Introduction

To convert an improper fraction to an equivalent mixed number, we proceed as follows:

Step 1: Divide the numerator by the denominator.

Step 2: Express the resulting division problem as a mixed number.

Let's use this method to convert the following improper fraction to a mixed number:

\dfrac{14}{3}

First, we divide 14 by {\color{blue}{3}}\mathbin{:} 14\div 3 = 4 \, \textrm{R}\,{\color{red}2}

So, our division gives 4 wholes, and we're left with \dfrac{\color{red}2}{\color{blue}3}. Therefore, \dfrac{14}{3} = 4 \, \dfrac{\color{blue}2}{\color{red}3}.

So, we conclude that \dfrac{14}{3} expressed as a mixed number is 4\,\dfrac23.

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Example: Converting an Improper Fraction to a Mixed Number

What mixed number is equivalent to \dfrac{71}{8} ?

EXPLANATION

First, we divide 71 by {\color{blue}{8}}{:} 71 \div 8 = 8\, \textrm{R}\,{\color{red}{7}}

So, our division gives 8 wholes, and we're left with \dfrac{\color{red}7}{\color{blue}8}. Therefore, we conclude that \dfrac{71}{8} = 8\,\dfrac{\color{red}7}{\color{blue}8}.

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Practice: Converting an Improper Fraction to a Mixed Number

$\dfrac{23}{5} =$

a
 $2\,\dfrac{1}{5}$
b
 $1\,\dfrac{3}{5}$
c
 $4\,\dfrac{1}{5}$
d
 $4\,\dfrac{3}{5}$
e
 $\dfrac{3}{5}$
Practice: Converting an Improper Fraction to a Mixed Number

Expressed as a mixed number in lowest terms, $\dfrac{23}{3} =$

a
b
c
d
e
Practice: Converting an Improper Fraction to a Mixed Number

Expressed as a mixed number in lowest terms, $\dfrac{19}{9} = $

a
b
c
d
e
Reducing the Fraction Part of a Mixed Number to Lowest Terms

Sometimes, it's necessary to reduce the fraction part to the lowest terms.

For instance, let's represent the following fraction as a mixed number:

\dfrac{18}{4}

First, we divide 18 by {\color{blue}{4}}\mathbin{:}

\dfrac{18}{4} = 4 \, \textrm{R}\, {\color{red}{2}}

So, our division gives 4 wholes, and we're left with \dfrac{\color{red}2}{\color{blue}4}.

We can reduce the fraction \dfrac{\color{red}2}{\color{blue}4} to its lowest terms by dividing the numerator and denominator by 2{:}

\begin{align} \dfrac{\color{red}2}{\color{blue}4} &= \dfrac{2 \div 2}{4 \div 2} = \dfrac{1}{2} \end{align}

Therefore, our mixed number is equivalent to

4 \,\dfrac{1}{2}.

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Example: Converting an Improper Fraction to a Mixed Number Expressed in Lowest Terms

Find a mixed number equivalent to \dfrac{51}{6}.

EXPLANATION

First, we divide 51 by {\color{blue}{6}}{:} 51 \div 6 = 8 \, \textrm{R}\, {\color{red}{3}}

So, our division gives 8 wholes, and we're left with \dfrac{\color{red}3}{\color{blue}6}.

We can reduce the fraction \dfrac{\color{red}3}{\color{blue}6} to its lowest terms by dividing the numerator and denominator by 3{:} \begin{align} \dfrac{\color{red}3}{\color{blue}6} & = \dfrac{3 \div 3}{6 \div 3} = \dfrac{1}{2} \end{align}

Therefore, our mixed number is equivalent to 8 \,\dfrac{1}{2}.

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Practice: Converting an Improper Fraction to a Mixed Number Expressed in Lowest Terms

$\dfrac{55}{10} = $

a
 $5 \,\dfrac{2}{5}$
b
 $6 \,\dfrac{1}{2}$
c
 $6 \,\dfrac{2}{5}$
d
 $5 \,\dfrac{1}{2}$
e
 $5 \,\dfrac{1}{5}$
Practice: Converting an Improper Fraction to a Mixed Number Expressed in Lowest Terms

$\dfrac{21}{6} =$

a
 $3 \,\dfrac{2}{3}$
b
 $4 \,\dfrac{1}{2}$
c
 $3 \,\dfrac{1}{3}$
d
 $3 \,\dfrac{1}{2}$
e
 $4 \,\dfrac{2}{3}$
Practice: Converting an Improper Fraction to a Mixed Number Expressed in Lowest Terms

Expressed as a mixed number in lowest terms, $\dfrac{70}{8} = $

a
b
c
d
e
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