Number: Fractions, Decimals, Percentages
Fractions, decimals and percentages covers converting between the three forms, ordering them by size, and using them to calculate quantities such as percentage increase and decrease, compound interest, and calculations with fractions of amounts. These skills are essential for GCSE and for everyday contexts like shopping discounts, wages and savings, and questions often combine several steps such as a percentage change followed by another calculation.
Method
- Convert between fractions, decimals and percentages by dividing (fraction to decimal), multiplying by 100 (decimal to percentage), or writing over 100 and simplifying (percentage to fraction).
- To find a percentage of an amount, either use an equivalent fraction, find 1% and scale up, or multiply by the decimal multiplier.
- To increase or decrease by a percentage, find the multiplier (e.g. a 12% increase is x1.12, a 12% decrease is x0.88) and multiply the original amount by it.
- To add or subtract fractions, find a common denominator first, then combine the numerators.
- To multiply fractions, multiply the numerators together and the denominators together, simplifying where possible; to divide, multiply by the reciprocal of the second fraction.
- For multi-step problems, work through the calculation in the order the events happen, using your previous answer as the starting point for the next step.
Worked example
A jacket has a normal price of 84 pounds. In a sale it is reduced by 20%. Calculate the sale price of the jacket.
- A 20% reduction means the sale price is 80% of the original price.
- Write 80% as a decimal multiplier: 0.8.
- Multiply the original price by the multiplier: 84 x 0.8.
- Work out 84 x 0.8 = 67.20.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A shop's sales rise from 18000 pounds to 20700 pounds in one year. Calculate the percentage increase in sales.
Maya invests 1800 pounds in a savings account paying compound interest at a rate of 4% per annum. Calculate the value of her investment after 3 years, giving your answer to the nearest penny.
Ben spends 1/3 of his monthly pay on rent. He then spends 1/5 of what remains on travel. After paying for rent and travel, Ben has 640 pounds left. Calculate Ben's monthly pay.
Free printable worksheet
Want more practice on paper? Download the number: fractions, decimals, percentages worksheet pack - 9 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.