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]
Answer:
[latex-display]\frac{5}{6}[/latex-display]
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].
