Learning Outcomes
- Model addition of mixed numbers with a common denominator
- Add mixed numbers with a common denominator
Model addition of two mixed numbers with a common denominator
So far, we’ve added and subtracted proper and improper fractions, but not mixed numbers. Let’s begin by thinking about addition of mixed numbers using money.
If Ron has 11 dollar and 11 quarter, he has 114114 dollars.
If Don has 22 dollars and 11 quarter, he has 214214 dollars.
What if Ron and Don put their money together? They would have 33 dollars and 22 quarters. They add the dollars and add the quarters. This makes 324324 dollars. Because two quarters is half a dollar, they would have 33 and a half dollars, or 312312 dollars.
114114+214214
________________
324=312324=312
When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.
114+214114+214
We can use fraction circles to model this same example:
114+214114+214 | |||
Start with 114114 | one whole and one 1414 pieces | ![]() |
114114 |
Add 214214 more. | two wholes and one 1414 pieces | ![]() |
+214+214 |
The sum is: | three wholes and two 1414‘s | ![]() |
324=312324=312 |
Doing the Manipulative Mathematics activity “Model Mixed Number Addition/Subtraction” will help you develop a better understanding of adding and subtracting mixed numbers.
Example
Model 213+123213+123 and give the sum.
Solution:
We will use fraction circles – whole circles for the whole numbers and 1313 pieces for the fractions.
two wholes and one 1313 | ![]() |
213213 |
plus one whole and two 1313 s | ![]() |
+123+123 |
sum is three wholes and three 1313 s | ![]() |
333=4333=4 |
This is the same as 44 wholes. So, 213+123=4213+123=4.
Try It
Example
Model 135+235135+235 and give the sum as a mixed number.
Try It
Model, and give the sum as a mixed number. Draw a picture to illustrate your model.
256+156256+156
Model, and give the sum as a mixed number. Draw a picture to illustrate your model.
158+178158+178
Add mixed numbers with like denominators
Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.
Add mixed numbers with a common denominator: Method 1
Step 1. Add the whole numbers.
Step 2. Add the fractions.
Step 3. Simplify, if possible.
Example
Add: 349+229349+229
Solution:
349+229349+229 | |
Add the whole numbers. | 349349
+2295+2295 |
Add the fractions. | 349349
+229569+229569 |
Simplify the fraction. | 569=523569=523 |
Try It
In the example above, the sum of the fractions was a proper fraction. Now we will work through an example where the sum is an improper fraction.
Example
Find the sum: 959+579959+579
Try It
In the following video we show another example of how to add two mixed numbers.
Another way to add mixed numbers with like denominators
An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.
Add mixed numbers with a common denominator: Method 2
Step 1. Convert the mixed numbers to improper fractions.
Step 2. Add the improper fractions.
Step 3. Rewrite as a mixed number.
Step 4. Simplify, if possible.
Example
Add by converting the mixed numbers to improper fractions: 378+438.
Try It
The table below compares the two methods of addition, using the expression 325+645 as an example. Which way do you prefer?
Mixed Numbers | Improper Fractions |
---|---|
325+6459659+659+1151015 | 325+645175+3455151015 |
Candela Citations
- Question ID: 146357, 146367, 146368, 146380. Authored by: Alyson Day. License: CC BY: Attribution. License Terms: IMathAS Community License CC-BY + GPL
- Ex: Add Mixed Numbers with Like Denominators. Authored by: James Sousa (mathispower4u.com). Located at: https://youtu.be/2iHExOrBUvw. License: CC BY: Attribution
- Ex: Find the Sum of Two Mixed Numbers Using Pattern Blocks. Authored by: James Sousa (Mathispower4u.com). Located at: https://youtu.be/SngHXtqs_UE. 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