GCSE Maths: Fractions Of An Amount
Introduction
It is important that you are able to understand that a fraction is simply an equivalent part of a whole.
Quite often you will be asked to find say \frac{4}{5} of an amount and knowing how to perform this type of calculation is important. This is known as finding a fraction of an amount.
You should also be aware that the top number of a fraction is the numerator and that the bottom number is the denominator.
Fractions of an Amount - Example
Take a look at the following question:
With this fractions of an amount question, what you need to be able to do here is to essentially determine what value 35 of the 200 tissues has.
Well suppose that the following block (as a whole) represents the 200 tissues and because the denominator is the number “5” the block will be split into 5 equal pieces as shown below:
So how can you use this diagram to answer the question? Well the whole block is equivalent to 200 tissues and there are 5 equal pieces so this means that each piece must have a value of 200 \div 5=40 .e. one piece is 40 tissues. In other words \frac{1}{5} must be 40 tissues. But the question is asking to find the value of \frac{3}{5} .
You can see from the diagram that three blocks can be totalled to give 40 + 40 + 40 = 120 or you simply could have done 40 x 3 = 120.
So the value of \frac{3}{5} is 120 tissues.
Fractions of an Amount - Visualise the Maths
When doing an fractions of an amount question, drawing blocks can help you to visualise and understand the process of what is needed to help solving such questions.
When it comes to fractions many students do struggle especially at Foundation level. The most common problems are remembering the rules of whether you divide by the bottom number or do you multiply by the bottom number and then divide by the top number??? It can get confusing very quickly.
You will notice that above the use of a bar model and this can be very useful in determining the correct operations that you need to do. In this case you are dividing by the bottom number and then multiplying by the top number.
Don’t be afraid to dry a bar model because once you have a visual representation you can then make better sense of the maths behind the question. If you are looking for ongoing support then you may want to consider the use of an online maths tutor for GCSE who can give you additional guidance on these topics as well as understanding much more.
Example
The question below can often be seen in everyday life and this demonstrates that actual uses fractions of an amount.
To answer this, you can use a block to represent the £24.90 and because the denominator is a 3, the block can be divided into 3 equal parts as shown below:
Only the value of the shaded part is needed. This can be found by performing the calculation £24.90 ÷ 3 = £8.30.
With this question it is important that you understand the meaning of the word “off”. This is saying that the amount that has just been calculated, £8.30, is taken off the normal price, so this means “to subtract”.
The price that is paid will then be £24.90 – £8.30 = £16.60
Question Practice
Try the following fractions of an amount question on your own before looking at the solution.
So how did you get on? Hopefully you found the answer to be 605.
First you need to determine how many boys are in the school and this is done by a simple subtraction calculation.
Number of boys = 1200 – 575 = 625
Next you need to determine the fractional amounts for boys and girls.
Boys:
The above block represents 625 boys and because the denominator is a 5 it has been divided into 5 equal parts, so each part is 625 ÷ 5 = 125. Now \frac{3}{5}
f the boys like sport, so this would be a total of 125 x 3 = 375 boys.
Girls:
The above block represents 575 girls and because the denominator is a 5 it has been divided into 5 equal parts, so each part is 575 ÷ 5 = 115. Now \frac{2}{5} of the girls like sport, so this would be a total of 115 x 2 = 230 girls.
The total number of girls and boys who like sports is 375 + 230 = 605.
You should now see if you can do these questions again on your own. Look at the questions again but without looking at the solutions and see if you are able to get the correct answer. But please be careful that getting and understanding how to get to the answer is important, rather than remembering what you may have just read.
Attending a maths revision course for GCSE whether you are doing the foundation paper or the higher paper will help you to further understand how to best answer questions in order to maximise all the marks that are available.
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