Question

Divide.

$2\frac{1}{2}$$÷$$5$

Answer 1

Here, we have given a fraction and a whole number. To divide a fraction by a natural number, we multiply the fraction by the reciprocal of the natural number.

The given fraction is $2\frac{1}{2}$ (which is a mixed fraction) and the given natural number is $5$.

Reciprocal of natural number $5$ is $\frac{1}{5}$.

Firstly, converting $2\frac{1}{2}$ into improper form. We have

$2\frac{1}{2}=\frac{2\times 2+1}{2}=\frac{5}{2}$

Now, multiplying the given fraction $\frac{5}{2}$ with the reciprocal of $5$ i.e. $\frac{1}{5}$.

Thus, $\frac{5}{2}$$\times$$\frac{1}{5}$ $=$$\frac{5\times 1}{2\times 5}$ [multiplying the numerators and denominators of the fractions]

$=$$\frac{5}{10}$

Therefore, $2\frac{1}{2}$$÷$$\frac{1}{5}$$=$$\frac{5}{2}$$\times$$\frac{1}{5}$$=$$\frac{5}{10}$