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.