## Teaching Ratio and Proportion KS2: Everything You Need to Know

Posted on August, 2022

It is vital for children in KS2 to have a good grasp on ratio and proportion, as it is useful within school, but also in everyday life, which is why we put together a dedicated post on ratio and proportion KS2.

Ratio and proportion questions come in various forms so it is important for children to feel prepared to answer questions from simplifying ratios to recipe problems.

This post will act as an end-to-end guide on ratio and proportion for parents and teachers of children in KS2, in order to help with their learning.

This post will also include a full breakdown of what ratio and proportion is, what the difference is between them, and include some examples of questions that may come up in the SATs maths exam.

Now, let’s get started.

## What is Ratio?

To put it simply, a ratio shows how much of one thing there is compared to another. A good phrase to use is ‘for every’ for example “for every 1 pair of blue shoes, there are two pairs of green shoes”.

A ratio is written as a colon in between two numbers (in this example we will use two letters)

A:B

So, let’s get into an example of a ratio that can be used with your class or children to help explain ratios in a simple way.

If you are making a glass of blackcurrant juice and you use:

• 1 part of blackcurrant squash
• And

• 3 parts of water

The ratio of blackcurrant juice to water would be represented as 1:3, as there is one part of blackcurrant juice for every 3 parts of water.

The placement of these numbers must always stay the same for each ratio you have, as otherwise this changes the meaning of the ratio altogether.

If we go back to our earlier example:

If we swapped the numbers around and the ratio became 3:1 this would mean that the blackcurrant juice was now 3 parts blackcurrant squash for every one part of water.

This changes the ratio altogether, so it’s important to explain to children that ratio number placement must always stay the same.

### Simplifying Ratios

Alongside ratio questions, problems involving simplifying ratios are also common on the SATs maths paper.

Some ratios will use smaller numbers such as the one in the example above: 1:3.

However, some ratios will use larger numbers for example.

If we have 12 blue marbles and 18 green marbles the ratio would be 12:18 (12 blue marbles for every 18 green marbles).

These numbers are bigger so we can simplify them down to smaller numbers.

So, we will keep going with this example of the ratio 12:18.

Luckily both of these numbers can be divided by 2, as they are multiples of 2.

So, we have:

12 ÷ 2 = 6

18 ÷ 2 = 9

So our new ratio is 6:9 or ‘6 blue marbles for every 9 green marbles’.

This ratio has been simplified once and can be left like this, however some questions may ask to simplify ratio’s down to the smallest numbers possible.

Luckily, for this example each of the numbers (6 and 9) can be divided by 3.

So, we have:

6 ÷ 3 = 2

9 ÷ 3 = 3

So our new ratio is 2:3 or ‘2 blue marbles for every 3 green marbles’.

Alternatively, you can divide both 12 and 18 by 6 and you will arrive at the same answer, i.e. 2:3.

We have done the same process as before but this time divided each number by 3 before showing them as the final ratio of 2:3.

It is important to note that when simplifying any ratio, you must make sure you are dividing both numbers by the same amount every time.

As otherwise, the new simplified ratio will not represent the same numbers in the original ratio.

## What is Proportion?

Now that we have gone through the ratio portion of this post, we will go into proportion in a bit more detail.

A proportion tells us about a part or portion of something in relation to the whole, making it different to a ratio.

Let’s break this down.

A proportion may be explained in a question as:

In every 5 triangles 2 of them are green

Notice that the language differs. Here instead of saying, “for every…” we are saying, “in every…

So, if we have a group of 5 triangles, where 2 are green and 3 are blue, we express this as:

Either

In every 5 triangles, 2 of them are green

Or

2/5 as a fraction” as 2 out of 5 are green.

This is different to the ratio as the ratio for this problem would be 2:3.

As there are 2 green triangles for every 3 blue triangles, which equals the whole group of 5 triangles.

## Solving Ratio and Proportion Questions

Now that we have walked through the difference between ratio and proportion and how to work them out, it is useful for children to have a go at some question examples.

