What is a mixed number?

A mixed number is a number made up of a whole number and a proper fraction together. For example, the number 21/3 is a mixed number.

Mixed numbers are sometimes called mixed fractions.

What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example,7/3 is an improper fraction, since 7 is larger than 3.

You can see the improper fraction 7/3 below. There are 7 thirds:

Improper fractions are sometimes called “top-heavy” fractions.

How do you convert a mixed number to an improper fraction?

You might notice that the pictures for 213 and 73 above are the same! You can use mixed numbers and improper fractions to show the same amount. This picture shows 2 and 13, and it also shows 7 thirds.

Let’s say you have a mixed number and want to write it as an improper fraction. This can be helpful for when you want to multiply or divide mixed numbers. To change a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator.
2. Add that number to the numerator.
3. Write that sum on top of the original denominator.

Let’s try it with 2 3/4. First, multiply the whole number by the denominator.

2×4=8

Next, add that number to the numerator.

8+3=11

Now write the improper fraction!

11/4

So, 2 3/4 is the same as 11/4.

How do you convert an improper fraction to a mixed number?

You can go the other direction, too! To change an improper fraction to a mixed number, follow these steps:

1. Divide the numerator by the denominator.
2. Write down the whole number part of the quotient.
3. Take the remainder and write it over the original denominator.

Let’s try it with 9/4.

 First, divide.

9/4=9÷4=2 R1

Write down the whole number part, 2. Then take the remainder and write it over the original denominator. That’s your answer!

2 1/4

So, 94 is the same as 2 1/4.

What if there’s no remainder?

That means you have a whole number! Look at 12/4 as an example.

First, divide the numerator by the denominator.

12/4=12÷4=3

There’s no remainder, so your answer is just the whole number 3!

Learn with an example

Let’s practice!