# Fractions

## Add and Subtract Mixed Numbers


### Model Addition of 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  dollar and  quarter, he has  dollars.
If Don has  dollars and  quarter, he has  dollars.
What if Ron and Don put their money together? They would have  dollars and  quarters. They add the dollars and add the quarters. This makes  dollars. Because two quarters is half a dollar, they would have  and a half dollars, or  dollars.
When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.
We can use fraction circles to model this same example:

### Add Mixed Numbers

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.
In , the sum of the fractions was a proper fraction. Now we will work through an example where the sum is an improper fraction.
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.
 compares the two methods of addition, using the expression  as an example. Which way do you prefer?

### Model Subtraction of Mixed Numbers

Let’s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.
We will use fraction circles (pizzas!) to help us visualize the process.
Start with one whole.
Algebraically, you would write:
What if we start with more than one whole? Let’s find out.
In the next example, we’ll subtract more than one whole.
What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a  bill and one quarter. What could you do? You could change the dollar bill into  quarters. The value of  quarters is the same as one dollar bill, but the  quarters are more useful for the parking meter. Now, instead of having a  bill and one quarter, you have  quarters and can put  quarters in the meter.
This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.
We can also model this using fraction circles, much like we did for addition of mixed numbers.

### Subtract Mixed Numbers with a Common Denominator

Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.
Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number.

### Add and Subtract Mixed Numbers with Different Denominators

To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we used above for adding or subtracting fractions with like denominators.

### Key Concepts

1. Add mixed numbers with a common denominator.
2. Subtract mixed numbers with common denominators.

3. Subtract mixed numbers with common denominators as improper fractions.

### Practice Makes Perfect

Model Addition of Mixed Numbers 
In the following exercises, use a model to find the sum. Draw a picture to illustrate your model.
Add Mixed Numbers with a Common Denominator 
In the following exercises, add.
Model Subtraction of Mixed Numbers 
In the following exercises, use a model to find the difference. Draw a picture to illustrate your model.
Subtract Mixed Numbers with a Common Denominator 
In the following exercises, find the difference.
Add and Subtract Mixed Numbers with Different Denominators 
In the following exercises, write the sum or difference as a mixed number in simplified form.
Mixed Practice 
In the following exercises, perform the indicated operation and write the result as a mixed number in simplified form.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.



ⓑ After reviewing this checklist, what will you do to become confident for all objectives?
