Skill: Decompose fractions into sums

A fraction’s denominator tells the size of the parts, and its numerator tells how many of those parts there are. To decompose a fraction, split the numerator into smaller numbers while keeping the denominator the same.

Example: Decompose $\frac{5}{7}$ into a sum of two fractions.

1. Keep the denominator, $7$, the same in both fractions.
2. Split the numerator, $5$, into two parts. For example, $5=2+3$.
3. Write the two fractions:

$$\frac{5}{7}=\frac{2}{7}+\frac{3}{7}$$

This is correct because there are still five sevenths altogether: two sevenths plus three sevenths.

You can also decompose it into unit fractions:

$$\frac{5}{7}=\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}$$

The denominator stays the same because all the parts are sevenths.