GCSE Maths • Foundation & Higher
GCSE Number Revision Guide
Master essential GCSE Number skills including BIDMAS, rounding, estimation, bounds, factors, multiples, prime numbers, HCF, LCM and recurring decimals.
Foundation
Exam practice
Worked examples
What You'll Learn
Use BIDMAS
Apply the correct order of operations to calculations involving brackets, indices, division, multiplication, addition and subtraction.
Simplify Ratios
Convert compatible units, then divide every part by a common factor to reach simplest form.
Share an Amount
Add the ratio parts, find one part and multiply to calculate every required share.
Use Ratios as Fractions
Express each share as its ratio part divided by the total number of parts.
Compare Best Buys
Calculate the same unit price for every option and identify the lowest equivalent cost.
Combine and Model Ratios
Link ratios through a common quantity and solve multi-stage or algebraic ratio problems.
Key Rules and Formulas
Number Lessons
BIDMAS
Use the correct order of operations in calculations involving brackets, powers and mixed operations.
Bounds
Find lower and upper bounds for rounded values and apply them to measurement problems.
Estimation
Round values to make quick approximate calculations and check exact answers.
Factors, Multiples and Prime Numbers
Identify factors, multiples and primes and use prime factor decomposition.
HCF and LCM
Find highest common factors and lowest common multiples using lists and prime factors.
Recurring Decimals
Recognise recurring decimals and convert recurring decimals into exact fractions.
Rounding
Round whole numbers and decimals to place values, decimal places and significant figures.
CORE SUBTOPICS
Ratios with Different Units
Convert quantities to the same unit before comparing or simplifying their numerical values.
Scaling Recipes
Find a scale factor or one-part value and apply it equally to every ingredient.
Missing Ratio Quantities
Use equivalent ratios, fractions of a total or a unitary method to calculate an unknown amount.
Ratio and Percentage
Convert a ratio share into a fraction of the total, then multiply by 100 to obtain a percentage.
Combining Two Ratios
Create matching values for the shared category before forming a complete three-part ratio.
Algebraic Ratio Problems
Translate a stated ratio into an equation when quantities are represented by expressions.
Worked Example
Sharing a Total in a Three-Part Ratio
QUESTION
A charity fund of £378 is shared between Projects A, B and C in the ratio 2:3:4. Calculate each share.
- Given information: The ratio order is A:B:C = 2:3:4, and the three shares must total £378.
- Method: Find the total number of equal parts, calculate the value of one part, then multiply by each ratio number.
- Add the ratio parts: 2 + 3 + 4 = 9 parts.
- Find one part: £378 ÷ 9 = £42.
- Project A receives 2 × £42 = £84.
- Project B receives 3 × £42 = £126.
- Project C receives 4 × £42 = £168.
- Check the total: £84 + £126 + £168 = £378.
- Project A receives £84, Project B receives £126 and Project C receives £168.
- The shares simplify to 84:126:168 = 2:3:4 after dividing every part by 42, and they add to £378.
- Do not divide £378 by 4, the largest ratio number. Divide by the total number of parts, 9.
- Common GCSE Mistakes
- Changing the Ratio Order
- Ignoring Different Units
- Dividing Only Some Parts
- Using One Ratio Number as the Total Parts
- Comparing Total Prices in Best Buys
- Rounding Unit Prices Too Early
- Exam Tips
- Write labels beside the ratio parts so the required order remains clear.
- Convert quantities to compatible units before simplifying, scaling or comparing them.
- For sharing questions, show the sum of parts, the value of one part and every final share.
- For best buys, state the common comparison unit and use it for every option.
- Keep full calculator values until the final decision or requested rounding step.
Ready to Practice?
Printable Worksheet
Practise simplifying, unit conversions, sharing totals, recipe scaling, combined ratios and best-buy comparisons.
Interactive Quiz
Check ratio order, equivalent ratios, total parts, unit prices and common misconceptions.
Exam-Style Questions
Apply ratio methods to money, measures, recipes, maps and multi-stage GCSE contexts.
Watch the Ratio Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Brackets, Indices, Division, Multiplication, Addition and Subtraction.
No. They have equal priority, so work from left to right. The same applies to addition and subtraction.
Look at the next digit: 0–4 rounds down and 5–9 rounds up.
Estimation means rounding numbers to simpler values to find an approximate answer.
Find half the rounding interval, subtract it for the lower bound and add it for the upper bound.
A prime number has exactly two positive factors: 1 and itself.
No. The source states that 1 is not a prime number.
The highest common factor is the largest factor shared by two or more numbers.
The lowest common multiple is the smallest multiple shared by two or more numbers.
A recurring decimal has one or more digits that repeat forever.
Use algebra: let x equal the decimal, multiply by a suitable power of 10, subtract and solve for x.
