### Learning Outcomes

- Model fraction subtraction
- Subtract fractions with a common denominator
- Subtract fractions with a common denominator that contain variables

## Model Fraction Subtraction

Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into [latex]12[/latex] slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or [latex]{\Large\frac{7}{12}}[/latex] of the pizza) left in the box. If Leonardo eats [latex]2[/latex] of these remaining pieces (or [latex]{\Large\frac{2}{12}}[/latex] of the pizza), how much is left? There would be [latex]5[/latex] pieces left (or [latex]{\Large\frac{5}{12}}[/latex] of the pizza).

[latex]{\Large\frac{7}{12}}-{\Large\frac{2}{12}}={\Large\frac{5}{12}}[/latex]

Let’s use fraction circles to model the same example, [latex]{\Large\frac{7}{12}}-{\Large\frac{2}{12}}[/latex].

Start with seven [latex]{\Large\frac{1}{12}}[/latex] pieces. Take away two [latex]{\Large\frac{1}{12}}[/latex] pieces. How many twelfths are left?

Again, we have five twelfths, [latex]{\Large\frac{5}{12}}[/latex].

### Example

Use fraction circles to find the difference: [latex]{\Large\frac{4}{5}}-{\Large\frac{1}{5}}[/latex]

Solution:

Start with four [latex]{\Large\frac{1}{5}}[/latex] pieces. Take away one [latex]{\Large\frac{1}{5}}[/latex] piece. Count how many fifths are left. There are three [latex]{\Large\frac{1}{5}}[/latex] pieces left, or [latex]{\Large\frac{3}{5}}[/latex].

### Try It

## 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 [latex]a,b,\text{ and }c[/latex] are numbers where [latex]c\ne 0[/latex], then

[latex]{\Large\frac{a}{c}}-{\Large\frac{b}{c}}={\Large\frac{a-b}{c}}[/latex]

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

### Example

Find the difference: [latex]{\Large\frac{23}{24}}-{\Large\frac{14}{24}}[/latex]

### Try It

Watch the following video for more examples of subtracting fractions with like denominators.

## Subtract Fractions with Variables

### Example

Find the difference: [latex]{\Large\frac{y}{6}}-{\Large\frac{1}{6}}[/latex]

### Try it

### Example

Find the difference: [latex]{\Large-\frac{10}{x}-\frac{4}{x}}[/latex]

### Try It

Now lets do an example that involves both addition and subtraction.

### Example

Simplify: [latex]{\Large\frac{3}{8}}+\left(-{\Large\frac{5}{8}}\right)-{\Large\frac{1}{8}}[/latex]

### Try It

In the next video we show more examples of subtracting fractions with a common denominator. Make note of the second example, it addresses a common mistake made by students when simplifying fractions with variables.

### Candela Citations

- Subtract Fractions with Variables and Common Denominators.
**Authored by**: James Sousa (Mathispower4u.com) for Lumen Learning.**Located at**: https://youtu.be/-mLFZT2KgWI.**License**:*CC BY: Attribution* - Question ID: 146190, 146191, 146192, 146249, 146250.
**Authored by**: Alyson Day.**License**:*CC BY: Attribution*.**License Terms**: IMathAS Community License CC-BY + GPL

- Ex: Subtract Fractions with Like Denominators.
**Authored by**: James Sousa (mathispower4u.com).**Located at**: https://youtu.be/7CeAQcpOJw0.**License**:*CC BY: Attribution*

- Prealgebra.
**Provided by**: OpenStax.**License**:*CC BY: Attribution*.**License Terms**: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757