Fraction Help. A complete guide to everything you need to know about fractions in your math exam.

Here you will learn all the basics of fractions. You will find help on converting between improper and mixed numbers, adding fractions, subtracting fractions, multiplying fractions, dividing fractions, equivalent fractions and simplifying fractions.


What is a fraction?

A fraction can be used to represent a value which is not a whole amount. In the diagram shown you have 2/5 of the shape shaded red. This is because 2 out of the 5 squares are shaded red. The top number of fraction is called the numerator and the bottom number of the fraction is called the denominator.

How to simplify fractions?

To simplify a fraction look for the largest divisor of the numerator and denominator. Once you have found it divide the numerator and denominator of the fraction by this number.

Example

What fraction of the shape is shaded? Simplify your answer.

9 out of the 15 squares are shaded blue.

So the fraction shaded is 9/15.

To simplify the fraction you need the largest divisor of 9 and 15 which is 3.

All you need to do now is divide the numerator and denominator of the fraction by 3:

9 ÷ 3 = 3

15 ÷ 3 = 5

So 9/15 simplified is the same as 3/5.

For some more help on simplifying fraction take a read of this page below.

Simplifying algebraic fractions. Learn how to simplify a fraction which contains algebra (math help)

What is an equivalent fraction?

Equivalent fractions are two fractions of the same size but look different. An equivalent fraction can be obtained by multiplying the numerator and denominator of the fractions by the same number.

For example, 2/3 and 4/6 are equivalent fractions. This is because if you multiply the numerator and denominator of 2/ 3 by 2 you get 4/6.


More help on equivalent fractions can be found here:

What is an equivalent fraction and how to work out an equivalent fraction (2/4 = 4/8)

Converting between mixed numbers and improper fractions?

A mixed number is when you have a whole number followed by a proper fraction (a fraction whose numerator is smaller than the denominator). Whereas an improper fraction has a larger numerator.

Example

Convert 2 3/5 into an improper fraction .

To do this multiply the whole part by the denominator and add on the numerator:

2 × 5 + 3 = 13

So the improper fraction is 13/5 (the denominator remains the same as the mixed number)

Example 2

Convert 6 3/10 into an improper fraction:

10 × 6 + 3 = 63

So the improper fraction is 63/10

Example 3

Convert 19/7 into a mixed number.

To do this divide the numerator by the denominator.

17 ÷ 7 = 2 remainder 5.

So the mixed number is 2 5/7

Example 4

Convert 38/5 into a mixed number.

38 ÷ 5 = 7 remainder 3.

So the mixed number is 7 3/5

For more fraction help on converting between mixed and improper fraction click here:

Mixed numbers. Changing mixed numbers into improper fraction using a quick method.

Adding, Subtracting, Dividing and Multiplying Fractions

How do you add two fractions?

To add together two fractions you need to make the denominators the same on both fractions. There are several ways to do this - but the best method is to find the least common multiple of the denominators and then make two new fractions with this denominator. This is known as making a common denominator.

Example

Work out 3/7 + 2/5

The least common multiple of 7 and 5 is 35 (since 7 and 5 both divide into 35). Next, make equivalent fractions with 35 on the denominator.

3/7 = 15/35 (multiply the top and bottom by 5)

2/5 = 14/35 (multiply the top and bottom of the fraction by 7)

So 15/35 + 14/35 = 29/35

Example 2

Work out 2/3 + 7/9

The least common multiple of 3 and 9 is 9 (since 3 and 9 both divide into 9). So like the last example, make two new fraction with 9 on the denominator (the second fraction doesn’t have to be changed as 9 is already on the denominator).

2/3 = 6/9 (multiply the top and bottom of the fraction by 3).

Therefore, 6/9 + 7/9 = 13/9 (or 1 4/9 of you prefer mixed numbers).

How do you subtract fractions?

This can be done in exactly the same way as adding fractions, so you will need to make common denominators again:

Example

Work out 3/4 - 2/7.

The least common multiple of 4 and 7 is 28 (since 4 and 7 both divide into 28). Next, make equivalent fractions with 28 on the denominator.

3/4 = 21/28 (multiply the top and bottom by 7)

2/7 = 8/28 (multiply the top and bottom of the fraction by 4)

So 21/28 – 8/28 = 13/28

Check out this guide for more examples on addition and subtraction of fractions:

Adding (or taking) two fractions together. Step by step fraction guide.

How do you multiply fractions?

Multiplying fractions is actually quite easy to do as you don’t need to make new fractions. All you do is multiply the top numbers and multiply the bottom numbers!

Example

Work out 2/7 × 3/11 = 6/77

Example 2

Work out 4/5 × 6/7 = 24/35

How do you divide fractions?

Again, there is no need to make a common denominator when dividing by a fraction. Just follow these two simple steps:

1) Change the divide sign to a multiply sign.

2) Turn the second fraction over.

Example

Work out 2/7 ÷ 3/5

This becomes 2/7 × 5/3 = 10/21

Example 2

Work out 3/11 ÷ 3/8.

This becomes 3/11 × 8/3 = 24/33

How do you add, subtract, divide and multiply mixed numbers?

Always convert mixed number into improper fractions and then follow the examples above.

Example

Work out 2 1/3 + 1 2/5

First change both fractions into improper fractions:

7/3 + 7/5

Next make common denominators as you are adding fractions:

35/15 + 21/15

= 56/15 (or 3 11/15 if the questions asks for a mixed number as your answer).

How do you find a fraction of an amount?

To do this divide the amount by the denominator and multiply the answer by the numerator. So to work out 2/3 of 21 you do 21 ÷ 3 × 2 = 14.

Example

In a class there are 24 pupils. 3/8 of the pupils are girls, how many girls are in the class?

All you need to do is work out 3/8 of 24. Just divide 24 by the denominator and multiply the numerator by 3:

24 ÷ 8 × 3 = 9.

So 9 of the pupils in the class are girls.

For more help on finding a fraction of amount click on the link below:

Fractions of amounts worksheet or homework sheet.

So that basically covers everything on the basics of fractions. Most pupils get stuck on adding and subtracting fractions so make sure you make new fractions with the same denominators. However, there is no need to make common denominators when dividing and multiply fractions. Also, working out a fraction of amount is a frequent question in most math tests so make sure that this topic has been revised. Thanks for looking.

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joanwz profile image

joanwz 4 years ago from Katy, Texas

Great information. Added this to my favorites for future reference.

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