GCSE Maths: Fractions Made Easy
Introduction
It is important that you are able to work with fractions in a confident manner. And after this article, you will discover fractions made easy!
Fractions are equal parts of a whole amount.
There are a number of processes that you must be able to perform which include:
- Addition and subtraction of fractions by finding a common denominator
- Multiplication of fractions
- Division of fractions
- Being able to convert a top heavy fraction to a mixed number and vica versa
- You should also be able to simplify fractions in its lowest form
- Have an understanding of equivalent fractions
Fractions Made Easy - Multiplication
Take a look at the following question:
\frac{3}{4} \times \frac{1}{5}The question deals with multiplication of fractions and this is generally the most straightforward of fraction calculations.
Simply multiply top numbers together and multiply bottom numbers together. Simply the result, if possible.
Following this rule, we would have: \frac{3}{4} \times \frac{1}{5}=\frac{3}{20}.
his cannot be simplified any further and so this is the answer.
Example
Take a look at the following question:
3 \frac{3}{4} \times 2 \frac{2}{3}.
This is another question involving fractions but this time you are dealing with mixed numbers. They are called mixed numbers because you have a whole number and a fraction. Here you need to be able to convert the mixed number into a top heavy fraction.
If you take 3 \frac{3}{4} for instance, the process is to multiply the denominator 4 with the whole number 3, add the result to the numerator 3, and put this result over the denominator 4. Doing this will give a final result of 15 which is then placed over the denominator 4, so the mixed number as a top heavy fraction is \frac{15}{4}
The same can be done for the mixed number 2 \frac{2}{3}=\frac{8}{3} .
Having now obtained top heavy fractions, it is now possible to do the actual multiplication: 3 \frac{3}{4} \times 2 \frac{2}{3}=\frac{15}{4} \times \frac{8}{3}=\frac{120}{12}=10
Fractions Made Easy - Division
Take a look at the following question:
\text { Work out } \quad 12 \frac{1}{2} \div \frac{5}{8}This question involves a division of fractions. You will see that there is a mixed number as well as a fraction. First you need to convert the mixed number to a top heavy fraction to give \frac{25}{2} .
You now have: \frac{25}{2} \div \frac{5}{8}
Now you need to apply the rule for division of fractions which is:
Change the ÷ symbol to x and then flip the second term only.
Following this you will have: \frac{25}{2} \times \frac{8}{5}
And this now follows the same process for multiplication of fractions. \frac{25}{2} \times \frac{8}{5}=\frac{200}{10}=20
Fractions Made Easy – Addition
Take a look at the following question:
Work out \frac{1}{3}+\frac{1}{12}
This involves the addition of two fractions. The rules for addition of fractions are similar to that of subtraction of fractions, except of course you subtract where appropriate.
You can see that the denominators are not the same and they need to be in order to perform the calculation.
A common denominator needs to be found that both 3 and 12 will go into. Try help minimise any excess calculations you should always look for the lowest common denominator in this case it is 12.
You can then use the process of equivalent fractions to complete the calculation.
\frac{1}{3}=\frac{4}{12}Now there is nothing to do with the fraction \frac{1}{12} because the denominator is also 12. The calculation can now be done: \frac{1}{3}+\frac{1}{12}=\frac{4}{12}+\frac{1}{12}=\frac{5}{12}.
This is the final answer which cannot be simplified any further.
Fractions Made Easy – Subtraction
Take a look at the following question:
\text { Work out } 5 \frac{2}{3}-2 \frac{3}{4}First convert the mixed numbers into top heavy fractions. 5 \frac{2}{3}=\frac{17}{3} ; 2 \frac{3}{4}=\frac{11}{4}
So the question can be written as: \frac{17}{3}-\frac{11}{4}
Now what is the lowest common denominator? In this case it is 12 so using equivalent fractions you will have: \frac{17}{3}=\frac{68}{12} ; \frac{11}{4}=\frac{33}{12}
The calculation can now be performed: 5 \frac{2}{3}-2 \frac{3}{4}=\frac{17}{3}-\frac{11}{4}=\frac{68}{12}-\frac{33}{12}=\frac{35}{12}
This is the final answer and you can leave your answer as a top heavy fraction unless of course the question asks you to leave your answer as a mixed number.
The topic of fractions is one that is misunderstood by many and for those who are not particularly keen on maths overall, it is a subject that can cause maths to seem almost impossible.
There are no secrets other than to keep working and to keep trying until you have managed to understand the topic fully. You are able to use the services of an online maths tutor for GCSE who can give you weekly guidance and support in preparation for your GCSE exams in topics such as fractions and of course other areas.
Our half term GCSE maths revision courses are strategically positioned throughout the academic year to help students consolidate any gaps in knowledge in preparation for any mock exams and also for the final exams in the summer. The courses are suitable regardless of whether they are doing foundation or higher. There are of course separate classes for two but they are packed full of useful insights in terms of looking at clues within a question in determining what maths needs to be done next.
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