Introduction

Colorful illustration of numbers. Sometimes you will need to work with fractions that are a combination of a whole number and a fraction. These are called mixed numbers. For example, $\mathsf{ 2\frac{3}{4} }$ is a mixed number because it has both a whole number (2) and a fraction $\mathsf{ \frac{3}{4} }$ . This number is between 2 and 3 on the number line.

Adding mixed numbers uses many of the steps that you have learned for adding other fractions. Let’s take a closer look at adding mixed numbers. To start, review the slides to learn how to add mixed numbers with like denominators.

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Where to start?

The best place to start with any problem is setting up your work neatly. Consider the problem:

Two and two fourths plus three and three fourths equals.

Add the Fractions

When the fractions have like (same) denominators, add them using what you have learned about adding other fractions with like denominators.

1. Keep the denominator the same, and record it in your sum.

Two fourths plus three fourths equals (?) fourths.

2. Add your numerators.

Two fourths plus three fourths equals five fourths.

Your fractions are added, and you are ready to add your whole numbers.

Add the Whole Numbers

Adding the whole numbers in a set of mixed numbers is just like adding any other whole numbers. You will use the same strategies you have always used, like this:

Two and two fourths plus three and three fourths; the sum is five and five fourths.

2 + 3 = 5.

Simplify the Fraction

When adding whole numbers, you might need to simplify your sum. First evaluate the fraction part of your answer. Look at the fraction sum below; can you make any additional whole groups from this sum?

$\mathsf{ \frac{5}{4} }$ is more than one whole, which would be $\mathsf{ \frac{4}{4} }$ . When the numerator is larger than the denominator, called an improper fraction, you can make additional whole values.

To do this, subtract the value of a whole, which is the denominator, from the numerator.

In this example you will subtract: 5 – 4 = 1

Record your answer over the denominator.

Now the denominator is less than the numerator. You have simplified the fraction to a whole value. So, in this example, $\mathsf{ \frac{5}{4} }$ became:

One last step before returning to your whole number: decide if the fraction can be simplified by a common factor. In this example, $\mathsf{ \frac{1}{4} }$ is already simplified.

Finish It Up!

After simplifying the improper fraction, we get another mixed fraction ( $\mathsf{ \frac{5}{4} }$ became $\mathsf{ 1\frac{1}{4} }$ ). Now you need to add the whole number of this new mixed fraction to the whole number previously calculated. This means we must add the whole numbers 5 and 1:

Put your whole number together with your simplified fraction for your final answer:

Five plus one and one fourth; the sum is six and one fourth.

Altogether:

Two and two fourths plus three and three fourths equals five and five fourths equals six and one fourth.

Practice makes perfect! Use your understanding of mixed fractions and addition to work through these practice problems. When ready, click each problem to check your answers.

$\mathsf{ 2\frac{3}{6} + 1\frac{5}{6} = }$

Add the fractions.

$\mathsf{ \frac{3}{6} + \frac{5}{6} = \frac{8}{6} }$

Add the whole numbers.

$\mathsf{ 2\frac{3}{6} + 1\frac{5}{6} = 3\frac{8}{6} }$

Simplify the improper fraction to a mixed number.

$\mathsf{ \frac{8}{6} = 1\frac{2}{6} }$

Add the whole numbers with the mixed number you created when you added your fractions.

$\mathsf{ 3 + 1\frac{2}{6} = 4\frac{2}{6} }$

One last step: the fraction $\mathsf{ \frac{2}{6} }$ can be simplified further.
2 and 6 share the GCF of 2. Divide the fraction by the GCF to simplify.

$\begin{align*} \underline{2} \div 2 &= \underline{1} \\ 6 \div 2 &= 3 \end{align*}$

So, the final answer is:

$\mathsf{ 4\frac{1}{3} }$

$\mathsf{ 4\frac{5}{7} + 5\frac{2}{7} = }$

Add the fractions.

$\mathsf{ \frac{5}{7} + \frac{2}{7} = \frac{7}{7} }$

Add the whole numbers.

$\mathsf{ 4\frac{5}{7} + 5\frac{2}{7} = 9\frac{7}{7} }$

When the numerator and denominator of a fraction are the same, you have 1 whole.

$\mathsf{ \frac{7}{7} }$ is the same as 1 whole.

So... $\mathsf{ 9\frac{7}{7} }$ can be simplified to 9 + 1 = 10.

Your final answer is 10.

$\mathsf{ 3\frac{6}{10} + 5\frac{8}{10} = }$

Add the fractions.

$\mathsf{ \frac{6}{10} + \frac{8}{10} = \frac{14}{10} }$

Add the whole numbers.

$\mathsf{ 3\frac{6}{10} + 5\frac{8}{10} = 8\frac{14}{10} }$

Simplify the improper fraction to a mixed number.

$\mathsf{ \frac{14}{10} = 1\frac{4}{10} }$

Add the whole numbers with the mixed number you created when you added your fractions.

$\mathsf{ 8 + 1\frac{4}{10} = 9\frac{4}{10} }$

One last step: the fraction $\mathsf{ \frac{4}{10} }$ can be simplified further.
4 and 10 share the GCF of 2. Divide the fraction by the GCF to simplify.

$\begin{align*} \underline{\hspace{5px}4 \hspace{5px}} \div 2 &= \underline{2} \\ 10 \div 2 &= 5 \end{align*}$

So, the final answer is:

$\mathsf{ 9\frac{2}{5} }$

Learning Coach — Adding Mixed Numbers

Objectives

Skills Needed

Keywords

Learning Coach Notes

Introduction

How do you add mixed numbers with like denominators?

Where to start?

Add the Fractions

Add the Whole Numbers

Simplify the Fraction

Finish It Up!