We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

TEXT

# 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 $2$ 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 [latex-display]\Large\frac{1}{4}\normalsize+\Large\frac{2}{4}\normalsize=\Large\frac{3}{4}[/latex-display] 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 $\Large\frac{3}{8}\normalsize+\Large\frac{2}{8}\normalsize=\Large\frac{5}{8}$.

### 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]
The following video shows more examples of how to use models to add fractions with like denominators. https://youtu.be/GTkY34kl6Kw

## 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 $a,b,\text{ and }c$ are numbers where $c\ne 0$, 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: $\Large\frac{3}{5}\normalsize+\Large\frac{1}{5}$

Answer: Solution:

 $\Large\frac{3}{5}\normalsize+\Large\frac{1}{5}$ Add the numerators and place the sum over the common denominator. $\Large\frac{3+1}{5}$ Simplify. $\Large\frac{4}{5}$

### Example

Find the sum: $\Large-\frac{3}{12}+\left(-\frac{5}{12}\right)$

Answer: Solution:

 $\Large-\frac{3}{12}+\left(-\frac{5}{12}\right)$ Add the numerators and place the sum over the common denominator. $\Large\frac{-3+\left(-5\right)}{12}$ Add. $\Large\frac{-8}{12}$ Simplify the fraction. $\Large-\frac{2}{3}$

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!

### 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.