# Add and Subtract Fractions with Common Denominators

## Add and Subtract Fractions with Common Denominators

#### 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

Let's use fraction circles to model the same example, .

So again, we see that

#### Add Fractions with a Common Denominator

Example 4.52 shows that to add the same-size pieces - meaning that the fractions have the same denominator - we just add the number of pieces.To add fractions with a common denominators, add the numerators and place the sum over the common denominator.

#### Model Fraction Subtraction

Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into 12 slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or of the pizza) left in the box. If Leonardo eats 2 of these remaining pieces (or of the pizza), how much is left? There would be 5 pieces left (or of the pizza).

Let's use fraction circles to model the same example, .

Start with seven pieces. Take away two pieces. How many twelfths are left?

Again, we have five twelfths, .

#### Subtract Fractions with a Common Denominator

We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.

#### FRACTION SUBTRACTION

If , and are numbers where , then

To subtract fractions with common denominators, we subtract the numerators and place the difference over the common denominator.

Source: Rice University, https://openstax.org/books/prealgebra/pages/4-4-add-and-subtract-fractions-with-common-denominators

This work is licensed under a Creative Commons Attribution 4.0 License.