Question

Divide $6\frac{2}{5}$ by $\frac{16}{25}$

Answer 1

Dividing two fractions:

Dividing two fractions is equal to the multiplication of a fraction by the reciprocal of another fraction.

A fraction $\frac{a}{b}$ which is divided by $\frac{c}{d}$. Then we can solve the division as $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

Given,

Divide $6\frac{2}{5}$ by $\frac{16}{25}$

Step:$1$

We have here mixed fraction convert into improp[er fraction.

$$\begin{gathered} 6\frac{2}{5}÷\frac{16}{25}=\left(\frac{5\times 6+2}{5}\right)÷\frac{16}{25} \\ =\left(\frac{30+2}{5}\right)÷\frac{16}{25} \\ 6\frac{2}{5}÷\frac{16}{25}=\frac{32}{5}÷\frac{16}{25} \end{gathered}$$

Step:$2$

Now we can divide the above two fractions.

$$\begin{gathered} \frac{32}{5}÷\frac{16}{25}=\frac{32}{5}\times \frac{25}{16}\left(\therefore \frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\right) \\ =\frac{32}{16}\times \frac{25}{5} \\ =\frac{2}{1}\times \frac{5}{1} \\ =10 \end{gathered}$$

Therefore, Divide $6\frac{2}{5}$ by $\frac{16}{25}$ is equal to $10$.