Learning about fractions at KS2 are useful, not only in the classroom but in everyday life. It’s important for children to develop a good understanding of fractions as they are an important part of the KS2 maths curriculum and are fundamental to a lot of other topics that children learn as they get older.

They can however be difficult to grasp. Here’s your must-have guide for helping kids understand what fractions are and how to use them in KS2 Primary school maths.

What are fractions? – What does my child need to know at about fractions at KS2?

When we divide a whole into equal parts, each part is a fraction of the whole. For example, if you fold a piece of paper in half, there is now a line dividing the piece of paper in 2. Each section is now ½ of the whole piece of paper.

A fraction is written as 2 whole numbers above each other with a line between them. The number on the bottom is called the denominator and represents the number of parts the whole has been divided into. The number on top is called the numerator and represents the number of equal parts we are interested in. So if I have a pizza and I want to eat 3/8 of it, I can achieve this by cutting it into 8 equal slices and eating 3 of them.

How do you explain a fraction to a child?

When helping a child understand a fraction for the first time, it can be helpful to use diagrams and everyday objects. Here are a few ideas to try:

• Give them a sheet of paper and ask how they can split it into 2 equal halves. Discuss simple ways of doing it: folding it in half horizontally, vertically or diagonally. Each side is half of the whole if the 2 sections are equal in size.
• Fold the piece of paper in half again. How many equal sections is it now split up into? As there are 4 equal sections, the piece of paper has now been split into quarters; each section is ¼ of the total sheet.
• Draw a circle and split it into equal parts. E.g. if it is split into 6 equal parts, each part is 1/6 of the whole circle. Shade in 1 section to illustrate 1/6.

How to teach fractions?

Below are guides to help you with the different sections of the topic of fractions for KS2 Maths. Here is a summary of which parts your child should be focusing on for their year group:

If your child is studying year 3 fractions or year 4 fractions, you should focus more on the basics: what do fractions mean, what are equivalent fractions, comparing the value of fractions with the same denominator and adding and subtracting fractions with the same denominator.

If your child is studying year 5 fractions, in addition to the above, they should learn about improper fractions and mixed numbers and how to convert between them. They should also build on their knowledge of similar fractions to start to be able to add, subtract and compare fractions with different denominators. They should also understand how to multiply fractions and mixed numbers by whole numbers.

If your child is studying year 6 fractions, in addition to the above, they should learn to simplify fractions, add and subtract mixed numbers, multiply fractions by each other and divide fractions by whole numbers.

By the end of the KS2 Maths course, children should be comfortable with all the topics covered here in order to be able to tackle KS2 SATs fractions problems.

How do you work out fractions at KS2?

In KS2 Primary school maths, you may be given a diagram which is split into equal sections and you need to find what fraction is shaded. First you need to count the total number of sections which are shaded. This will be the numerator. Then you need to count the overall number of sections (both shaded and unshaded). This will be the denominator. Here’s an example:

In this diagram, the circle is split into equal sections (we know they are equal as they are all the same size and shape). 5 sections are shaded and there are 8 sections overall which means 5/8 of the shape is shaded.

Sometimes, the diagram won’t be split into equal sections. For example:

This square is split into 3 sections of which 1 is shaded, but because the sections are not equal, we cannot say that 1/3 of the shape is shaded. We need to look for a way to draw extra lines to make equal sections:

With this additional line, the square is now split into 4 equal sections of which 1 is shaded so ¼ of the shape is shaded.

Some questions may ask what fraction of a total is a number, for example what fraction of 14 is 5 This could also be incorporated into a word problem: if a bag of sweets contains 14 sweets and I eat 5, what fraction of the bag do I eat?

We solve these in a very similar way. The one difference now is that instead of equal sections of a shape, we can think of the number 14 as 14 ones and 5 as 5 ones. Then 5 ones out of a total of 14 ones can be written as the fraction 5/14.

Fractions of an amount KS2

Children studying year 4 fractions should learn how to find fractions of amounts. For example, you might want to find out what ¾ of 16 is. Like with dividing a shape into equal sections, we would have to treat 16 as our whole and divide 16 into equal parts.

