Question

Check whether the given two ratios forms proportion or not:

$3\frac{1}{2}:2\frac{1}{2}$ and $21:15$

Answer 1

Two ratios forms proportion if their lowest terms are exactly same.

Given ratios are $3\frac{1}{2}:2\frac{1}{2}$ and $21:15$

Convert the mixed fraction into improper fraction $3\frac{1}{2}:2\frac{1}{2}$$=\frac{7}{2}:\frac{5}{2}$

Simplest form of ratio $\frac{7}{2}:\frac{5}{2}$ is obtained by dividing both term by LCM of their denominator $2$

$\frac{7}{2}\times 2:\frac{5}{2}\times 2$$=7:5$

Lowest term $=\frac{7}{5}$

Lowest term of ratio $21:15$ is obtained by dividing both term by their HCF $3$

$21:15$$=\frac{21}{15}=\frac{7}{5}$

Since lowest term for both given ratios are same.

Hence, ratios $3\frac{1}{2}:2\frac{1}{2}$ and $21:15$ forms proportion.