# Convert Improper FractionSupport 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.

## How to Convert Improper Fractions

### 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.

## How to Convert a Mixed Number to an Improper Fraction

### 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.

### More Recommended Math Resources

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### Convert Improper Fractions Online Quiz

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