# How do you multiply 7/12 div 3/4?

Oct 17, 2016

$\textcolor{b l u e}{\frac{7}{9}}$

#### Explanation:

we can get the quotient of fractions by simply multiplying the reciprocal of the second fraction to the first, it doesn't matter as the commutative property of multiplication is still obeyed :)

you can get quotient by:

$\frac{\frac{a}{b}}{\frac{c}{d}}$

as the reciprocal of $\frac{c}{d}$ is $\frac{d}{c}$,

$\left(\frac{a}{b}\right) \cdot \left(\frac{d}{c}\right)$ = $\frac{a d}{b c}$

we can apply the same property to the problem,

$\left(\frac{7}{12}\right) \cdot \left(\frac{3}{4}\right)$ = ?

get the reciprocal of the second fraction, then multiply it,
numerator to numerator, denominator to denominator,

$\left(\frac{7}{12}\right) \cdot \left(\frac{4}{3}\right)$ = $\frac{\left(7\right) \left(4\right)}{\left(12\right) \left(3\right)}$ = $\frac{28}{36}$

In mathematics, answers must always be in simplest form, so we must get the lowest term by dividing the number by its divisible numbers until there are no divisible number that can't be divided for both numerator and the denominator.

Divisible by $2$ and $4$,

$\frac{28}{4} / \frac{36}{4}$ = $\frac{7}{9}$

since, there are no single number that can divide both numerator and the denominator, hence, $\frac{7}{9}$ is the final answer :)

= $\textcolor{b l u e}{\frac{7}{9}}$