Page 14 - Start Up Mathematics_7

Example 9: Write down a pair of integers whose:

(a) sum is –4 (b) difference is –10 (c) sum is 0
Solution: One such pair could be

(a) –7 and 3 (b) 3 and 13 (c) –2 and 2

There are infinite pairs of integers satisfying the above cases.

Example 10: (a) Write a pair of negative integers whose difference is 7.

(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 –5.

Solution: (a) –3 and –10,  –3 – (–10) = –3 + 10 = 7.
(b) –8 and 3,  –8 + 3 = –(8 – 3) = –5.

(c) –4 and +1,  –4 – (+1) = –4 – 1 = –5.

There are infinite pairs of integers satisfying the above cases.

Example 11: In a quiz, team A scored –40, 50, 0 and team B scored 50, 0, –40 in three successive
rounds. Which team scored more? Can integers be added in any order?
Solution: Total score of team ‘A’ = –40 + 50 + 0 = (–40 + 50) + 0 = 10 + 0 = 10

Total score of team ‘B’ = 50 + 0 – 40 = 50 + {0 + (–40)} = 50 – 40 = 10
Thus, the score of both the teams is same.

Yes, we can add integers in any order.
Example 12: Fill in the blanks to make the following statements true:

(a) (–3) + (–7) = (–7) + (...........) (b) –28 + ........... = 0

(c) 19 + (...........) = 0 (d) {9 + (–12)} + (...........) = 9 + {(–12) + (–7)}
Solution: (a) –3 (b) 28 (c) –19 (d) –7

EXERCISE 1.2

1. Write down a pair of integers whose:

(a) sum is –9 (b) difference is –18 (c) sum is –1
2. Write a negative integer and a positive integer whose sum is –15.

3. Write a negative integer and a positive integer whose difference is 11.
4. In a quiz, team A scored 20, –10, 34 and team B scored –10, 20, 34 in three successive
rounds. Which team scored more?

Multiplication of Integers

We all know how to multiply natural numbers. Now we will learn how to multiply two integers. In
fact multiplication of integers is equal to repeated addition. We will use number line to understand
multiplication of integers.

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