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Improper Fractions as Mixed Numbers

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

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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. 

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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

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