Fractions might seem tricky at first, but they're actually quite...
Maths193 views·Updated 12 Aug 2026·3 pagesUnderstanding Fractions in Mathematics
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1
of 3
Simplifying Fractions and Mixed Numbers
Cancelling down (or simplifying) fractions is like tidying up your answer to make it as neat as possible. You divide both the top and bottom numbers by the same number until they won't go any further.
Take 18/24 as an example. You can divide both by 3 to get 6/8, then divide both by 2 to get 3/4. That's your final answer because 3 and 4 don't share any common factors.
Mixed numbers have a whole number and a fraction stuck together, like 4⅔. To turn this into an improper fraction, think of it as 4 + ⅔. Convert the 4 into thirds and add: 12/3 + 2/3 = 14/3.
Quick tip: Going the other way is just as easy - divide 31 by 4 to get 7 remainder 3, so 31/4 = 7¾.
2
of 3
Multiplying Fractions and Finding Common Denominators
Multiplying fractions is actually easier than adding them. You multiply the tops together and the bottoms together - job done! The clever bit is cancelling down first to make your numbers smaller and easier to work with.
For 8/15 × 5/12, notice that 8 and 12 both divide by 4, and 15 and 5 both divide by 5. Cancel these down first, then multiply what's left: 2/3 × 1/3 = 2/9.
Common denominators are essential when you need to compare fractions or add them. Find a number that all the bottom numbers divide into - this becomes your new bottom number. For fractions like 8/3, 5/4, and 12/5, the common denominator is 60.
Remember: When expressing one number as a fraction of another (like 180 as a fraction of 50), just write the first over the second and simplify: 180/50 = 9/4.
3
of 3
Adding, Subtracting and Finding Fractions Of
Adding and subtracting fractions follows one golden rule: make the denominators the same first. Once the bottom numbers match, you only add or subtract the top numbers.
With mixed numbers like 2⅕ - 1½, convert to improper fractions first: 11/5 - 3/2. Find a common denominator (10), then calculate: 22/10 - 15/10 = 7/10.
Finding fractions of something means multiplying. To find 9/20 of £360, multiply £360 by 9, then divide by 20. It's often easier to divide first: £360 ÷ 20 = £18, then £18 × 9 = £162.
Pro tip: Always check if your final answer can be simplified further - it shows you've completed the problem properly!
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Maths193 views·Updated 12 Aug 2026·3 pagesUnderstanding Fractions in Mathematics
Fractions might seem tricky at first, but they're actually quite straightforward once you get the hang of the basic rules. Whether you're simplifying, converting between mixed numbers and improper fractions, or doing calculations, there are clear steps to follow that...
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Simplifying Fractions and Mixed Numbers
Cancelling down (or simplifying) fractions is like tidying up your answer to make it as neat as possible. You divide both the top and bottom numbers by the same number until they won't go any further.
Take 18/24 as an example. You can divide both by 3 to get 6/8, then divide both by 2 to get 3/4. That's your final answer because 3 and 4 don't share any common factors.
Mixed numbers have a whole number and a fraction stuck together, like 4⅔. To turn this into an improper fraction, think of it as 4 + ⅔. Convert the 4 into thirds and add: 12/3 + 2/3 = 14/3.
Quick tip: Going the other way is just as easy - divide 31 by 4 to get 7 remainder 3, so 31/4 = 7¾.
2
of 3Sign up to see the content. It's free!
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Multiplying Fractions and Finding Common Denominators
Multiplying fractions is actually easier than adding them. You multiply the tops together and the bottoms together - job done! The clever bit is cancelling down first to make your numbers smaller and easier to work with.
For 8/15 × 5/12, notice that 8 and 12 both divide by 4, and 15 and 5 both divide by 5. Cancel these down first, then multiply what's left: 2/3 × 1/3 = 2/9.
Common denominators are essential when you need to compare fractions or add them. Find a number that all the bottom numbers divide into - this becomes your new bottom number. For fractions like 8/3, 5/4, and 12/5, the common denominator is 60.
Remember: When expressing one number as a fraction of another (like 180 as a fraction of 50), just write the first over the second and simplify: 180/50 = 9/4.
3
of 3Sign up to see the content. It's free!
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Adding, Subtracting and Finding Fractions Of
Adding and subtracting fractions follows one golden rule: make the denominators the same first. Once the bottom numbers match, you only add or subtract the top numbers.
With mixed numbers like 2⅕ - 1½, convert to improper fractions first: 11/5 - 3/2. Find a common denominator (10), then calculate: 22/10 - 15/10 = 7/10.
Finding fractions of something means multiplying. To find 9/20 of £360, multiply £360 by 9, then divide by 20. It's often easier to divide first: £360 ÷ 20 = £18, then £18 × 9 = £162.
Pro tip: Always check if your final answer can be simplified further - it shows you've completed the problem properly!
We thought you’d never ask...
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
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Students love us — and so will you.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
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