As the denominator of ¾ is 4, we need to split 16 into 4 equal parts:

16 ÷ 4 = 4.

This tells us that ¼ of 16 is 4:

Now we look at the numerator of ¾ which is 3. This means that we need to add 3 equal parts together to find ¾ of the whole:

4 + 4 + 4 = 12

Or in other words, we just need to multiply one quarter (which is 4 here) by 3:

4 × 3 = 12.

Equivalent fractions KS2

In KS2 primary school maths, children will discover that there are fractions which have different numerators and denominators but have the same value. This can be seen with a diagram:

The first circle has been split into 2 equal sections of which 1 is shaded, so ½ of the circle is shaded.

The other 3 circles are the same as the first circle but with some extra lines drawn. That means they must all have ½ shaded like the first one. If we count the equal sections though, we would get that the second circle has 2/4 shaded, the third has 3/6 shaded and the fourth has 4/8 shaded.

So we have found 4 different fractions which all have the same value. These are equivalent fractions: ½ = 2/4 = 3/6 = 4/8.

To find equivalent fractions, all we need to do is multiply (or divide) the numerator and denominator of a fraction by the same number. Here’s an example:

We want to find the value the ‘?’ must take so that both fractions are equivalent. If we look at the numerators of both fractions, we see that the numerator of the second fraction (9) can be calculated by multiplying the numerator of the first fraction (3) by 3, 3×3=9. So all we need to do is also multiply the denominator by 3:

In KS2 primary school maths, a group of fractions which are all equivalent to each other are often referred to as a family of equivalent fractions.

Simplifying fractions KS2: how to put a fraction into lowest terms

Children studying year 6 fractions need to know how to simplify fractions. This builds on their knowledge of equivalent fractions.

A simplified fraction, also referred to as a fraction in its lowest terms, is a fraction from a family of equivalent fractions with the smallest possible denominator and numerator.

For example, 2/4 is not simplified because it is equivalent to ½ which has a smaller numerator and denominator. ½ is simplified as there is no equivalent fraction to ½ with a smaller numerator or denominator.

To simplify a fraction, all you need to do is find a number which is a factor of both the numerator and denominator and divide both numerator and denominator by this number. The fraction is fully simplified (or in lowest terms) when the numerator and denominator have no factors in common (except for 1 because 1 is a factor of every number!).

Here’s another example of simplifying a fraction. Let’s simplify 45/60:

5 is a common factor of 45 and 60 so we can divide both by 5 to get 9/12.

3 is a common factor of 9 and 12 so we can divide both by 3 to get ¾.

3 and 4 have no factors in common which means that ¾ is fully simplified (or in lowest terms).

Note here we could have fully simplified 45/60 in a single step by dividing the numerator and denominator by 15.

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Adding and subtracting fractions KS2

Children studying year 3 fractions and year 4 fractions only need to know how to add and subtract fractions with the same denominator. Let’s look at an example:

If we draw a circle and split it into 7 equal sections, we can then shade 2 sections (2 sevenths) in one colour and 4 in another colour:

We can now see that 6 out of 7 equal sections are shaded, so 6/7 of the circle is shaded. This means that:

The rule here is that we just need to add the numerators together and keep the denominator the same. We do exactly the same thing for subtracting fractions:

As the denominators are the same, we can subtract the numerators and keep the denominator the same to get the answer.

3 – 1 = 2 so:

Children studying year 5 fractions and year 6 fractions also need to know how to add and subtract fractions with different denominators, for example:

To do this, we need to convert each fraction we are adding to an equivalent fraction so that both have the same denominator. To do this, we need to find a number which is a multiple of 2 and a multiple of 3 because we find equivalent fractions by multiplying the numerator and denominator by the same number. 6 is a multiple of 2 and 3 so we can find equivalent fractions which both have a denominator of 6:

This means that we can now rewrite the original question as follows:

And now we know how to solve this:

Ordering fractions KS2

Children studying year 3 fractions and year 4 fractions only need to know how to order unit fractions and fractions with the same denominator.

