Question

Find: $4\frac{3}{7}÷7$

Answer 1

State the given data and simplify:

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

It can be simplified as,

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

$$\begin{gathered} \Rightarrow 4\frac{3}{7}÷7=\frac{28+3}{7}÷7 \\ \Rightarrow 4\frac{3}{7}÷7=\frac{31}{7}÷7 \end{gathered}$$

$\Rightarrow 4\frac{3}{7}÷7=\frac{31}{7}\times \frac{1}{7}$ $\left[\because \mathrm{the}\mathrm{reciprocal}\mathrm{of}7=\frac{1}{7}\right]$

$\Rightarrow 4\frac{3}{7}÷7=\frac{31\times 1}{7\times 7}$ $\left[\because \frac{a}{b}\times \frac{c}{d}=\frac{a\times c}{b\times d}\right]$

$\Rightarrow 4\frac{3}{7}÷7=\frac{31}{49}$

Hence, the value of $\mathbf{4}\frac{\mathbf{3}}{\mathbf{7}}\mathbf{÷}\mathbf{7}$ is $\frac{\mathbf{31}}{\mathbf{49}}$.