Fractions, Decimals & Percentages — GCSE Mathematics Revision
Revise Fractions, Decimals & Percentages for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Go to Percentages: Increase & DecreaseWhat is Fractions, Decimals & Percentages?
Fractions, decimals and percentages are three ways of representing the same value. Converting between them is essential: to convert a fraction to a decimal, divide the numerator by the denominator; to convert a decimal to a percentage, multiply by 100. You need to add, subtract, multiply and divide fractions fluently, including mixed numbers.
Step-by-step explanationWorked example
Calculate 2/3 + 3/4. Find the LCM of 3 and 4 = 12. Convert: 8/12 + 9/12 = 17/12 = 1 5/12.
Mini lesson for Fractions, Decimals & Percentages
1. Understand the core idea
Fractions, decimals and percentages are three ways of representing the same value. Converting between them is essential: to convert a fraction to a decimal, divide the numerator by the denominator; to convert a decimal to a percentage, multiply by 100.
Can you explain Fractions, Decimals & Percentages without copying the notes?
2. Turn it into marks
Calculate 2/3 + 3/4. Find the LCM of 3 and 4 = 12.
Underline the method, evidence, or command-word move that would earn credit in GCSE Number.
3. Fix the likely mark leak
Watch for this mistake: Adding fractions by adding numerators AND denominators (e.g. writing 1/3 + 1/4 = 2/7 instead of finding a common denominator).
Write one correction rule before doing another practice question.
Practise this topic
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Fractions, Decimals & Percentages practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Fractions, Decimals & Percentages is testing.
Answer: Fractions, decimals and percentages are three ways of representing the same value. Converting between them is essential: to convert a fraction to a decimal, divide the numerator by the denominator; to convert a decimal to a percentage, multiply by 100.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Fractions, Decimals & Percentages question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Adding fractions by adding numerators AND denominators (e.g. writing 1/3 + 1/4 = 2/7 instead of finding a common denominator)." What should their next repair task be?
Answer: Do one Fractions, Decimals & Percentages question and review the mistake type.
Mark focus: Error correction and next-step practice.
Fractions, Decimals & Percentages flashcards
Core idea
What is the main idea in Fractions, Decimals & Percentages?
Fractions, decimals and percentages are three ways of representing the same value. Converting between them is essential: to convert a fraction to a decimal, divide the numerator by the denominator; to convert a decima...
Common mistake
What mistake should you avoid in Fractions, Decimals & Percentages?
Adding fractions by adding numerators AND denominators (e.
Practice
What is one useful practice task for Fractions, Decimals & Percentages?
Answer one Fractions, Decimals & Percentages question and review the mistake type.
Exam board
How should you use board notes for Fractions, Decimals & Percentages?
Use your own GCSE specification for exact paper wording and depth.
Common mistakes
- 1Adding fractions by adding numerators AND denominators (e.g. writing 1/3 + 1/4 = 2/7 instead of finding a common denominator).
- 2Forgetting to flip the second fraction when dividing (keep-change-flip).
- 3Not converting mixed numbers to improper fractions before multiplying or dividing.
- 4Rounding a recurring decimal too early instead of giving an exact fraction.
Fractions, Decimals & Percentages exam questions
Exam-style questions for Fractions, Decimals & Percentages with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Fractions, Decimals & Percentages
Core concept
Fractions, decimals and percentages are three ways of representing the same value. Converting between them is essential: to convert a fraction to a decimal, divide the numerator by the denominator; to…
Frequently asked questions
How do I convert a recurring decimal to a fraction?
Let x equal the recurring decimal. Multiply x by 10 (or 100, 1000) to shift the recurring part, then subtract the original equation to eliminate the recurring digits. Solve for x and simplify.
What is the order of operations for fractions?
BIDMAS/BODMAS applies to fractions just like whole numbers. Work out brackets first, then indices, then division/multiplication, then addition/subtraction.