Fractions – iGCSE Mathematics OxfordAQA Revision

Fractions are numbers that represent part of a whole.
A fraction consists of a numerator (the top number) and a denominator (the bottom number).
The numerator shows the number of parts we have, and the denominator shows how many parts make a whole.

Addition and Subtraction: To add or subtract fractions, they must have the same denominator, which is called the common denominator.
Multiplication: To multiply fractions, multiply the numerators together for the numerator and the denominators together for the denominator.
Division: To divide fractions, invert (flip) the second fraction to its reciprocal and multiply.

Converting fractions to decimals: Divide the numerator by the denominator using long division.
Converting decimals to fractions: Write the decimal as the numerator over a denominator that is a power of ten based on the number of decimal places, and then simplify.

Proper fractions: Fractions where the numerator is less than the denominator.
Improper fractions: Fractions where the numerator is equal to or greater than the denominator.
Mixed numbers: A whole number and a fraction combined.
Simplifying Fractions: A fraction is in simplest form when the numerator and denominator are only divisible by 1.
Equivalent Fractions: Different fractions that represent the same quantity.

Beware of the common mistake of thinking that a bigger denominator makes the fraction larger. This is not true, because the denominator represents the number of equal parts that make up a whole.
Always make sure to simplify fractions where possible, as leaving an answer as an unsimplified fraction could lose you marks.
Practise a variety of questions involving fractions. Understanding fractions and being comfortable with their operations is a fundamental part of mastering number concepts.