# Adding Fractions With Common Denominators

### Learning Outcomes

- Use a model to find the sum of two fractions with the same denominator
- Add fractions with a common denominator without a model

## Model Fraction Addition

How many quarters are pictured? One quarter plus [latex]2[/latex] quarters equals [latex]3[/latex] quarters. Remember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that[latex]{\Large\frac{1}{4}}+{\Large\frac{2}{4}}=\Large{\frac{3}{4}}[/latex]

[latex]\text{one quarter }+\text{ two quarters }=\text{ three quarters} [/latex]

Let’s use fraction circles to model the same example, [latex]\Large\frac{1}{4}\normalsize+\Large\frac{2}{4}[/latex].Start with one [latex]\Large\frac{1}{4}[/latex] piece. | [latex]\Large\frac{1}{4}[/latex] | |

Add two more [latex]\Large\frac{1}{4}[/latex] pieces. | [latex]+\Large\frac{2}{4}[/latex] | |

The result is [latex]\Large\frac{3}{4}[/latex] . | [latex]\Large\frac{3}{4}[/latex] |

### example

Use a model to find the sum [latex]\Large\frac{3}{8}\normalsize+\Large\frac{2}{8}[/latex]. Solution:Start with three [latex]\Large\frac{1}{8}[/latex] pieces. | [latex]\Large\frac{3}{8}[/latex] | |

Add two [latex]\Large\frac{1}{8}[/latex] pieces. | [latex]+\Large\frac{2}{8}[/latex] | |

How many [latex]\Large\frac{1}{8}[/latex] pieces are there? | [latex]\Large\frac{5}{8}[/latex] |

### try it

Use a model to find each sum. Show a diagram to illustrate your model. [latex-display]\Large\frac{1}{8}\normalsize+\Large\frac{4}{8}[/latex-display]Answer: [latex-display]\frac{5}{8}[/latex-display]

Use a model to find each sum. Show a diagram to illustrate your model. [latex-display]\Large\frac{1}{6}\normalsize+\Large\frac{4}{6}[/latex-display]Answer: [latex-display]\frac{5}{6}[/latex-display]

[ohm_question height="270"]146178[/ohm_question]## 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.### Fraction Addition

If [latex]a,b,\text{ and }c[/latex] are numbers where [latex]c\ne 0[/latex], then [latex-display]\Large\frac{a}{c}\normalsize+\Large\frac{b}{c}\normalsize=\Large\frac{a+b}{c}[/latex-display] To add fractions with a common denominators, add the numerators and place the sum over the common denominator.### Example

Find the sum: [latex]\Large\frac{3}{5}\normalsize+\Large\frac{1}{5}[/latex]Answer: Solution:

[latex]\Large\frac{3}{5}\normalsize+\Large\frac{1}{5}[/latex] | |

Add the numerators and place the sum over the common denominator. | [latex]\Large\frac{3+1}{5}[/latex] |

Simplify. | [latex]\Large\frac{4}{5}[/latex] |

### Example

Find the sum: [latex]\Large-\frac{3}{12}+\left(-\frac{5}{12}\right)[/latex]Answer: Solution:

[latex]\Large-\frac{3}{12}+\left(-\frac{5}{12}\right)[/latex] | |

Add the numerators and place the sum over the common denominator. | [latex]\Large\frac{-3+\left(-5\right)}{12}[/latex] |

Add. | [latex]\Large\frac{-8}{12}[/latex] |

Simplify the fraction. | [latex]\Large-\frac{2}{3}[/latex] |

### Try It

[ohm_question height="270"]146187[/ohm_question]## Licenses & Attributions

### CC licensed content, Original

- Question ID: 146178, 146187.
**Authored by:**Alyson Day.**License:**CC BY: Attribution.**License terms:**IMathAS Community License CC-BY + GPL. - Revision and Adaptation.
**Provided by:**Lumen Learning**License:**CC BY: Attribution.

### CC licensed content, Shared previously

- Ex: Add Fractions with Like Denominators.
**Authored by:**James Sousa (mathispower4u.com).**License:**CC BY: Attribution. - 0:00 / 3:09 Ex 1: Adding Signed Fractions.
**Authored by:**James Sousa (Mathispower4u.com).**License:**CC BY: Attribution.

### CC licensed content, Specific attribution

- Prealgebra.
**Provided by:**OpenStax**License:**CC BY: Attribution.**License terms:**Download for free at http://cnx.org/contents/[email protected].