# How do you simplify  1/5 + 3/5?

Sep 4, 2016

$\frac{4}{5}$

#### Explanation:

The top number of a fraction (numerator) is the count.

The bottom number (denominator) is the size indicator of what you are counting. In this case the size indicator is 5 which means it takes 5 of what you are counting to make a complete 1 of something.

As the 'size indicators' (denominators) are the same we can directly add the counts (numerators).

Write as:

$\frac{1 + 3}{5} = \frac{4}{5}$

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$\textcolor{b l u e}{\text{Tip about notation}}$

Suppose we had: $\frac{3}{10} + \frac{2}{10} + \frac{16}{10}$

What we a counting is all of size type 10 (have the same denominator of 10)

As they are all of the same size it is perfectly correct to write it as:

$\left(\text{count")/("size indicator")" "->" "(3+2+16)/10" " ->" "("numerator")/("denominator}\right)$

This simply means that every one of what we are counting is size type 10. If you like: they are sharing the one size indicator notation(denominator of 10).