Number - Fractions, decimals and percentages — Edexcel GCSE Mathematics

This topic covers the relationships between fractions, decimals and percentages, and how to convert between them fluently. You will learn to compare and order these forms, and apply them to real-world problems such as percentage increase, decrease, reverse percentages, and compound interest. Mastery of these skills is essential for many other areas of GCSE Mathematics, including ratio, proportion, and algebra.

In Pearson Edexcel GCSE exams, this topic appears across both calculator and non-calculator papers, often in problem-solving contexts. You need to be confident with mental and written methods, and know when to use a multiplier for efficiency. Understanding these concepts also supports financial literacy and data interpretation in everyday life.

• →Converting between fractions, decimals and percentages: divide numerator by denominator for decimal; multiply decimal by 100 for percentage.
• →Using multipliers for percentage change: increase = 1 + rate, decrease = 1 - rate.
• →Reverse percentages: to find the original amount, divide by the multiplier.
• →Compound interest: use the formula Final = Initial x (multiplier)^n, where n is the number of time periods.
• →Comparing and ordering fractions, decimals and percentages by converting them to the same form.

• Writing the decimal over the correct power of ten, such as 375/1000 for 0.375, even if the cancelling is then incorrect.
• Cancelling by a correct common factor to reach the simplest form.
• Setting out a short division correctly when converting a fraction to a decimal, even if a calculation error is made.
• Writing the final value in the form the question asked for, whether decimal or fraction.
• setting up the equation, writing x as the recurring decimal with enough digits to show the repeat
• multiplying by the correct power of ten so that the recurring tails match, such as reaching 100x for a two digit block
• the subtraction that clears the recurring part, giving a whole number on the right
• the fraction cancelled to its simplest form, and for a proof question a closing statement tying it back to the decimal you started with
• finding the total number of parts, such as eight parts from the ratio 3:5
• the correct fraction of the whole written down before any arithmetic
• the value of one part when the question supplies a single share or a difference, even if the final answer is wrong
• the final quantities, with the check that they add back to the total given
• turning the percentage into a decimal multiplier, such as 1.15 for a rise of 15%
• a correct method seen, such as finding 10% and 5% and adding them, even if the arithmetic slips
• dividing rather than multiplying when the question gives the value after the change and asks for the original
• the final value written with its units or its pound sign, rounded as the question directs

• 💡Learn common conversions by heart, such as 1/8 = 0.125, 1/4 = 0.25, and 3/4 = 0.75, to save time in non-calculator questions.
• 💡Check a conversion by multiplying back: if you found 3/8 = 0.375, check that 0.375 × 8 = 3.
• 💡When ordering a list of mixed decimals and fractions, it is usually easiest to convert everything to decimals first, order them, then write the answer using the original numbers.
• 💡Write both lines one under the other with the decimal points aligned, so the subtraction is obviously exact.
• 💡Test your fraction on the calculator when the paper allows one; it should reproduce the recurring digits.
• 💡If the question says show that, finish with a line naming the fraction you were asked to reach rather than stopping at the algebra.
• 💡Sketch a bar split into the parts and label one part; most ratio questions then read straight off the bar.
• 💡Add your final shares together and compare with the total in the question as a check before moving on.
• 💡Decide first whether the fraction asked for is part to whole or part to part, because the two answers differ.
• 💡Write the multiplier down before you touch the calculator; most method marks here are for the multiplier.
• 💡Ask whether the answer should be bigger or smaller than the starting number, and check your result against that.
• 💡For money, give two decimal places, so an answer of 45.5 is written as £45.50.
• 💡Always show your working clearly, especially when using multipliers, as method marks are often available even if the final answer is wrong.
• 💡For non-calculator papers, simplify fractions fully and show conversions step by step to secure all marks.
• 💡Read the question carefully to identify whether it asks for a percentage increase, decrease, or reverse percentage, and check if the answer requires a monetary unit or percentage sign.

• Writing 0.375 as 375/100 instead of 375/1000. Correction: Count the decimal places carefully; three places means the denominator is 1000.
• Stopping at 375/1000 when the question asks for the simplest form. Correction: Always check if the numerator and denominator share common factors.
• Reading 3.5 as 3/5 rather than as three and a half (7/2). Correction: The number before the decimal point is a whole number.
• Dividing the denominator by the numerator, so turning 3/8 into 8 ÷ 3 = 2.666... instead of 3 ÷ 8 = 0.375. Correction: The fraction bar means divide the top by the bottom.
• multiplying by ten when the repeating block has two digits, so the tails do not line up and nothing cancels
• writing only the digits shown on the page rather than continuing the decimal, which hides the fact that the tails are identical
• leaving the answer as 45/99 when the question asks for the simplest form
• treating a decimal such as 0.375 as recurring and starting the algebra on it when short cancelling would finish the job
• reading the ratio 3:5 as the fraction 3/5 of the whole instead of 3/8
• sharing the difference between two shares as if it were the total
• writing the parts in the wrong order when the question names the quantities in a different order from the ratio
• forgetting to simplify a ratio built from fractions with unlike denominators before using it
• taking a 10% rise followed by a 10% fall back to the starting value, when the multipliers give 1.1 × 0.9 = 0.99
• multiplying by 0.15 for a 15% increase instead of by 1.15
• finding the percentage of the wrong amount in a two stage question, using the original where the new value is needed
• multiplying by 1.2 to reverse a 20% rise instead of dividing by it
• Students often think that 0.5% is the same as 50%. Correction: 0.5% = 0.005 as a decimal, while 50% = 0.5.
• When converting a fraction to a decimal, students may incorrectly divide the denominator by the numerator. Correction: always divide numerator by denominator.
• In percentage increase, students may add the percentage as a whole number instead of using a multiplier. Correction: use 1 + rate as a decimal.

1. 1Day 1-2: Revise conversion methods between fractions, decimals and percentages. Practice with a variety of examples, including recurring decimals.
2. 2Day 3-4: Learn and apply multipliers for percentage increase and decrease. Solve problems involving simple interest and depreciation.
3. 3Day 5-6: Master reverse percentages and compound interest. Work through exam-style questions, checking your steps.
4. 4Day 7-8: Practice comparing and ordering fractions, decimals and percentages. Use past paper questions to test your speed and accuracy.
5. 5Day 9-10: Complete a full past paper section on this topic under timed conditions. Review mistakes and revisit weak areas.

• 📋Conversion questions: e.g., 'Write 0.45 as a fraction in its simplest form.' Advice: simplify fully and show your method.
• 📋Percentage change problems: e.g., 'Increase 240 by 17%.' Advice: use a multiplier and show the calculation.
• 📋Reverse percentage problems: e.g., 'After a 20% discount, a TV costs 320. Find the original price.' Advice: divide by the multiplier (0.8) and explain your reasoning.
• 📋Compound interest problems: e.g., 'Calculate the value of an investment after 3 years with 5% compound interest.' Advice: use the formula and show each year's calculation or the power.