Fractions – GCSE Mathematics Eduqas Revision

Understanding Fractions

A fraction is a mathematical expression representing the division of one whole number by another.
Every fraction consists of a numerator (the top number) and a denominator (the bottom number).
The numerator of a fraction represents how many parts we have.
The denominator of a fraction tells us the total number of equal parts the whole is divided into.
Fractions can represent both whole numbers and numbers less than one, depending how they’re structured.

A fraction can be simplified when the numerator and the denominator have common factors, other than 1.
For example, in the fraction 8/12, the common factor is 4. Dividing both the numerator and the denominator by 4 simplifies the fraction to 2/3.

To add or subtract fractions, they must have the same denominator (be like fractions).
If fractions have different denominators, turn them into equivalent fractions with the same denominator, then add or subtract the numerators.

To multiply fractions, simply multiply the numerators together for the new numerator, and do the same with the denominators for the new denominator.
To divide fractions, you have to first flip the second fraction (this gives you its reciprocal), then multiply as you would normally.

Problem: Simplify the fraction 24/32.
- Solution: The simplified fraction is 3/4.
Problem: Add the fractions 1/4 and 2/8.
- Solution: The sum is 3/4.
Problem: Multiply the fractions 1/2 and 3/4.
- Solution: The product is 3/8.
Problem: Divide the fractions 3/4 by 2/3.
- Solution: The result is 9/8 or 1 1/8.

Always strive to present your fraction in its simplest form.
When dealing with mixed fractions (ones containing whole numbers and fractions), convert them into improper fractions (where the numerator is larger than the denominator) before multiplication or division.
It is crucial to master the basic skills of adding, subtracting, multiplying, and dividing fractions to solve complex problems efficiently.