Unit fractions: this means fractions with a numerator of 1, e.g. 1/3, ¼, 1/5. When comparing two unit fractions, the one with the larger denominator must be smaller. We can see this with a diagram:

The more sections we divide a whole into, the smaller each section is. So in order from smallest to largest, we have:

1/5, ¼, 1/3.

Fractions with the same denominator: Let’s say we want to order the following fractions:

As they are all out of 7, the more sevenths we have the higher the number is so we can order these based on the numerator alone. So ordered from smallest to largest:

Children studying year 5 fractions also need to know how to order fractions with different denominators. For example:

In order to compare these, we need to find equivalent fractions with a common denominator. To do this, we need to find a number which is a multiple of 2, 4 and 5. 20 works for this.

Now that they have the same denominator, we just need to look at the numerators to order them. So from smallest to largest:

Finally, we want to convert the fractions back to their original forms. We can check our working from finding the equivalent fractions to see which is which. So from smallest to largest:

Multiplying fractions KS2

Children studying year 5 fractions need to know how to multiply fractions by whole numbers. Here’s an example of how to do this:

Let’s say we want to multiply 2/5 by 3. We can write this as 3 × 2/5.

All we need to here is multiply the numerator of the fraction by the whole number to find our new numerator and keep the denominator the same.

Numerator: 3 × 2 = 6

Denominator: still 5

So the answer is 6/5, or 1 1/5 as a mixed number (see more on mixed numbers and improper fractions below).

Children studying year 6 fractions also need to know how to multiply fractions by fractions. To do this, all you need to do is multiply the numerators together and multiply the denominators together. Here’s an example:

The answer to this question is in its lowest terms so we cannot simplify. Sometimes though with multiplication of fractions, we will need to simplify our answer. It can save time to simplify before multiplying. Even if the fractions we are multiplying are fully simplified, we can simplify the multiplication if the numerator of one fraction has a factor in common with the denominator of the other. Here’s an example of when we can do this:

Because 25 (a denominator) and 5 (a numerator) are both divisible by 5, we can simplify by dividing both of these by 5.

So the multiplication has now become:

Because 21 (a numerator) and 14 (a denominator) are both divisible by 7, we can simplify again by dividing both of these by 7:

So now all we have to do is:

If we multiplied the numerators and denominator first and then simplified, we would’ve got the same answer, but we would’ve had to multiply much bigger numbers and it would’ve taken longer.

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Dividing fractions KS2

Children studying year 6 fractions need to know how to divide fractions by whole numbers. For example, we may want to calculate 4/7 ÷ 2. Like with multiplication, we can solve this by dividing the numerator of the fraction by the whole number and keeping the same denominator.

4 ÷ 2 = 2

So the answer is 2/7.

We can’t do this though if the numerator is not divisible by the whole number, for example if we wanted to calculate 2/5 ÷ 3. In this case, we can instead multiply the denominator of the fraction by the whole number and keep the numerator the same.

5 × 3 = 15

So the answer is 2/15.

Dividing fractions by fractions is beyond the National Curriculum for KS2 Maths, but once you have learned to multiply fractions by fractions, dividing is not much harder. All you need to do is flip the fraction you are dividing by upside down (swap numerator and denominator) and change the division sign to a multiplication sign. For example:

Now we know how to find the answer because we already know how to multiply fractions:

Improper fraction KS2: improper fractions and mixed numbers

Children studying year 5 fractions and year 6 fractions need to know what improper fractions and mixed numbers are, how to use them and how to convert between them.

Mixed numbers are made up of a whole number and a fraction, e.g.

We read this as “one and two thirds”.

The whole number 1 could be written as 2/2, 3/3, 4/4 etc. so instead of writing “1 and two thirds” as a mixed number, we could write it as an improper fraction:

An improper fraction just means a fraction where the numerator is larger than the denominator.

To convert a mixed number to an improper fraction, we use the method from above to write the whole number part as a fraction to add to the fractional part. Here’s another example:

This time, because the whole number part is 2, we add 2 wholes to the fractional part.

