# How do you solve \frac { 2} { 3} n + 3\frac { 1} { 3} = 9\frac { 1} { 3}?

Apr 30, 2018

$n = 9$

#### Explanation:

First you want to have like terms on the same side. Subtract 3 1/3 from both sides.

$\frac{2}{3} n = 6$

Now multiply both sides by the reciprocal of 2/3, 3/2.

$n = 9$

Check:
$\left(\frac{2}{3} \cdot 9\right) + 3 \frac{1}{3} = 9 \frac{1}{3}$

$6 + 3 \frac{1}{3} = 9 \frac{1}{3}$

$9 \frac{1}{3} = 9 \frac{1}{3}$

Apr 30, 2018

$n = 9$

#### Explanation:

First, subtract $3 \frac{1}{3}$ from $9 \frac{1}{3}$ to get $6$ and from the left side. This should give you the equation

$\frac{2}{3} n = 6$

In order to solve for $n$, we multiply both sides by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$.

$6$ multiplied by $\frac{3}{2}$ is

$6 \cdot \frac{3}{2} = \frac{18}{2} = 9$

so

$\frac{2}{3} n \cdot \frac{3}{2} = 9$