Question

Which is greater: $\left(\frac{2}{7}\right)of\left(\frac{3}{4}\right)$or $\left(\frac{3}{5}\right)of\left(\frac{5}{8}\right)$

Answer 1

Determine the greater number: $\left(\frac{2}{7}\right)of\left(\frac{3}{4}\right)$or $\left(\frac{3}{5}\right)of\left(\frac{5}{8}\right)$

Separate the given equation into two parts and then solve its value.

Solve equation $\left(\frac{2}{7}\right)of\left(\frac{3}{4}\right)$:

$$\begin{gathered} \left(\frac{2}{7}\right)of\left(\frac{3}{4}\right)=\left(\frac{2}{7}\right)\times \left(\frac{3}{4}\right) \\ \Rightarrow =\frac{3}{14} \end{gathered}$$

Solve equation $\left(\frac{3}{5}\right)of\left(\frac{5}{8}\right)$:

$$\begin{gathered} \left(\frac{3}{5}\right)of\left(\frac{5}{8}\right)=\left(\frac{3}{5}\right)\times \left(\frac{5}{8}\right) \\ \Rightarrow =\frac{3}{8} \end{gathered}$$

After calculating the equation are $\frac{3}{14}$and $\frac{3}{8}$ and equivalting the LCM of $14and8$ that is $56$.

Converting given fractions into an equivalent fraction having 56 as the denominator.

$$\begin{gathered} \frac{3}{14}\times \frac{4}{4}=\frac{12}{56} \\ \frac{3}{8}\times \frac{7}{7}=\frac{21}{56} \end{gathered}$$

Now we get to know that

$\left(\frac{12}{56}\right)<\left(\frac{21}{56}\right)$

So,

$\left(\frac{3}{14}\right)<\left(\frac{3}{8}\right)$

Hence, the $\left(\frac{3}{5}\right)of\left(\frac{5}{8}\right)$ is greater than $\left(\frac{2}{7}\right)of\left(\frac{3}{4}\right)$.