To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator to work out how many wholes we can pull out of the fraction. The remainder from division will then be the numerator of the fractional part of the mixed number.

Here’s an example to see how this works:

Convert 17/5 to a mixed number.

First, we divide the numerator by the denominator: 17 ÷ 5 = 3 remainder 2.

This means there are 3 wholes to come out of the improper fraction 17/5 with 2/5 left over:

To add, subtract, multiply and divide with mixed numbers, it is easiest to convert first to improper fractions, then carry out the calculation and then convert back to a mixed number. Here are some examples:

KS2 fraction questions

Here are some questions based on the KS2 primary school maths syllabus to help you practice working with fractions. KS2 SATs fractions questions could be just like these.

KS2 maths fractions questions for year 3 and above:

1. What fraction of each of the following shapes is shaded?

2. I have a bag of 11 sweets. I eat 3 of them and give half of the remaining sweets to my friend. What fraction of the sweets do I give to my friend?
3. Fill in the blanks to find families of equivalent fractions:

4. Calculate the following:

(i) 2/5  +  1/5

(ii) 4/7  +  2/7

(iii) 8/11  –  3/11

(iv) 5/9  –  4/9

5. Put the following sets of fractions in order of size from smallest to largest:

(i) 1/6, ¼, 1/10, 1/3, 1/8

(ii) 4/7, 6/7, 3/7, 5/7

(iii) 3/10, 9/10, 7/10, 1/10

KS2 maths fractions questions for year 4 and above:

6. Find the following:

(i) 2/5 of 20

(ii) 3/7 of 35

(iii) 5/6 of 18

7. Jack has a box of 24 muffins. If he gives ½ of them to his friends and 1/3 of them to his family, how many muffins does he have left for himself?

KS2 maths fractions questions for year 5 and above

8. Put the following sets of fractions in order of size from smallest to largest:

(i) ¾, ½, ¼, 5/8, 7/8

(ii) 1/3, 5/6, 5/12, 7/12, 2/3

9. Convert the following improper fractions to mixed numbers

(i) 27/4

(ii) 31/5

(iii) 15/7

(iv) 16/3

10. Convert the following mixed numbers to improper fractions:

(i) 3  4/5

(ii) 4  2/3

(iii) 2  5/7

(iv) 5  1/6

11. Calculate the following leaving your answers as mixed numbers where applicable:

12. Calculate the following leaving your answers as mixed numbers:

KS2 maths fractions questions for year 6

13. Fully simplify the following fractions:

(i) 6/8

(ii) 60/72

(iii) 50/75

(iv) 16/20

(v) 105/180

14. Calculate the following:

15. Calculate the following:

Answers:

1. ¼, 3/8
2. 4/11
3. ¾ = 6/8 = 9/12 = 15/20

2/5 = 4/10 = 6/15 = 10/25

1/3 = 3/9 = 6/18 = 4/12

4. (i) 3/5, (ii) 6/7, (iii) 5/11, (iv) 1/9
5. (i) 1/10, 1/8, 1/6, ¼, 1/3

(ii) 3/7, 4/7, 5/7, 6/7

(iii) 1/10, 3/10, 7/10, 9/10

6. (i) 8, (ii) 15, (iii) 15
7. 4
8. (i) ¼, ½, 5/8, ¾, 7/8

(ii) 1/3, 5/12, 7/12, 2/3, 5/6

9. (i) 6 ¾, (ii) 6 1/5, (iii) 2 1/7, (iv) 5 1/3
10. (i) 19/5, (ii) 14/3, (iii) 19/7, (iv) 31/6
11. (i) 1 ¼, (ii) 1 ½, (iii) 3/8, (iv) ¼
12. (i) 5 2/5, (ii) 13 ¾, (iii) 7 1/3, (iv) 17 1/7
13. (i) ¾, (ii) 5/6, (iii) 2/3, (iv) 4/5, (v) 7/12
14. (i) 1/12, (ii) 3/10, (iii) ¼, (iv) 5/14
15. (i) 1/5, (ii) 2/15, (iii) 5/36, (iv) 1/12

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