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    Fractions, Decimals and Percentages — OCR GCSE Mathematics

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    Fractions, Decimals and Percentages explained

    This topic covers the fundamental relationships between fractions, decimals, and percentages, including conversion between these forms and their application in calculations.

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    It also encompasses ordering these values and performing arithmetic operations with them, including the use of multipliers for percentage change and interest.

    What to demonstrate

    1. Correct conversion between fractions, decimals, and percentages
    2. Accurate calculation of fractions of quantities
    3. Correct application of percentage multipliers for increase and decrease
    Show all 6 objectives
    1. Accurate ordering of mixed types (fractions, decimals, percentages)
    2. Correct use of arithmetic operations with fractions and decimals
    3. Correct identification of recurring decimals as fractions (Higher tier)

    Fractions, Decimals and Percentages exam tips

    Topic Overview

    Fractions, decimals, and percentages are three different ways of representing parts of a whole, and they are fundamental to many areas of mathematics. In the OCR GCSE specification, this topic covers converting between these forms, performing calculations, and applying them to real-world problems such as discounts, interest rates, and statistical data. Mastering this topic is essential because it appears in almost every other area of maths, from algebra to probability.

    Understanding the relationships between fractions, decimals, and percentages allows you to choose the most efficient method for a given problem. For example, percentages are often easier for mental calculations, while fractions are useful for exact values. This topic also builds a strong foundation for more advanced concepts like ratio, proportion, and rates of change. In exams, questions often require you to convert fluently and apply operations in context, so practice with all three forms is key.

    In the OCR GCSE, you will be expected to convert between fractions, decimals, and percentages without a calculator in some questions, and with a calculator in others. You should also be able to order and compare them, find percentages of amounts, and solve problems involving percentage increase and decrease. Real-life applications include calculating VAT, understanding interest rates on loans, and interpreting survey results.

    Key Concepts
    • →Converting between fractions, decimals, and percentages: e.g., 3/4 = 0.75 = 75%; 0.3 = 3/10 = 30%; 12.5% = 1/8 = 0.125.
    • →Finding a percentage of an amount: multiply by the percentage as a decimal (e.g., 15% of £80 = 0.15 × 80 = £12).
    • →Percentage increase and decrease: increase by 12% means multiply by 1.12; decrease by 8% means multiply by 0.92.
    • →Ordering and comparing fractions, decimals, and percentages: convert all to the same form (usually decimals) to compare easily.
    • →Using fractions in calculations: adding, subtracting, multiplying, and dividing fractions with different denominators.
    Marking Points
    • Correct conversion between fractions, decimals, and percentages
    • Accurate calculation of fractions of quantities
    • Correct application of percentage multipliers for increase and decrease
    • Accurate ordering of mixed types (fractions, decimals, percentages)
    • Correct use of arithmetic operations with fractions and decimals
    • Correct identification of recurring decimals as fractions (Higher tier)
    Examiner Tips
    • 💡Always show full working for multi-step fraction or percentage problems
    • 💡Check if a question requires an exact answer (e.g., fraction) or a rounded decimal
    • 💡Use estimation to check the reasonableness of decimal calculations
    • 💡Remember that percentage change multipliers are often more efficient than calculating the percentage and adding/subtracting it
    • 💡Show all working, especially when converting between forms. Even if you do it mentally, write down the steps to avoid losing marks for arithmetic errors.
    • 💡When using a calculator, check that you have entered the percentage correctly (e.g., 15% as 0.15 or using the % button). Many calculators require you to divide by 100 if using the % key.
    • 💡For word problems, identify the 'whole' (the original amount) and the 'part' (the amount you are comparing). This helps you decide whether to use multiplication or division.
    Common Mistakes
    • Confusing the order of operations when calculating with fractions
    • Incorrectly converting percentages to decimals (e.g., 5% as 0.5 instead of 0.05)
    • Failing to simplify fractions to their lowest terms
    • Errors in place value when multiplying or dividing decimals
    • Misinterpreting percentage change multipliers (e.g., using 0.1 for a 10% increase instead of 1.1)
    • Thinking that a larger denominator means a larger fraction: e.g., 1/4 is smaller than 1/3 because the whole is divided into more parts. Always compare fractions by converting to a common denominator or decimal.
    • Confusing percentage increase with percentage of: e.g., increasing £50 by 20% gives £60, not £10. The increase is 20% of the original, not the final amount.
    • Forgetting to simplify fractions: e.g., leaving 4/8 as is instead of 1/2. Always simplify to lowest terms unless the question specifies otherwise.
    Frequently Asked Questions
    How do I convert a fraction to a decimal without a calculator?
    Divide the numerator by the denominator using short division. For example, to convert 3/8 to a decimal, divide 3 by 8: 8 goes into 3 zero times, so add a decimal point and a zero to make 30. 8 goes into 30 three times (24), remainder 6. Bring down a zero to make 60, 8 goes into 60 seven times (56), remainder 4. Bring down a zero to make 40, 8 goes into 40 five times exactly. So 3/8 = 0.375.
    What is the difference between a percentage increase and a percentage point increase?
    A percentage increase refers to the relative change based on the original value. For example, if a value increases from 10% to 15%, that is a 50% increase (since 5 is 50% of 10). A percentage point increase is the absolute difference in the percentages themselves, so from 10% to 15% is a 5 percentage point increase. In GCSE maths, you usually deal with percentage increases, not percentage points, unless specified.
    How do I find the original amount after a percentage increase or decrease?
    If you know the final amount and the percentage change, you can reverse the operation. For example, if a price after a 20% increase is £60, the original price is £60 ÷ 1.20 = £50. For a decrease, if the final price after a 15% decrease is £85, the original is £85 ÷ 0.85 = £100. Always divide by the multiplier (1 + percentage as decimal for increase, 1 - percentage as decimal for decrease).
    Why do we sometimes multiply by 100 when converting a decimal to a percentage?
    A percentage means 'out of 100', so to convert a decimal to a percentage, you multiply by 100 to find how many parts per hundred. For example, 0.35 as a percentage is 0.35 × 100 = 35%. This works because 0.35 is 35 hundredths, which is 35%. Similarly, to convert a percentage to a decimal, you divide by 100 (e.g., 45% = 45 ÷ 100 = 0.45).
    How do I add fractions with different denominators?
    First, find a common denominator (the least common multiple of the denominators). Convert each fraction to an equivalent fraction with that denominator, then add the numerators. For example, to add 1/3 and 1/4, the LCM of 3 and 4 is 12. 1/3 = 4/12, 1/4 = 3/12, so 4/12 + 3/12 = 7/12. Simplify if possible.
    What does 'of' mean in percentage problems, like '20% of 50'?
    In mathematics, 'of' usually means multiplication. So '20% of 50' means 20% × 50. Convert 20% to a decimal (0.20) and multiply: 0.20 × 50 = 10. Alternatively, you can find 10% first (5) and double it to get 10. This is a common method for mental calculations.

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