Skill: Interpret a fraction as a sum of unit fractions

A unit fraction has a numerator of $1$, such as $\frac14$.

To write a fraction as a sum of unit fractions:

1. Look at the denominator. It tells the size of each unit fraction.
2. Look at the numerator. It tells how many unit fractions to use.
3. Write that many copies of the unit fraction and add them.

Example: Write $\frac{7}{4}$ as a sum of unit fractions.

• The denominator is $4$, so each unit fraction is $\frac14$.
• The numerator is $7$, so use seven copies of $\frac14$.

$$\frac{7}{4} = \frac14+\frac14+\frac14+\frac14+\frac14+\frac14+\frac14$$

This means that $\frac74$ is made of seven equal fourths. Four fourths make one whole, and the other three fourths extend past that whole. The denominator stays $4$ because every part is the same size.