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 $\frac{3}{7}$
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 $\frac{3}{7}$.
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