Fractions, decimals and percentages Revision Notes for Edexcel GCSE Maths

Fractions, decimals and percentages

Understanding how to convert between fractions, decimals, and percentages is essential for GCSE maths. These three ways of expressing numbers are interconnected, and being able to switch between them quickly will help you solve many different types of problems.

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Mastering conversions between fractions, decimals, and percentages is one of the most fundamental skills in GCSE mathematics. This topic appears across many areas of the syllabus, from basic number work to advanced statistics and probability.

Key conversion facts

There are three fundamental principles you need to master:

Converting decimals to percentages

To change a decimal into a percentage, you multiply by 100. This works because "percent" means "out of 100".

The decimal point effectively moves two places to the right when you multiply by 100.

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Worked Example: Converting Decimals to Percentages

Step 1: Take the decimal 0.6 Step 2: Multiply by 100: $0.6 \times 100 = 60$ Step 3: Add the percentage sign: 60%

Another example: Step 1: Take the decimal 0.03
Step 2: Multiply by 100: $0.03 \times 100 = 3$ Step 3: Add the percentage sign: 3%

Writing percentages as fractions

Any percentage can be written as a fraction with 100 as the denominator. Once you have this fraction, you should always simplify it as much as possible.

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Always look for common factors to simplify your fraction to its lowest terms. This is essential for getting full marks in exams.

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Worked Example: Converting Percentages to Fractions

Step 1: Write 60% as a fraction: $\frac{60}{100}$ Step 2: Find the highest common factor of 60 and 100 (which is 20) Step 3: Divide both numerator and denominator by 20: $\frac{60 \div 20}{100 \div 20} = \frac{3}{5}$

Therefore: 60% = $\frac{3}{5}$

Ordering different number types

You can arrange a mixture of fractions, decimals, and percentages in order of size by converting them all to the same type. Choose whichever form makes the comparison easiest.

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When comparing mixed number types, converting everything to decimals is often the most efficient approach as decimals are easiest to order from smallest to largest.

Essential equivalents to memorise

Learning these common equivalents will save you time in exams:

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Essential Equivalents Table

Fraction	$\frac{1}{100}$	$\frac{1}{10}$	$\frac{1}{5}$	$\frac{1}{4}$	$\frac{1}{2}$	$\frac{3}{4}$
Decimal	0.01	0.1	0.2	0.25	0.5	0.75
Percentage	1%	10%	20%	25%	50%	75%

These equivalents appear frequently in exam questions, so memorising them will help you work more efficiently.

Solving word problems

When tackling percentage problems, it's crucial to approach them systematically. Word problems often combine multiple concepts and require careful reading to identify what's being asked.

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Systematic Approach to Word Problems:

Read the whole question before starting any working
Identify what the question is asking for - this determines whether your final answer should be a percentage, fraction, or decimal
Convert fractions to percentages if the question asks for a percentage answer
Work systematically through each piece of information given

For problems involving multiple percentages, remember that all the parts must add up to 100%. If you know some percentages, you can find the remaining percentage by subtracting from 100%.

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Worked Example: Multiple Percentages Problem

A survey shows that 35% of students prefer maths, 28% prefer English, and the rest prefer science. What percentage prefer science?

Step 1: Add the known percentages: $35\% + 28\% = 63\%$ Step 2: Subtract from 100%: $100\% - 63\% = 37\%$

Therefore, 37% of students prefer science.

Exam tips

Understanding the key strategies for exam success will help you maximise your marks and avoid common pitfalls.

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Key Exam Strategies:

Show all working clearly - even if you make an error, you can still gain marks for your method
Simplify fractions to their lowest terms unless told otherwise
Check your answer makes sense - percentages should be between 0% and 100% in most contexts
Convert to the same type when comparing or ordering mixed numbers
Use the equivalents table to speed up your calculations

Practice approach

When converting between forms, follow these key processes:

Decimals to percentages: multiply by 100
Percentages to fractions: put over 100 and simplify
For ordering: convert everything to decimals for easy comparison

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Converting to decimals for comparison is usually the most efficient method because decimal comparison follows the same rules as whole number comparison - you simply read from left to right to determine which is larger.

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Key Points to Remember:

Any decimal can be converted to a percentage by multiplying by 100
All percentages can be written as fractions with denominator 100
Learn the common equivalents table - it will save you time in exams
When solving word problems, read carefully and identify what type of answer is needed
Always simplify fractions to their lowest terms

Fractions, decimals and percentages (Edexcel GCSE Maths): Revision Notes