers whose: (a) sum is –7
Solution:
(i) -7 and 0
-7 + 0
= -7
(ii) -2 and -5
-2 + (-5)
= -2 - 5
= -(2 + 5)
= -7
Question 1: Write down a pair of integers whose: (b) difference is –10
Solution:
(i) -10 and 0
= -10 - 0
= -10
(ii) -5 and 5
= -5 - 5
= - (5 + 5)
= -10
Question 2 (a): Write a pair of negative integers whose difference gives 8.
Solution:
(i) -4 and -12
= -4 - (-12)
= -4 + 12
= 12 - 4
= 8
(ii) -2 and -10
-2 - (-10)
= -2 + 10
= 10 - 2
= 8
Question 2 (b): Write a negative integer and a positive integer whose sum is –5
Solution:
(i) 2 and -7
= 2 + (-7)
= 2 - 7
= -(-2 + 7)
= -(7 - 2)
= -5
(ii) -6 and 1
= -6 + 1
= - (6 - 1)
= -5
Question 2 (c): Write a negative integer and a positive integer whose difference is –3.
Solution:
(i) -1 and 2
= -1 - 2
= -(1 + 2)
= -3
(ii) -2 and 1
-2 - 1
= - (2 + 1)
= -3
Question 3: In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0, – 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?
Solution:
Team A Total score of Team A = -40 + 10 + 0
= -40 + 10
= -(40 -10)
= -30
Team B Total score of Team B = 10 + 0 + (-40)
= 10 – 40
= -(-10 + 40)
= -(40 - 10)
= -30
∴ Both team scored the same, -30
Note: We can add the integers in any order
Question 4: Fill in the blanks to make the following statements true:
(i) (–5) + (– 8) = (– 8) + (............)Using commutatively
Solution:
a + b = b + a
∴ (-5) + (-8) = (-8) +(-5)
(ii) –53 + ............ = –53
Solution:
a + 0 = a
-53 + 0 = -53
(iii) 17 + ............ = 0
Solution:
a + (-a) = 0
∴ 17 + (-17) = 0
(iv) [13 + (-12)] + (............) = 13 + [(-12) + (-7)]
Solution:
a + b + c = a + c + b
∴ [13 + (-12)] + (-7) = 13 + [(-12) + (-7)]
(v) (-4) + [15 + (-3)] = [-4 + 15] + ............
Solution:
a + (b + c) = (a + b) + c
∴ (-4) + [15 + (-3)] = [-4 + 15] + (-3)