# How do you simplify \frac { 11x ^ { 2} } { 33x } + \frac { 5x ^ { 2} } { 15x }?

Nov 10, 2017

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

#### Explanation:

$\left(\frac{11 {x}^{2}}{33 x}\right) + \left(\frac{5 {x}^{2}}{15 x}\right)$

$= \left(\frac{11 \cdot x \cdot x}{11 \cdot 3 \cdot x}\right) + \left(\frac{5 \cdot x \cdot x}{5 \cdot 3 \cdot x}\right)$

$= \left(\frac{\cancel{11 \cdot x} \cdot x}{\cancel{11 \cdot x} \cdot 3}\right) + \left(\frac{\cancel{5 \cdot x} \cdot x}{\cancel{5 \cdot x} \cdot 3}\right)$

$= \left(\frac{x}{3}\right) + \left(\frac{x}{3}\right)$
$= \frac{2 x}{3}$

Nov 10, 2017

$\frac{2 x}{3}$

#### Explanation:

1) First cancel any factors that are in common in the numerators and in their own denominators.
Because this is an addition problem (not a multiplication problem), you can cancel common factors only within the same fraction.

For the first term
$\frac{11 {x}^{2}}{33 x}$

$\frac{11}{33}$ reduces to $\frac{1}{3}$

$\frac{{x}^{2}}{x}$ reduces to $\frac{x}{1}$

So the first term simplifies to
$\frac{1}{3}$ × $\frac{x}{1}$

$\frac{x}{3}$
................................

For the second term
$\frac{5 {x}^{2}}{15 x}$

$\frac{5}{15}$ reduces to $\frac{1}{3}$

$\frac{{x}^{2}}{x}$ reduces to $\frac{x}{1}$

So the second term simplifies to
$\frac{1}{3}$ × $\frac{x}{1}$

$\frac{x}{3}$
..................

Now the problem has been simplified to
$\frac{x}{3}$ + $\frac{x}{3}$

The fractions have a common denominator, so you can just add.
Add the numerators and keep the common denominator.
$\frac{x + x}{3}$

$\frac{2 x}{3}$