Below we have provided a selection of ratio and proportion questions, and we will walk through how to get to each answer, as it can be useful to see workings out to help children understand how to get to each answer.

### Ratio Problems

1. To make green paint, blue and yellow paint need to be mixed in the ratio 3:1. If I use 9 tins of blue, how many yellow tins do I need?

The ratio 3:1 means that for every 3 tins of blue paint, I need to use 1 tin of yellow paint.

So if I am using 9 tins of blue paint that means I am using 3 times as much, so I need to use 3 times as much yellow paint too.

This means we need to multiply 1 tin of yellow paint by 3, which is 3.

This means our new ration is 9:3, as we are using 9 tins of blue paint so we need to use 3 tins of yellow paint.

2. I am mixing cement in the ratio 10:15. What is this ratio when it is simplified?

To simplify this ratio we need to find a number that both 10 and 15 can be divided by.

10 and 15 can be divided by 5.

10 ÷ 5 = 2

15 ÷ 5 = 3

Therefore, our new ratio is 2:3.

As 10:15 means the same as 2:3, which is our answer, and our simplified ratio.

### Recipe Problem

We thought we would include a recipe problem here as they are common for KS2 exam questions and can sometimes require a bit more time.

It is a good idea to encourage children to practise these questions plenty of times as they can feel overwhelmed. This is because these questions come in different forms but they only require simple ratio, proportion and division.

3. Here is the recipe to make 20 shortbread biscuits

• 300g flour
• 50g butter
• 100g sugar
• 2 eggs

Josh wants to make 25 shortbread biscuits, so how much sugar does he need?

We only need to focus on one ingredient for this question and that is the sugar.

The recipe makes 20 biscuits and uses 100g of sugar.

We need to divide 20 into a number that can be then multiplied to get us to 25.

This is because Josh wants to make 25 biscuits.

So first let’s divide 20 by 4 which = 5.

That means we have to divide 100g by 4 which = 25g.

So now we know that to make 5 biscuits we need 25g of sugar, but Josh wants to make 25 biscuits.

So to get to 25 we need to find the right number to multiply with 5, which in this case is 5!

5 x 25g = 125g

Josh needs 125g of sugar to make 25 shortbread biscuits.

### Problems involving Proportion

Longer method question example:

4. There are 12 sweets in a jar. 1 in every 4 sweets is orange flavoured. How many orange flavoured sweets are there?

So, the simplest way to work through this problem is to draw a diagram of the sweets.

Start by drawing 12 sweets using an O for the orange flavoured sweets, and an X for the other flavoured sweets, for example, there is 1 orange flavoured sweet in ever 4 sweets so that would look something like this:

X O O O
X O O O
X O O O

This totals up to 12 sweets altogether, and we can see that 3 of those sweets are orange flavoured.

Quicker method question example:

5. There are 45 apples in a box. 1 in every 5 apples is bruised. How many apples are bruised altogether in the box?

Now, for this question it would take a long time to draw out 45 apples in a diagram so there is a quicker method to try once your children get the hang of proportion.

So, if 1 in every 5 apples are bruised, we need to find out how many groups of 5 there are in 45.

To do this we work out:

45 ÷ 5 = 9

So, we have 9 groups of 5, and within each of those 9 groups 1 apple is bruised.

The last thing left to do is multiply 9 by 1:

9 x 1 = 9.

Therefore, 9 apples in the box are bruised altogether.

## Teaching Ratio and Proportion KS2: Everything You Need to Know

This post has provided a useful guide to ratio and proportion, with everything you need to know, so that the children you are teaching gain the best understanding possible.

Ensuring children in KS2 have a good understanding and grasp of ratio and proportion is important not only for their SATs papers, but for life around them too.

At Redbridge Tuition our tutors have experience across the board in all stages of maths including the KS2 curriculum, so if you feel we could help you, please get in touch with us.