Lesson 1: Model Addition of Fractions

Property

To add quantities, they must have the same unit.
For example, we can add 3 apples and 2 apples to get 5 apples.
In fractions, the denominator tells us the fractional unit (e.g., fourths, eighths).
We can only directly add fractions that have the same unit, meaning they have a common denominator.

Examples

Property

To model fraction addition, you combine parts of the same size.
For example, to add $\frac{1}{4} + \frac{2}{4}$, you can visualize one quarter coin plus two quarter coins, which equals three quarter coins.
This shows that adding fractions with the same denominator means adding the number of pieces (numerators).

Let's use fraction circles to model the same example, $\frac{1}{4} + \frac{2}{4}$.
Start with one $\frac{1}{4}$ piece.
Add two more $\frac{1}{4}$ pieces.
The result is $\frac{3}{4}$.

Examples

• To model $\frac{2}{7} + \frac{3}{7}$, you would combine two $\frac{1}{7}$ pieces with three $\frac{1}{7}$ pieces. This gives you a total of five $\frac{1}{7}$ pieces, so the sum is $\frac{5}{7}$.
• Imagine a chocolate bar split into 10 equal squares. If you eat $\frac{1}{10}$ and then eat another $\frac{4}{10}$, you have eaten $\frac{1+4}{10} = \frac{5}{10}$ of the bar.
• Using fraction strips, if you place a $\frac{3}{8}$ strip next to another $\frac{3}{8}$ strip, the combined length is $\frac{6}{8}$.

Property

To add fractions with like denominators, add the numerators and keep the denominator the same.
This can be represented on a number line as combining lengths from a starting point.

Examples