Question

Choose the correct answer:
When $2\frac{2}{3}÷4\frac{1}{5}$ equals to?

• A. $\frac{56}{5}$
• B. $\frac{40}{63}$
• C. $\frac{63}{40}$

Answer 1

The correct option is B $\frac{40}{63}$

First we have to convert mixed numbers into improper fractions.
$2\frac{2}{3}=\frac{2\times 3+2}{3}=\frac{8}{3}$
and
$4\frac{1}{5}=\frac{4\times 5+1}{5}=\frac{21}{5}$

Now, $2\frac{2}{3}÷4\frac{1}{5}=\frac{8}{3}÷\frac{21}{5}$

Take a reciprocal of the second fraction and multiply that reciprocal by the first fraction as follows.

$=\frac{8}{3}\times \frac{5}{21}$

$=\frac{8\times 5}{3\times 21}$

$=\frac{40}{63}$

It can not be simplified further.
$\therefore 2\frac{2}{3}÷4\frac{1}{5}=\frac{40}{63}$