# How do you simplify 6 div 4/9 ?

May 24, 2017

$\frac{27}{2}$

#### Explanation:

When a number/variable is divided by another number, the result is the same as the former number/variable multiplied by the reciprocal of the other number.

Therefore, $6 \div \frac{4}{9} = 6 \div \frac{1}{\frac{4}{9}}$ (eg reciprocal of 2 is $\frac{1}{2}$)

$= 6 \cdot \frac{9}{4}$

$= \frac{54}{4}$

This simplifies to $\frac{27}{2}$

May 29, 2017

$\frac{27}{2}$

#### Explanation:

$6 \div \frac{4}{9}$

Dividing by a fraction is the same as multiplying by the reciprocal.

$= \frac{6}{1} \times \frac{9}{4}$

Cancelling like factors at this point makes it easier to find the answer, rather than simplifying with bigger numbers later.

$= {\cancel{6}}^{3} / 1 \times \frac{9}{\cancel{4}} _ 2 \text{ } \leftarrow$ multiply straight across

$= \frac{27}{2}$