Page 90 - ICSE Math 8

8 Ratio and Proportion

Key Concepts

• Comparison of Ratios • Direct and Inverse Proportions
• Dividing a Quantity in a Given Ratio • Rule of Three
• Continued Ratio • Proportional Parts
• Proportion

Ratio is a relation between any two quantities of the same kind and in the same unit, which expresses how
many times one quantity is of the other quantity. Ratio between two quantities is obtained by dividing the
first quantity by the second quantity. As ratio is the quotient of two quantities of the same kind, therefore
it has no unit. For example, if x = 40 g and y = 50 g then the ratio between x and y denoted by x : y is
40 g 4 50 g 5
4
50 g = = 4 : 5, and ratio between y and x is y : x = 40 g = = 5 : 4. The two quantities in a ratio are
5
called its terms. Also, the first term is called antecedent and the second term is called consequent. A ratio
must always be expressed in its lowest terms by cancelling the common factors from the antecedent and
consequent.

Comparison of Ratios
We can compare ratios using the methods given below.

Method 1: Convert the given ratios into decimals. 3 2
For example, to compare 3 : 4 and 2 : 5, convert them into decimals to get = 0.75 and = 0.4.
5
4
3 2
As 0.75 > 0.4, therefore > .
4
5
Method 2: Make the consequents of the given ratios equal and then compare their antecedents.
For example, to compare 5 : 3 and 4 : 7, make their consequents equal to get:
5 × 7 = 35 = 35 : 21 and 4 × 3 = 12 = 12 : 21
3 × 7 21 7 × 3 21

As 35 > 12, therefore 5 : 3 > 4 : 7.
Method 3: Multiply the antecedent of the first ratio by the consequent of the second ratio and the antecedent
of the second ratio by the consequent of the first ratio and compare the products. For any two ratios p : q and
r : s, if:

(i) p × s > q × r ⇒ p : q > r : s Try These
(ii) p × s < q × r ⇒ p : q < r : s 1. Arrange the following ratios
in ascending order.
(iii) p × s = q × r ⇒ p : q = r : s 6 : 7, 11 : 13, 5 : 4, 3 : 4, 17 : 19
For example, compare the ratios 8 : 9 and 14 : 17. 2. Reduce the following to their
We have p = 8, q = 9, r = 14 and s = 17. lowest terms.
(a) 975 : 650
p × s = 8 × 17 = 136 and q × r = 9 × 14 = 126 (b) 8 L : 48 mL
As 8 × 17 > 9 × 14, therefore 8 : 9 > 14 : 17.

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