# 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 $\frac{3}{7}$

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To do:

We have to find which among the given 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 $\frac{3}{7}$

Solution:

(i) $\frac{2}{7}$ of $\frac{3}{4}=\frac{2}{7}\times\frac{3}{4}$

$=\frac{2\times3}{7\times4}$

$=\frac{1\times3}{7\times2}$

$=\frac{3}{14}$

$\frac{3}{5}$ of $\frac{5}{8}=\frac{3}{5}\times\frac{5}{8}$

$=\frac{3\times5}{5\times8}$

$=\frac{3\times1}{1\times8}$

$=\frac{3}{8}$

$\frac{3}{14}$ and $\frac{3}{8}$ have numerators same and $14>8$

This implies,

$\frac{3}{14}<\frac{3}{8}$

So, $\frac{3}{5}$ of $\frac{5}{8}$ is greater than $\frac{2}{7}$ of $\frac{3}{4}$.

(ii) $\frac{1}{2}$ of $\frac{6}{7}=\frac{1}{2}\times\frac{6}{7}$

$=\frac{1\times6}{2\times7}$

$=\frac{1\times3}{1\times7}$

$=\frac{3}{7}$

$\frac{2}{3}$ of $\frac{3}{7}=\frac{2}{3}\times\frac{3}{7}$

$=\frac{2\times3}{3\times7}$

$=\frac{2\times1}{1\times7}$

$=\frac{2}{7}$

$3>2$

This implies,

$\frac{3}{7}>\frac{2}{7}$

So, $\frac{1}{2}$ of $\frac{6}{7}$ is grater than $\frac{2}{3}$ of $\frac{3}{7}$.

Updated on 10-Oct-2022 13:32:36