IGCSE Maths / Fractions, decimals and rounding

Mixed numbers and improper fractions revision notes

Edexcel International GCSE Maths (4MA1), chapter 1: Fractions, decimals and rounding, specification point 1.2b. Free lesson.

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A mixed number and an improper fraction are two ways to write the same amount. Convert mixed numbers to improper fractions for calculations, then convert back only if the question asks for a mixed number.

What mixed numbers and improper fractions mean

A mixed number has a whole number and a fraction, such as 2 3/4. An improper fraction has a numerator larger than its denominator, such as 11/4. They can represent the same amount: 2 3/4 = 11/4, because 2 whole ones are 8/4, and 8/4 + 3/4 = 11/4. Improper fractions are not wrong. They are the useful form for working with fractions.

How to change a mixed number into an improper fraction

Keep the denominator the same. Change the whole number into a fraction with that denominator, then add the fraction part. This gives the shortcut: multiply the denominator by the whole number, then add the numerator.

How to change an improper fraction into a mixed number

Divide the numerator by the denominator. The quotient is the whole-number part, and the remainder becomes the new numerator. The denominator stays the same.

Which form to use for calculations

Convert mixed numbers to improper form before calculating. This matters especially in multiplication: both the whole part and the fraction part must be multiplied. Convert the result back only if the question asks for a mixed number. You can leave an answer as an improper fraction when the question does not ask for a mixed number.

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