Model Fraction Addition

How many quarters are pictured? One quarter plus $2$ quarters equals $3$ quarters.

Remember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that

${\Large\frac{1}{4}}+{\Large\frac{2}{4}}=\Large{\frac{3}{4}}$

$\text{one quarter }+\text{ two quarters }=\text{ three quarters}$

Let’s use fraction circles to model the same example, $\Large\frac{1}{4}\normalsize+\Large\frac{2}{4}$.

Start with one $\Large\frac{1}{4}$ piece.		$\Large\frac{1}{4}$
Add two more $\Large\frac{1}{4}$ pieces.		$+\Large\frac{2}{4}$
The result is $\Large\frac{3}{4}$ .		$\Large\frac{3}{4}$

So again, we see that

$\Large\frac{1}{4}\normalsize+\Large\frac{2}{4}\normalsize=\Large\frac{3}{4}$
Doing the Manipulative Mathematics activity “Model Fraction Addition” will help you develop a better understanding of adding fractions

example

Use a model to find the sum $\Large\frac{3}{8}\normalsize+\Large\frac{2}{8}$.

Solution:

Start with three $\Large\frac{1}{8}$ pieces.		$\Large\frac{3}{8}$
Add two $\Large\frac{1}{8}$ pieces.		$+\Large\frac{2}{8}$
How many $\Large\frac{1}{8}$ pieces are there?		$\Large\frac{5}{8}$

There are five $\Large\frac{1}{8}$ pieces, or five-eighths. The model shows that $\Large\frac{3}{8}\normalsize+\Large\frac{2}{8}\normalsize=\Large\frac{5}{8}$.

The following video shows more examples of how to use models to add fractions with like denominators.

Add Fractions with a Common Denominator

The example above shows that to add the same-size pieces—meaning that the fractions have the same denominator—we just add the number of pieces.

Tip:  A negative sign on a fraction can be written in the following locations: by the numerator, by the denominator or out in front of the fraction bar.  It is your choice!