The school 6^{th} grade class had a bake sale. Missy brought 48 muffins to sell. At the end of the day, there were still 15 muffins left. How many dozen muffins were left? Write the amount as a mixed number.

In this concept, you will learn to write improper fractions as mixed numbers.

### Writing Improper Fractions as Mixed Numbers

An **improper fraction** is a fraction where the numerator is larger than the denominator. An improper fraction can be written as a mixed number. A **mixed number** is composed of a whole number and a fraction.

To change an improper fraction to a mixed number, divide the numerator by the denominator. This will tell you the number of wholes. If there is a remainder, it is the fraction part of a mixed number.

Here is an improper fraction.

There are 18 parts and the whole has only been divided into 4 parts. Remember that when the numerator is larger than the denominator, there is more than one whole.

Convert

to a mixed number.First, divide the numerator by the denominator.

Then, write the quotient as a mixed number with the **remainder** as a fraction. The remainder is the numerator of the fraction.

Next, look at the fraction. Simplify the fraction if you can. Divide the numerator and denominator by the greatest common factor, 2.

The improper fraction

is expressed as or .Sometimes, you will have an improper fraction that converts to a whole number and not a mixed number.

Here 18 divided by 9 is 2. There is no remainder, so there is no fraction. This improper fraction converts to a whole number.

The improper fraction

is expressed as 2.### Examples

#### Example 1

Earlier, you were given a problem about Missy and her muffins.

Missy had 15 muffins left over from the bake sale and a dozen contains 12 muffins. Convert 15 muffins as a fraction out of 12 to find the number of dozen muffins left.

First, divide the numerator by the denominator.

Then, write the quotient as a mixed number with the remainder as a fraction.

Next, look at the fraction. Simplify the fraction if you can. Divide the numerator and denominator by the greatest common factor, 3.

There were

dozen muffins left over.#### Example 2

Express this improper fraction as a mixed number.

First, divide the numerator by the denominator.

Then, write the quotient as a mixed number with the remainder as a fraction. The remainder is the numerator of the fraction.

The improper fraction

is expressed as .#### Example 3

Express this improper fraction as a mixed number.

First, divide the numerator by the denominator.

Then, write the quotient as a mixed number with the remainder as a fraction. The remainder is the numerator of the fraction.

The improper fraction

is expressed as .

Example 4

Express this improper fraction as a mixed number.

First, divide the numerator by the denominator.

This fraction has no remainder and is not a mixed number.

The improper fraction

is equal to 7.#### Example 5

Express this improper fraction as a mixed number.

First, divide the numerator by the denominator.

Next, look at the fraction. Simplify the fraction if you can. Divide the numerator and denominator by the greatest common factor, 2.

The improper fraction

is expressed as or .### Review

Convert each improper fraction to a mixed number. Simplify when necessary.

- \begin{align*}\frac{7}{2}\end{align*}
- \begin{align*}\frac{43}{8}\end{align*}
- \begin{align*}\frac{89}{8}\end{align*}