Question

Find: $5÷3\frac{4}{7}$

Answer 1

State the given data and simplify:

The given expression is $5÷3\frac{4}{7}$.

It can be simplified as,

$5÷3\frac{4}{7}=5÷\frac{\left(3\times 7\right)+4}{7}$ $\left[\because a\frac{b}{c}=\frac{\left(a\times c\right)+b}{c}\right]$

$$\begin{gathered} \Rightarrow 5÷3\frac{4}{7}=5÷\frac{21+4}{7} \\ \Rightarrow 5÷3\frac{4}{7}=5÷\frac{25}{7} \end{gathered}$$

$\Rightarrow 5÷3\frac{4}{7}=5\times \frac{7}{25}$ $\left[\because thereciprocalof\frac{25}{7}=\frac{7}{25}\right]$

$$\begin{gathered} \Rightarrow 5÷3\frac{4}{7}=1\times \frac{7}{5} \\ \Rightarrow 5÷3\frac{4}{7}=\frac{7}{5} \end{gathered}$$

Hence, the value of $\mathbf{5}\mathbf{÷}\mathbf{3}\frac{\mathbf{4}}{\mathbf{7}}$ is $\frac{\mathbf{7}}{\mathbf{5}}$.