Ratio and Proportions | Form 1 Mathematics

Ratio and Proportions

Ratios compare quantities of the same kind, while proportions state that two ratios are equal.

Ratio

A ratio a:b compares a with b. Simplify a ratio by dividing all terms by their greatest common factor. The order matters: 2:3 is not the same as 3:2.

Proportion

If a/b = c/d, the quantities are proportional and a × d = b × c. In a direct proportion, increasing one quantity increases the other in the same ratio.

Worked examples

1. Simplify 18:24 by dividing by 6 to obtain 3:4.
2. If 3 notebooks cost 900 FCFA, one costs 300 FCFA and 7 cost 2,100 FCFA.
3. Solve x/5 = 6/10: cross-multiplication gives 10x = 30, so x = 3.

Practice

1. Divide 560 in the ratio 3:4.
2. If 5 kg of rice costs 4,000 FCFA, find the cost of 8 kg at the same rate.
3. Solve 7:9 = x:36.