# How do you evaluate \frac{(4x)/{4}}{(3x)/2}?

Dec 14, 2017

$\frac{\frac{4 x}{4}}{\frac{3 x}{2}} = \frac{2}{3}$

#### Explanation:

$\frac{\frac{4 x}{4}}{\frac{3 x}{2}} = \frac{4 x}{4} \times \frac{2}{3 x}$
$\frac{4 x}{4} \times \frac{2}{3 x} = \frac{8 x}{12 x}$
$\frac{8 x}{12 x} = \frac{2}{3}$

Dec 14, 2017

$\frac{\frac{4 x}{4}}{\frac{3 x}{2}}$ simplifies to $\frac{2}{3}$.

#### Explanation:

Simplify:

$\frac{\frac{4 x}{4}}{\frac{3 x}{2}}$

This is a fraction divided by a fraction.

$\frac{4 x}{4} \div \frac{3 x}{2}$

Cancel $4$.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}^{1} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}} ^ 1 \div \frac{3 x}{2}$

Simplify. Any single number or variable is understood to be $\frac{n}{1}$.

$\frac{x}{1} \div \frac{3 x}{2}$

When dividing by a fraction, multiply by its reciprocal.

$\frac{x}{1} \times \frac{2}{3 x}$

Multiply the numerators and denominators.

$\frac{x \times 2}{1 \times 3 x}$

Simplify.

$\frac{2 x}{3 x}$

Cancel $x$.

${\left(2 \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}}\right)}^{1} / {\left(3 \textcolor{red}{\cancel{\textcolor{b l a c k}{x}}}\right)}^{1}$

Simplify.

$\frac{2}{3}$