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How to Find the Fraction of an Amount

Updated: Dec 7, 2023

Finding fractions of amounts is a concept that many children struggle to remember. It is one of the more abstract concepts within Maths introduced in Key Stage Two. However, with lots of real-life, practical exploration, children can conquer this concept and apply it confidently in their maths. As a primary school teacher, I tend to teach fractions straight after a topic on multiplication and division. My reason for this is to help children see the connections between their times tables facts and fractions. Children that struggle to see this connection, tend to struggle to understand and apply fractions. If your child is not confident with their times tables, a Multiplication Mat is a handy tool for this topic (download your FREE copy, link at the bottom of the page).


Before diving in to finding the fraction of an amount, it's important to explore the basic principle of fractions and what each part of a fraction means. A fraction is made up of two parts:

Pciture of a fraction with an explanation of the denominator and the numerator.
What do the parts of a fraction mean?

The denominator of the fraction is the number of equal parts that something has been divided into.


The numerator of the fraction is the nunber of those parts that are being focussed on in the particular question (see diagram).


As with all concepts in Maths, children need lots of experience working with fractions practically to help them understand the process and make connections. Using household items like lego or food (pizza, sweets, blueberries) is a good way of providing children with opportunities to explore the key vocabulary and principles surrounding fractions: whole number, equal parts, the denominator and the numerator.


 A picture of a pizza divided into eighths.  An example of finding the fraction of a whole in real life.
Finding the fraction of a whole in real life.

The first step, is to check that children understand and can express the fraction of a whole e.g.can your child recognise a third, a fifith or a seventh of a shape or object for example? This could be explored with food like cake, pizza, fruit and so on but it can also be explored through pictures too. Download my FREE Introduction to Fractions Worksheet Bundle. Take your time at this stage and make sure your child feels really confident before moving on. Once your child has developed confidence with fractions of a whole, they are ready to move onto finding fractions of an amount also referred to as the fraction of a quantity or fractions of a number. It's best to start off with basic fractions first, where the numerator is one. e.g.


Question:

Find one third of the bag of sweets? ..... How many sweets are in the bag? 15

A picture of some sweets with a selection of fractions, showing to divide by the denominator first.
Finding the Fraction of an Amount: Dividing by the denominator first.

The strategy to calculate every fraction of a quantity is the same: divide the total quantity by the denominator first (see picture). When we look at a fraction, we work with the denomiantor first as this will define how many equal parts the quantity will be split into.

A picture showing how to find the fraction of a number: one third of 15 by dividing by 3.
Finding the Fraction of a Number: Finding one third of 15.

Children need lots of practice with finding fractions of amounts, where the numerator is just one before moving on. Games like Fractions of an Amount Bingo by Gordon's Maths are great mini games to practice this. Don't be afraid to ask your child to use arrays to support their calculation (drawing rows of dots using the denominator value - see picture). Jottings like this help children develop confidence and proof for their answers.

Finding the fraction of an amount by drawing rows of dots to the value of the denominator.
Finding the fraction of an amount by drawing an array.

When your child has mastered finding one third, one fifth, one seventh, one twelth and so on, they are likely to be ready to work with fractions whose numerator is more than one. This is typically around Year 5 for most pupils although this concept is introduced in Year 4. Remember, children's understanding develops at different rates. A steady approach to mastering different mathematical concepts will have a much bigger impact on developing a solid maths foundation in the long term. Racing through the curriculum objectives to keep up with their peers, usually creates gaps in understanding, which can become a real source of frustration to them in later years. Take your time and have fun with each step.

Question: How do I find three quarters of 24?

A picture showing an array of 24 sweets.  Step One: How to find the fraction of an amount - divide by the denominator first.
Step One: Finding the fraction of a quantity - Divide by the denominator.


Step One: We always divide by the denominator first. In this question, the total 24 is divided into 4 equal groups to find one quarter of 24 first, 6 (see picture).




An array of sweets showing how to find the fraction of an amount.  Step Two - Multiply your answer in step one to the numerator.
Step Two: Finding the fraction of amount - Multiply by the Numerator.

Step Two: Now that you have found one quarter of 24 is 6. We need to find out what 3 times as many is (three quarters). We multiply our answer 6 by 3 (see picture).





Answer: Three quarters of 24 is 18.



Children often find 'Step One' fairly straight forward and can therefore often find one quarter, one third or one fifth easily. 'Step Two' is the area that children often become rusty with as they try to remember a calculation process, rather than focussing on understanding the question:


e.g. three quarters of an amount is the amount split into four equal groups and then three lots of one quarter.


The more this concept is applied to real life situations the more confident children become in their understanding. Asking children to explain what steps they are taking in their calculations and asking them to explain why they carry out each step, is a strong strategy to develop mathematical understanding. There are lots more Maths topics in my Primary Blog series. Why not take a look. Don't forget to download your FREE Multiplication Mat and your FREE Introduction to Fractions Worksheet Bundle. You may also find my Busy Bee Times Tables Workbook useful, if your child is currently learning their multiplication facts. Available on Amazon.

Author of the blog Joanne Adams (primary teacher and private tutor)
Author, Primary Teacher and Private Tutor - Joanne Adams

Keep an eye on the Primary Tuition Ltd. website for more Maths topics, resources and programmes coming soon.


Have fun

Joanne Adams






















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