Question

Which is greater:
(i) $\frac{2}{7}$of $\frac{3}{4}$ or $\frac{3}{5}$ of $\frac{5}{8}$
(ii) $\frac{1}{2}$ of $\frac{6}{7}$ or $\frac{2}{3}$ of $\frac{3}{7}$

Answer 1

(i) $\frac{2}{7}$ × $\frac{3}{4}$= $\frac{3}{14}$ or $\frac{3}{5}$ × $\frac{5}{8}$ =$\frac{3}{8}$
Converting these fractions into like fractions,
$\frac{3}{14}$ = $\frac{3\times4}{14\times 4}$ = $\frac{12}{56}$
$\frac{3}{8}$= $\frac{3\times 7}{8\times 7}$ =$\frac{21}{56}$
Since $\frac{21}{56}$> $\frac{12}{56}$,
∴ $\frac{3}{8}$> $\frac{3}{14}$
Therefore, $\frac{3}{5}$ of $\frac{5}{8}$ is greater.

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(ii) $\frac{1}{2}$ × $\frac{6}{7}$ = $\frac{3}{7}$
$\frac{2}{3}$ × $\frac{3}{7}$ = $\frac{2}{7}$
Since 3 > 2,
∴ $\frac{3}{7}$> $\frac{2}{7}$
Therefore, $\frac{1}{2}$of $\frac{6}{7}$ is greater.