# How do you write 9/12 as a sum of unit fractions?

Dec 15, 2016

$\frac{9}{12} = \frac{1}{2} + \frac{1}{4}$

#### Explanation:

This can be done in an unlimited number of ways. Which you choose depends on what you are trying to achieve.

If you want to convey the meaning of "nine twelfths" directly then you could write:

$\frac{9}{12} = \frac{1}{12} + \frac{1}{12} + \frac{1}{12} + \frac{1}{12} + \frac{1}{12} + \frac{1}{12} + \frac{1}{12} + \frac{1}{12} + \frac{1}{12}$

If you want to express it as the sum of the minimum number of unit fractions, then:

$\frac{9}{12} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \cdot 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \cdot 4} = \frac{3}{4} = \frac{1}{2} + \frac{1}{4}$

A sum of distinct unit fractions such as $\frac{1}{2} + \frac{1}{4}$ is called an Egyptian fraction.

If you require all of the unit fractions to be identical then the minimum solution is:

$\frac{9}{12} = \frac{3}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}$