# How do you simplify 30/80 + 40/100?

Mar 24, 2018

Find a common denominator and divide out common factors.

#### Explanation:

$80 = 2 \times 2 \times 2 \times 2 \times 5$
$30 = 3 \times 2 \times 5$

The common factors of $2 \times 5$ can be divided out leaving

$\frac{30}{80} = \frac{3}{8}$

$100 = 2 \times 2 \times \times 5 \times 5$
$40 = 2 \times 2 \times 2 \times 5$

The common factors of $2 \times 5$ can be divided out leaving

$\frac{40}{100} = \frac{4}{10}$

8 and 10 have a common multiply of 40

$8 = 2 \times 2 \times 2$
$10 = 2 \times 5$

The unique factors are $2 \times 2 \times 2 \times 5 = 40$
( the factor of 2 in ten is a repeat of the 3 factors of 2 in 8)

Now change both fractions to a faction with a denominator of 40

$\frac{3 \times 5}{8 \times 5} + \frac{4 \times 4}{10 \times 4} = \frac{15}{40} + \frac{16}{40}$

These fractions can be added giving

$\frac{15}{40} + \frac{16}{40} = \frac{31}{40}$

there are no common factors between 31 and 40 so $\frac{31}{40}$ is the final answer.