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)