<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

Improper Fractions as Mixed Numbers

14/3 = 4 remainder 2 = 4 and 2/3

Atoms Practice
Estimated6 minsto complete
%
Progress
Practice Improper Fractions as Mixed Numbers
Practice
Progress
Estimated6 minsto complete
%
Practice Now
Improper Fractions as Mixed Numbers
License: CC BY-NC 3.0

The school 6th 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.

\begin{align*}\frac{18}{4}\end{align*}

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.

\begin{align*}1 \text{ whole} = \frac{4}{4}\end{align*}

Convert \begin{align*}\frac{18}{4}\end{align*} to a mixed number.

First, divide the numerator by the denominator.

\begin{align*}18 \div 4 = 4 R2\end{align*}

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

\begin{align*}\frac{18}{4} = 4\frac{2}{4}\end{align*} 

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

\begin{align*}\frac{2}{4} = \frac{1}{2}\end{align*}

The improper fraction \begin{align*}\frac{18}{4}\end{align*} is expressed as \begin{align*}4\frac{2}{4}\end{align*} or \begin{align*}4 \frac{1}{2}\end{align*}.

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

\begin{align*}\frac{18}{9}\end{align*}

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 \begin{align*}\frac{18}{9}\end{align*} 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.

\begin{align*}\text{Muffins left over} = \frac{15}{12}\end{align*}

First, divide the numerator by the denominator.

\begin{align*}15 \div 12 = 1 R 3\end{align*}

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

\begin{align*}\frac{15}{12} = 1 \frac{3}{12}\end{align*}

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

\begin{align*}\frac{3}{12} = \frac{1}{4}\end{align*}

There were \begin{align*}1 \frac{1}{4}\end{align*} dozen muffins left over.

Example 2

Express this improper fraction as a mixed number.

\begin{align*}\frac{82}{5}\end{align*}

First, divide the numerator by the denominator.

\begin{align*}82 \div 5 = 16 R2\end{align*}

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

\begin{align*}\frac{82}{5} = 16 \frac{2}{5}\end{align*}

The improper fraction \begin{align*}\frac{82}{5}\end{align*} is expressed as \begin{align*}16 \frac{2}{5}\end{align*}.

Example 3

Express this improper fraction as a mixed number.

\begin{align*}\frac{24}{5}\end{align*}

First, divide the numerator by the denominator.

\begin{align*}24 \div 5 = 4 R4\end{align*}

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

\begin{align*}\frac{24}{5} = 4 \frac{4}{5}\end{align*}

The improper fraction \begin{align*}\frac{24}{5}\end{align*} is expressed as \begin{align*}4 \frac{4}{5}\end{align*}.


Example 4

Express this improper fraction as a mixed number.

\begin{align*}\frac{21}{3}\end{align*}

First, divide the numerator by the denominator.

\begin{align*}21 \div 3 = 7\end{align*}

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

The improper fraction \begin{align*}\frac{23}{3}\end{align*} is equal to 7.

Example 5

Express this improper fraction as a mixed number.

\begin{align*}\frac{32}{6}\end{align*}

First, divide the numerator by the denominator.

\begin{align*}32 \div 6 = 5 R 2\end{align*}

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

\begin{align*}\frac{32}{6} = 5 \frac{2}{6}\end{align*}

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

\begin{align*}\frac{2}{6} = \frac{1}{3}\end{align*}

The improper fraction \begin{align*}\frac{32}{6}\end{align*} is expressed as \begin{align*}5 \frac{2}{6}\end{align*} or \begin{align*}5 \frac{1}{3}\end{align*}.

Review

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

  1. \begin{align*}\frac{22}{3}\end{align*}
  2. \begin{align*}\frac{44}{5}\end{align*}
  3. \begin{align*}\frac{14}{3}\end{align*}
  4. \begin{align*}\frac{7}{2}\end{align*}
  5. \begin{align*}\frac{10}{3}\end{align*}
  6. \begin{align*}\frac{47}{9}\end{align*}
  7. \begin{align*}\frac{50}{7}\end{align*}
  8. \begin{align*}\frac{60}{8}\end{align*} 
  9. \begin{align*}\frac{43}{8}\end{align*}
  10. \begin{align*}\frac{19}{5}\end{align*}
  11. \begin{align*}\frac{39}{7}\end{align*}
  12. \begin{align*}\frac{30}{4}\end{align*}
  13. \begin{align*}\frac{11}{7}\end{align*}
  14. \begin{align*}\frac{26}{5}\end{align*} 
  15. \begin{align*}\frac{89}{8}\end{align*}
  16. \begin{align*}\frac{70}{14}\end{align*}

Review (Answers)

To see the Review answers, open this PDF file and look for section 5.15. 

Resources

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / notes
Show More

Vocabulary

Equivalent

Equivalent means equal in value or meaning.

improper fraction

An improper fraction is a fraction in which the absolute value of the numerator is greater than the absolute value of the denominator.

Mixed Number

A mixed number is a number made up of a whole number and a fraction, such as 4\frac{3}{5}.

Image Attributions

  1. [1]^ License: CC BY-NC 3.0

Explore More

Sign in to explore more, including practice questions and solutions for Improper Fractions as Mixed Numbers.
Please wait...
Please wait...