How to Solve Ratios and Proportions

The key is keeping the same kind of quantity in the same position. If cups are on top in one ratio, cups go on top in the other.

Worked examples

4 was multiplied by 5 to get 20.

Do the same to the top: $x = 3 \times 5 = 15$ .

$\frac{2}{5} = \frac{c}{20}$

$c = 2 \times 4 = 8$ cups.

Find the unit rate: $18 \div 6 = 3$ dollars each.

$10 \times 3 = 30$ dollars.

Boys to girls is 3:5 in a class of 24, so there are $\frac{3}{5} \times 24$ boys.

The ratio 3:5 means 8 equal parts in total. Boys are $\frac{3}{8}$ of the class, so there are $\frac{3}{8} \times 24 = 9$ boys and 15 girls.

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