Fractions (AQA GCSE Maths): Revision Notes
Fractions
You need to be able to work confidently with fractions, with or without a calculator.
Basic fraction concepts
A fraction represents part of a whole or a way to divide something into equal parts.
Every fraction has two parts:
- The numerator - the top number that shows how many parts you have
- The denominator - the bottom number that shows how many parts the whole is divided into
For example, in the fraction , the numerator is 2 and the denominator is 3.
Understanding the relationship between numerator and denominator is fundamental to working with fractions. The denominator tells you how the whole is divided, while the numerator tells you how many of those parts you're considering.
Dividing objects into parts
Fractions can be used to show how an object is divided into parts.
When you see a fraction like , this means:
- The whole object is divided into 3 equal parts (denominator)
- You are looking at 2 of those parts (numerator)
Example: If of a rectangle is shaded, this means the rectangle is split into 3 equal parts and 2 of them are coloured in.
Equivalent fractions
Equivalent fractions are different fractions that represent the same amount or value.
For example, and are equivalent fractions because they both represent half of something.
Finding equivalent fractions
To create equivalent fractions, multiply or divide both the numerator and denominator by the same number.
Key Rule: What you do to the top, you must do to the bottom. This is essential for maintaining the fraction's value.
Worked Example: Creating Equivalent Fractions
Starting with :
- Multiply both parts by 2:
- Multiply both parts by 3:
All these fractions (, , ) represent the same value.
Cancelling fractions
Cancelling (or reducing) a fraction means making it simpler by dividing both the numerator and denominator by the same number.
Method for cancelling fractions:
- Find a number that divides into both the numerator and denominator
- Divide both parts by this number
- Repeat until no common factors remain
Worked Example: Cancelling Fractions
To cancel :
- Both 12 and 18 can be divided by 6
- and
- So
When you cannot cancel a fraction any further, it is in its simplest form.
Always check if your answer can be simplified further. Many exam questions require answers in simplest form.
Finding a fraction of an amount
To find a fraction of an amount, follow these two key steps:
- Divide the amount by the denominator
- Multiply the result by the numerator
This method works because you first find what one part is worth (by dividing by the denominator), then find the value of the required number of parts (by multiplying by the numerator).
Worked Example: Finding a Fraction of an Amount
Work out of 200kg:
- Step 1: kg (this finds one-tenth)
- Step 2: kg (this finds three-tenths)
- Answer: of 200kg is 60kg
Worked example
Worked Example: Complete Solution
Question: Work out of £240
Solution:
- Step 1: £240 ÷ 5 = £48 (this is of £240)
- Step 2: £48 × 2 = £96 (this is of £240)
- Answer: of £240 is £96
Exam tips
Essential Exam Strategies:
- Always simplify fractions to their simplest form unless told otherwise
- When checking equivalent fractions, make sure only one fraction is different from the others
- Plan your strategy before starting complex fraction problems
- Show all your working clearly for full marks
- Double-check that your final answer makes sense in the context of the problem
Remember!
Key Points to Remember:
- The numerator is the top number, the denominator is the bottom number
- Equivalent fractions represent the same value but look different
- To cancel fractions, divide both top and bottom by the same number
- To find a fraction of an amount: divide by denominator, then multiply by numerator
- Always check if your final answer can be simplified further