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By the end of this section, you will be able to:
  • Model addition of mixed numbers with a common denominator
  • Add mixed numbers with a common denominator
  • Model subtraction of mixed numbers
  • Subtract mixed numbers with a common denominator
  • Add and subtract mixed numbers with different denominators

Before you get started, take this readiness quiz.

  1. Draw figure to model 7 3 .
    If you missed this problem, review Visualize Fractions .
  2. Change 11 4 to a mixed number.
    If you missed this problem, review Visualize Fractions .
  3. Change 3 1 2 to an improper fraction.
    If you missed this problem, review Visualize Fractions .

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 1 dollar and 1 quarter, he has 1 1 4 dollars.

If Don has 2 dollars and 1 quarter, he has 2 1 4 dollars.

What if Ron and Don put their money together? They would have 3 dollars and 2 quarters. They add the dollars and add the quarters. This makes 3 2 4 dollars. Because two quarters is half a dollar, they would have 3 and a half dollars, or 3 1 2 dollars.

1 1 4 + 2 1 4 ________ 3 2 4 = 3 1 2

When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.

1 1 4 + 2 1 4

We can use fraction circles to model this same example:

Start with 1 1 4 . one whole and one 1 4 pieces . .
Add 2 1 4 more. two wholes and one 1 4 pieces . .
The sum is: three wholes and two 1 4 's . .
Doing the Manipulative Mathematics activity "Model Mixed Number Addition/Subtraction" will help you develop a better understanding of adding and subtracting mixed numbers.

Model 2 1 3 + 1 2 3 and give the sum.

Solution

We will use fraction circles, whole circles for the whole numbers and 1 3 pieces for the fractions.

two wholes and one 1 3 . .
plus one whole and two 1 3 s . .
sum is three wholes and three 1 3 s . .

This is the same as 4 wholes. So, 2 1 3 + 1 2 3 = 4 .

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Use a model to add the following. Draw a picture to illustrate your model.

Use a model to add the following. Draw a picture to illustrate your model.

Model 1 3 5 + 2 3 5 and give the sum as a mixed number.

Solution

We will use fraction circles, whole circles for the whole numbers and 1 5 pieces for the fractions.

one whole and three 1 5 s . .
plus two wholes and three 1 5 s. . .
sum is three wholes and six 1 5 s . .

Adding the whole circles and fifth pieces, we got a sum of 3 6 5 . We can see that 6 5 is equivalent to 1 1 5 , so we add that to the 3 to get 4 1 5 .

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Model, and give the sum as a mixed number. Draw a picture to illustrate your model.

2 5 6 + 1 5 6

4 2 3
The figure shows five circles. The last two are divided into six equal sections. Two sections of the last circle are white.

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Model, and give the sum as a mixed number. Draw a picture to illustrate your model.

1 5 8 + 1 7 8

3 1 2
The figure shows four circles. The last two are divided into eight equal sections. Four sections of the last circle are white.

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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.

Add mixed numbers with a common denominator.

Step 1. Add the whole numbers.

Step 2. Add the fractions.

Step 3. Simplify, if possible.

Add: 3 4 9 + 2 2 9 .

Solution

3 4 9 + 2 2 9
Add the whole numbers. .
Add the fractions. .
Simplify the fraction. .
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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