# How do you simplify 1/10 + 1/9?

Apr 28, 2016

$\frac{1}{10} + \frac{1}{9} = \textcolor{b l u e}{\frac{19}{90}}$

#### Explanation:

$\frac{1}{10} + \frac{1}{9}$

In order to add fractions, their denominators must be the same. We accomplish this by finding the least common denominator (LCD). One way to do this is through prime factorization of each denominator.

$10 : 2 \times 5$

$9 : 3 \times 3$

This gives the LCD as $2 \times 5 \times 3 \times 3 = 90$.

Now multiply each fraction by a number that will make both denominators $90$.

$\frac{1}{10} \times \textcolor{red}{\frac{9}{9}} + \frac{1}{9} \times \textcolor{red}{\frac{10}{10}}$

Simplify.

$\frac{9}{90} + \frac{10}{90}$

Simplify.

$\frac{19}{90}$