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Which is greater : i 2 by 7 of 3 by 4 or 3 by 5 of 5 by 8

4. Which is greater:

  (i)\; \frac{2}{7}\; o\! f\; \frac{3}{4}\; \; or\; \; \frac{3}{5}\; \; of \; \frac{5}{8}

   (ii)\; \frac{1}{2}\; o\! f\; \frac{6}{7}\; \; or\; \; \frac{2}{3}\; \; of \; \frac{3}{7}

            

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(i)\; \frac{2}{7}\; o\! f\; \frac{3}{4}\; \; or\; \; \frac{3}{5}\; \; of \; \frac{5}{8}

\Rightarrow \; \frac{2}{7} \times\ \frac{3}{4}\; \; or\; \; \frac{3}{5}\; \times \frac{5}{8}

\Rightarrow \frac{2\times3}{7\times4}\:\:or\:\:\frac{3\times5}{5\times8}

\Rightarrow \frac{3}{14}\:\:or\:\:\frac{3}{8}

Now, As we Know, When the numerator of two fractions is the same the fraction with lesser denominator is the bigger fraction. So,

\Rightarrow \frac{3}{14}\:\:<\:\:\frac{3}{8}

Thus,

\; \frac{2}{7}\; o\! f\; \frac{3}{4}\; \; <\; \; \frac{3}{5}\; \; of \; \frac{5}{8}.

(ii)\; \frac{1}{2}\; o\! f\; \frac{6}{7}\; \; or\; \; \frac{2}{3}\; \; of \; \frac{3}{7}

\Rightarrow \; \frac{1}{2}\; \times\; \frac{6}{7}\; \; or\; \; \frac{2}{3}\; \; \times \; \frac{3}{7}

\Rightarrow \frac{1\times6}{2\times7}\:\:or\:\:\frac{2\times3}{3\times7}

\Rightarrow \frac{3}{7}\:\:or\:\:\frac{2}{7}

As we know, When the denominator of two fractions are the same, the fraction with the bigger numerator is the bigger fraction, so,

\Rightarrow \frac{3}{7}\:\:>\:\:\frac{2}{7}

Thus,

\; \frac{1}{2}\; \times\; \frac{6}{7}\; \; >\; \; \frac{2}{3}\; \; \times \; \frac{3}{7}.

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