Fractions (Edexcel GCSE Maths): Revision Notes
Fractions
Working confidently with fractions is essential for GCSE maths. You need to understand how to manipulate fractions both with and without a calculator.
What are fractions?
Fractions allow us to represent parts of whole objects or amounts. Every fraction has two key components that you must understand clearly:
- Numerator: The top number, which shows how many parts we have
- Denominator: The bottom number, which shows how many equal parts the whole is divided into
Think of fractions as a way of describing "how many out of how many". The denominator tells you the total number of equal parts, while the numerator tells you how many of those parts you're talking about.
For example, if a rectangle is divided into 3 equal parts and 2 are shaded, we write this as .
Equivalent fractions
Equivalent fractions represent the same value even though they look different. For instance, and both represent exactly half of something.
To create equivalent fractions, you can use two key operations:
- Multiply both the numerator and denominator by the same number, OR
- Divide both the numerator and denominator by the same number
This process maintains the fraction's value because you're essentially multiplying or dividing by 1. For example, .
Simplifying fractions (cancelling)
To simplify or cancel a fraction, you need to divide both the top and bottom numbers by their highest common factor.
Worked Example: Simplifying a Fraction
Simplify :
Step 1: Find the highest common factor of 12 and 18
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- Highest common factor = 6
Step 2: Divide both numerator and denominator by 6
Keep simplifying until you cannot divide both numbers by anything other than 1. When this happens, the fraction is in its simplest form.
Finding a fraction of an amount
This is a two-step process that's useful for many real-world problems. The method is straightforward once you understand the logic:
- Divide the amount by the denominator
- Multiply the result by the numerator
Worked Example: Finding a Fraction of an Amount
To find of 200kg:
Step 1: Divide the amount by the denominator
Step 2: Multiply the result by the numerator
Therefore, of 200kg = 60kg
Exam tips
Essential Exam Strategies:
- Always write fractions in their simplest form unless told otherwise
- When finding fractions of amounts, check your answer makes sense (it should be smaller than the original amount for proper fractions)
- Show all your working clearly - you can get marks for correct methods even if your final answer is wrong
- Be confident with your times tables as they help you spot common factors quickly
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 simplify fractions, divide both parts by their highest common factor
- To find a fraction of an amount: divide by denominator, then multiply by numerator
- Always check if your final fraction can be simplified further