Convert Improper Fraction
Support Page

Welcome to the Math Salamanders support page on How to Convert Improper Fraction to Mixed Numbers.

We have a selection of resources including worked examples, support sheets and practice sheets.

Want to check your working out? Try using our Improper Fraction Calculator!

What are Proper, Improper and Mixed Fractions?

A fraction is a number with the form: \[ {n \over d} \]

  • If the numerator is smaller than the denominator (if n < d), then the fraction is called a proper fraction, and its value is less than 1.
  • If the numerator is greater than the denominator (if n > d), then the fraction is called an improper fraction, and its value is greater than 1.
  • If the numerator is equal to the denominator (if n = d), then the fraction's value is equal to 1.
  • A mixed fraction (or mixed number) is a number that has a whole number part to it, and a fraction part to it.
  • Please note: if the value of n or d is negative, then we compare the absolute values of the numerator and denominator.

Types of Fractions Examples

\[{3 \over 7} \; , \; {2 \over 10} \; and \; {17 \over 26} \] are all proper fractions.

\[ {31 \over 5} \; , \; {15 \over 10} \; , \; -{7 \over 4} \; and \; {37 \over 23} \] are all improper fractions.

\[ 3{1 \over 5} \; , \; 2 {5 \over 8} \; and \; 4 {1 \over 2} \] are all mixed numbers or mixed fractions.

Improper Fraction Calculator

If you just want a calculator to do the hard work for you, then try our Improper Fraction Calculator.

The calculator will convert any mixed number to an improper fraction, or an improper fraction into a mixed number.

The great thing is that it will also show you all the working out - job done!

If you would rather learn how to do this for yourself, then ignore this part and keep reading.

How to Convert Improper Fractions

Frazer says "The important thing to remember when converting an improper fraction to a mixed fraction is that a fraction represent the division of the numerator by the denominator."

So in other words: \[ {a \over b} \; = \; a ÷ b \]

How to Convert an Improper Fraction to a Mixed Number:

Divide the numerator by the denominator.

  • The quotient (whole number) part of the answer gives you the number of ones.
  • The remainder part of the answer gives you the numerator of the fraction that you have left over.

Comverting Improper Fractions Examples

Example 1) Convert into a mixed number the fraction: \[ {23 \over 5 } \]

Dividing the numerator by the denominator gives us: 23 ÷ 5 = 4 r 3

So this means that \[ {23 \over 5} = 4 {3 \over 5} \]

Example 2) Convert into a mixed number the fraction: \[ {19 \over 7 } \]

Dividing the numerator by the denominator gives us: 19 ÷ 7 = 2 r 5

So this means that \[ {19 \over 7} = 2 {5 \over 7} \]

Example 3) Convert into a mixed number the fraction: \[ {27 \over 4 } \]

Dividing the numerator by the denominator gives us: 27 ÷ 4 = 6 r 3

So this means that \[ {27 \over 4} = 6 {3 \over 4} \]

Example 4) Convert into a mixed number the fraction: \[ {32 \over 9 } \]

Dividing the numerator by the denominator gives us: 32 ÷ 9 = 3 r 5

So this means that \[ {32 \over 9} = 3 {5 \over 9} \]

For further information and a printable support sheet, please see below.

Convert Improper Fractions to Mixed Fractions Practice Sheets

How to Convert a Mixed Number to an Improper Fraction

Frazer says "You can convert a mixed fraction, or mixed number, into an improper fraction by following these two simple steps:

Frazer the Fraction Salamander

Step 1

Change the whole number part into a fraction by multiplying it by the denominator, then putting it over the denominator.

Step 2

Add on the fraction part of the mixed number by adding the two numerators.

Examples Converting Mixed Numbers

Example 1) Convert into an improper fraction the number: \[ 3 {1 \over 5 } \]

Step 1)

Multiply the denominator by the integer part gives us: 3 x 5 = 15.

This means that: \[ 3 = {15 \over 5} \]

Step 2)

This gives us: \[ 3{1 \over 5} = {15 \over 5} + {1 \over 5} = {16 \over 5} \]

Final answer \[ 3{1 \over 5} \; = \; {16 \over 5} \]

Example 2) Convert into an improper fraction the number: \[ 5 {4 \over 7 } \]

Step 1)

Multiply the denominator by the integer part gives us: 5 x 7 = 35.

This means that: \[ 5 = {35 \over 7} \]

Step 2)

Add on the fraction part: \[ 5{4 \over 7} = {35 \over 7} + {4 \over 7} = {39 \over 7} \]

Final answer \[ 5{4 \over 7} \; = \; {39 \over 7} \]

Example 3) Convert into an improper fraction the number: \[ 9 {2 \over 3 } \]

Combining the two steps gives us:

\[ 9 {2 \over 3} = {(9 \times 3) + 2 \over 3} = {27 + 2 \over 3} = {29 \over 3} \]

Example 4) Convert into an improper fraction the number: \[ 3 {6 \over 7 } \]

Combining the two steps gives us:

\[ 3 {6 \over 7} = {(3 \times 7) + 6 \over 7} = {21 + 6 \over 7} = {27 \over 7} \]


For further information and a printable support sheet, please see below.

Convert Mixed Numbers to Improper Fractions Practice sheets

Convert Mixed Numbers to Improper Fractions Walkthrough Video

This short video walkthrough shows several problems from our Convert Mixed Numbers to Improper Fractions Sheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Resources

Take a look at some more of our worksheets and resources similar to these.

More Improper Fraction Worksheets

If you are not ready for the sheets on this page, we also have some simpler visual converting improper fraction worksheets.

What is a Mixed Number

This support page introduces mixed numbers with some examples and an interactive teaching app.

There are also some practice worksheets to help you identify and write mixed numbers.

Converting Decimals to Fractions

Here you will find some simple information and advice about how to convert a decimal to a fraction. Before you learn how to do this, you should also know about simplifying fractions.

You will also find a printable resource sheet and some practice sheets which will help you understand and practice this math skill.

Simplifying Fractions

Equivalent Fractions

The printable fraction page below contains more support, examples and practice using equivalent fractions.

Convert Improper Fractions Online Quiz

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