**Integers**

**Question 1.****Write down a pair of integers whose:(a)** The sum is – 7

**(b)**Difference is -10

**(c)**Sum is 0

**Solution.****(a)** A pair of integers whose sum is – 7 can be (- 1) and (- 6).

∵ (- 1) + (- 6) = – 7**(b)** A pair of integers whose difference is -10 can be (- 11) and (- 1)

∵ – 11 – (- 1) = – 11 + 1 = – 10**(c)** A pair of integers whose sum is 0 can be 1 and (- 1).

∵ (- 1) + (1) = 0.

**Question 2.****(a)** Write a pair of negative integers whose difference gives 8.**(b)** Write a negative integer and a positive integer whose sum is – 5.**(c)** Write a negative integer and a positive integer whose difference is – 3.

**Solution.****(a)** A pair of negative integers whose difference gives 8 can be – 12 and – 20.

∵ (-12) – (- 20) = -12 + 20 = 8 .**(b)** A negative integer and a positive integer whose sum is -5 can be – 13 and 8.

∵ (- 13) + 8 = -13 + 8 = – 5**(c)** A negative integer and a positive integer whose difference is -3 can be – 1 and 2.

∵ (- 1) – 2 = – 1 – 2 = – 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.**

Total scores of team A = (- 40) + 10 + 0

= – 40 + 10 + 0 = – 30

and, total scores of team B = 10 + 0 + (- 40)

= 10 + 0 – 40 = – 30

Since the total scores of each team are equal.

∴ No team scored more than the other but each has an equal score.

Yes, integers can be added in any order and the result remains unaltered. For example, 10 + 0 + (- 40) = – 30 = – 40 + 0 + 10

**Question 4.****Fill in the blanks to make the following statements true:(i)** (- 5) + (- 8) = (- 8) + (………)

**(ii)**– 53 + ……. = – 53

**(iii)**17 + …… = 0

**(iv)**[13 + (- 12)] + (……) = 13 + [(- 12) + (- 7)]

**(v)**(- 4) + [15 + (- 3)] = [- 4 + 15] + ……

**Solution.****(i)** (- 5) + (- 8) = (- 8) + (- 5)**(ii)** – 53 + 0 = – 53**(iii)** 17 + (-17) = 0**(iv)** [13 + (- 12)] + (- 7) = (13) + [(- 12) + (- 7)]**(v)** (- 4) + [15 + (- 3)] = [(- 4 ) + 15] + (- 3)