Page 27 - ICSE Math 8

−5 7
5. By what number should be multiplied to get the product as ?
14 12
−12 3
6. By what number should be divided to get ?
35 7

−12 13 −1 31
7. Divide the sum of and by the product of and .
7 5 2 7
8 12
8. Divide the sum of and by their difference.
3 7
Rational Numbers on a Number Line
Rational numbers include positive and negative numbers besides 0. The number line representing them extends
indefi nitely on both sides of 0. We have rational numbers between –1, 0; 0, 1; 1, 2; and so on.

–4 –3 –2 –1 0 1 2 3 4
If the segment between each pair of consecutive integers is divided into two equal parts, we get the following
series of rational numbers:
− −8 −7 −6 −5 −4 −3 −2 1 0 1 2 3 4
..., , , , , , , , ,,,,, ,...
2 2 2 2 2 2 2 2 2 2 2 2 2
This series of rational numbers can be represented on a number line as follows:
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

–4 –3 –2 –1 0 1 2 3 4
If the segment between each pair of consecutive integers is divided into three equal parts, we get the following
series of rational numbers:
− −6 5 − 3 − 2 −4 − 1 0 1 2 3 4 5 6
..., , , , , , , , , , , , , , ...
3 3 3 3 3 3 3 3 3 3 3 3 3
This series of rational numbers can be represented on a number line as follows.
–9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

–3 –2 –1 0 1 2 3
Example 32: Represent the following rational numbers on a number line.
7 −5
(a) (b)
4 2
7 3 3
Solution: (a) = 1 ⇒ 11< < 2
4 4 4
3
1 lies between 1 and 2. Since we have 4 in the denominator, we divide the part between
4 7
1 and 2 into 4 equal parts. Starting from 1, the third part to its right represents .
3 7 4
1 =
4 4

0 1 2

15