What is proportion and ratio?

A ratio is a way to compare two different things and is usually written as 1:2. A proportion is simply a statement that two ratios are equal. 

Writing a ratio

To write a ratio, we need to be comparing the same type/s of a thing, preferably so it is the same unit of measure. Ratios can only be whole numbers and a ratio that is worked out as 2 : 1/2 would need to be doubled up to 4 : 1.

The video to the right explains how we would write the ratio if we needed to write down 1 part 2-stroke oil to 10 parts petrol as a ratio.
Ratio notations
The order of a ratio is very important and must be followed. Whichever word or part came first in the ratio, when expressed in words, that number should come first in the ratio, e.g. Harry has 7 pencils and Joe has 3 pencils, show this in a ratio. The ratio would be 7:3 because Harry and his 7 pencils came first in the sentence.

There are three ways to express ratios. It can be expressed as words, for example '12 to 20', or as odds notation (which is usually how we write ratio) 12:20, or it can be written as a fraction notation 12/20.

​You will need to be able to recognise each notation in an exam as well as how to write them. 

Simplifying ratios

To simplify a ratio, factor out both numbers in the ratio and find the highest common factors that both numbers in the ratio share. Divide both numbers in the ratio by the highest common factor.

The video to the right shows my preferred way of simplifying small numbers in ratio and large numbers in ratio.
​Have a go at the multiple choice question below:

Sharing ratio (ratio in context)

These are the most common ratio you will see in the exam. These are the types of ratio you will need to use for exam questions that include adding ingredients, sharing pocket money out between children, sharing sweets out between children, or when reading a map. 
Example 1:
If Fred and Mark are sharing £300 in the ratio 2 : 3, how much money does Mark get?
How to work out this ratio: 

Step 1: Add the ratio together. 2 + 3 = 5.
Step 2: Divide £300 by 5.
Step 3: You should get £60. Multiply this by how much Fred gets (x2).
Step 4: Multiply £60 by how much Mark gets (x3).
Step 5: Your answer is £180!

The video to the right explains the step by step process. 

This is a grade 4 question so it is good to revise and make sure you're comfortable with before the exam!
Example 2:
I have 20 litres of mixed squash and need to work out how much water I used. The ratio is 1 part squash to 3 parts water. How much water did I use? 
How to work out this ratio:

​Step 1: Add the ratio together. 1 + 3 = 4.
Step 2: Divide 20 by 4.
Step 3: You should get 5. Multiply this by 1 litre (x1).
Step 4. Multiply 5 by 3 litres (x3). 
Step 5: Your answer is 15 litres!

This video the right explains the step by step process.

​This is a grade 4 question so it is good to revise and make sure you're comfortable with before the exam!
Coming soon... grade 5 and grade 6 example questions!

Ratio and fractions

For some questions, you might need to convert a fraction to a ratio. This sounds quite complicated but I have tried to break it down as much as possible. 

When looking at converting a fraction to a ratio, you need to consider the parts of the fraction. A fraction usually contains the whole at the bottom and whatever it is calling out at the top e.g. 4 chocolates in a box contains nuts so it will be written as 1/4, whereas as a ratio, that same question would be written as 1:3 because there's 4 chocolates, 1 has nuts and the other 3 do not but there are 4 whole parts. 
Example 1:
There are some chocolates in a box. 1/4 of the chocolate contains nuts. The rest of the chocolates do not contain nuts. Write down the ratio of the number of chocolates that contain nuts to the number of chocolates that do not contain nuts. Give your answer is the form 1 : n.
How to work out this ratio: 

Step 1: Identify the fraction. In this case, our fraction is 1 over 4. 
Step 2: Identify the parts of the fraction. We can see there are 4 parts, 1 part contains nuts and the other 3 parts do not contain nuts. 
Step 3: As ratio works in parts, we do not need to show the whole (like we would in a fraction), so we can just write it as 1 (part nuts) : 3 (parts no nuts).

This video the right explains the step by step process.

​This question was worth 2 marks in the exam so it's a great one to practice to become comfortable with converting fractions to ratio.
Example 2:
Have a go at the multiple choice questions. Be careful. I might have put a few in there to trip you up (it's nothing the examiner wouldn't do and their meaner!) 
Now that you've got it... I have bad news. It's not always that easy. 
Example 3:
James has 3/5 as many marbles as John. Write the total number of marbles as a simplified ratio. 
So we know there is no possible way of showing 3/5 : 1 as a ratio because ratio's have to be whole numbers.

Step 1: Multiply both sides by 5 (as that is the denominator). 3.5 x 5 = 3 and 1 x 5 = 5 so the answer is 3 : 5.

Have a look at the video to the right where I have explained the steps. 

This may not appear in a Foundation GCSE paper, however, it is good to have an idea of how it works just in case it makes an appearance.
Further resources:
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