What Are Mixed Numbers? - Definition & Examples

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  • 0:00 What Are Mixed Numbers?
  • 0:30 Why Do We Use Mixed Numbers?
  • 2:00 Examples
  • 3:10 Lesson Summary
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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

This lesson will give the definition of mixed numbers and explain the purpose mixed numbers serve. It will also provide plenty of examples to ensure complete understanding of this concept.

What are Mixed Numbers?

When we think of the word 'mixed,' we may think of something that consists of different qualities or elements. The first thing that comes to my mind is a favorite snack, Chex Mix. It's called a 'mix' because it combines different elements: pretzels, peanuts, Cheerios, and of course, rice and corn Chex.

Mixed numbers are numbers that entail both an integer and a fraction. You are mixing these two types of numbers, hence the name mixed numbers!

Here's an example of what a mixed number looks like:

5 and a third.

Why Do We Use Mixed Numbers?

Mixed numbers are helpful when we are counting whole things and parts of things together.

Let's look at an example involving pizza. Who doesn't love pizza?

Maria ordered three pepperoni pizzas for her and two girlfriends to enjoy for her slumber party Friday night. Uncle Joe ate a half of one of the pizzas without knowing they were for the girls.

Maria now has two and a half pepperoni pizzas.
Two and a half pepperoni pizzas.

Now Maria and her friends have two whole pizzas and one half pizza.

The mixed number would look like this:

Two and a half.

Saying 'two and a half' is like saying 'two plus one half.' They are ultimately the same thing, but 'two and a half' sounds much better!

We also use mixed numbers to simplify an improper fraction. An improper fraction looks something like this:


An improper fraction, by definition, is a fraction whose top number (numerator) is bigger or equal to the bottom number (denominator). The improper fraction in this example is quite easy to simplify, as it is merely a division problem with a whole number as a solution. 24 divided by 6 is 4.

But sometimes improper fractions are not as easy to simplify, and they can be turned into a mixed number.

Let's look at this example:

Example of improper fraction to mixed number conversion.

In the example, 7 goes into 48 six times with a remainder of 6. Therefore, you get 6 and 6/7.


  • Example 1

13 and 2/5

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