# How do you simplify 1/4 + 1/5?

May 6, 2018

$\therefore \frac{9}{20}$

#### Explanation:

To simplify $\frac{1}{4} + \frac{1}{5}$, we need to make both of the fractions as the same base.

$\implies \frac{1}{4} + \frac{1}{5}$

$\implies \frac{5}{20} + \frac{4}{20}$

$\therefore \frac{9}{20}$

May 6, 2018

Rewrite each fraction so they have the same denominator.

#### Explanation:

Least Common Multiple (LCM) Route:

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28
Multiples of 5 are 5, 10 ,15, 20, 25, 30
The Smallest Multiple that 4 and 5 have in common is 20.

Change $\frac{1}{4}$ to a denominator of 20 by multiplying top and bottom by 5: $\frac{1}{4} \cdot \frac{5}{5} = \frac{5}{20}$.

Change $\frac{1}{5}$ to a denominator of 20 by multiplying top and bottom by 4: $\frac{1}{5} \cdot \frac{4}{4} = \frac{4}{20}$.

Now Add the 2 new fractions together and simplify if possible:
$\frac{5}{20} + \frac{4}{20} = \frac{9}{20}$

Cross Multiply Route:
$\frac{a}{c} + \frac{b}{d} = \frac{a d + b c}{c d}$

$\frac{1}{4} + \frac{1}{5} = \frac{1 \cdot 5 + 1 \cdot 4}{4 \cdot 5} = \frac{5 + 4}{20} = \frac{9}{20}$

Remember to always Simplify if possible.