IGCSE Fractions, Decimals and Percentages: Complete Guide for Cambridge IGCSE Mathematics

IGCSE fractions, decimals and percentages are fundamental topics in Cambridge IGCSE Mathematics that appear throughout the curriculum. Mastering conversions between these forms, operations with fractions, and percentage calculations is essential for solving problems across all areas of mathematics.

This comprehensive IGCSE fractions, decimals and percentages guide covers everything you need to know, including converting between fractions, decimals, and percentages, adding, subtracting, multiplying, and dividing fractions, percentage increase and decrease, step-by-step worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to convert between fractions, decimals, and percentages, perform all operations with fractions, calculate percentages, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Fractions, Decimals and Percentages Matter

IGCSE fractions, decimals and percentages are essential skills that appear in almost every topic. Here’s why they’re so important:

• Foundation topic: Required for understanding algebra, ratios, probability, and all number work
• High frequency: Questions involving fractions, decimals, or percentages appear in every IGCSE maths paper
• Real-world applications: Used in shopping, cooking, finance, statistics, and everyday calculations
• Exam weight: Typically worth 8-12 marks per paper
• Common errors: Many students lose marks due to calculation errors - this guide will help you avoid them

Key insight from examiners: Students often make mistakes with fraction operations, especially addition/subtraction, and percentage change calculations. This guide will help you master these systematically.

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Understanding Fractions: The Basics

A fraction represents a part of a whole.

Notation: a/b where:

• a is the numerator (top number)
• b is the denominator (bottom number)
• The line between them is the fraction bar

Types of fractions:

• Proper fraction: Numerator < Denominator (e.g., 3/4)
• Improper fraction: Numerator ≥ Denominator (e.g., 5/4)
• Mixed number: Whole number + proper fraction (e.g., 1 1/4)

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Converting Between Fractions, Decimals, and Percentages

Fraction to Decimal

Method: Divide the numerator by the denominator.

Examples:

• 1/2 = 1 ÷ 2 = 0.5
• 3/4 = 3 ÷ 4 = 0.75
• 2/5 = 2 ÷ 5 = 0.4

Decimal to Fraction

Method:

1. Write the decimal as a fraction over 10, 100, 1000, etc. (depending on decimal places)
2. Simplify to lowest terms

Examples:

• 0.5 = 5/10 = 1/2
• 0.75 = 75/100 = 3/4
• 0.125 = 125/1000 = 1/8

Fraction to Percentage

Method: Convert to decimal first, then multiply by 100.

Examples:

• 1/2 = 0.5 = 50%
• 3/4 = 0.75 = 75%
• 1/5 = 0.2 = 20%

Percentage to Fraction

Method: Write percentage over 100, then simplify.

Examples:

• 50% = 50/100 = 1/2
• 75% = 75/100 = 3/4
• 25% = 25/100 = 1/4

Decimal to Percentage

Method: Multiply by 100.

Examples:

• 0.5 = 50%
• 0.75 = 75%
• 0.125 = 12.5%

Percentage to Decimal

Method: Divide by 100.

Examples:

• 50% = 0.5
• 75% = 0.75
• 12.5% = 0.125

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Operations with Fractions

Adding and Subtracting Fractions

Key rule: Fractions must have the same denominator before adding or subtracting.

Method:

1. Find the Lowest Common Multiple (LCM) of the denominators (this is the Lowest Common Denominator)
2. Convert each fraction to have this common denominator
3. Add or subtract the numerators
4. Simplify if possible

Example 1: 1/3 + 1/4

Solution:

1. LCM of 3 and 4 is 12
2. Convert: 1/3 = 4/12 and 1/4 = 3/12
3. Add: 4/12 + 3/12 = 7/12

Answer: 7/12

Example 2: 2/5 - 1/3

Solution:

1. LCM of 5 and 3 is 15
2. Convert: 2/5 = 6/15 and 1/3 = 5/15
3. Subtract: 6/15 - 5/15 = 1/15

Answer: 1/15

Multiplying Fractions

Method: Multiply numerators together and denominators together, then simplify.

Rule: a/b × c/d = (a × c)/(b × d)

Example: 2/3 × 3/4

Solution: 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2

Answer: 1/2

Dividing Fractions

Method: Multiply by the reciprocal (flip the second fraction).

Rule: a/b ÷ c/d = a/b × d/c = (a × d)/(b × c)

Example: 2/3 ÷ 3/4

Solution: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9

Answer: 8/9

Mixed Numbers

When working with mixed numbers, convert to improper fractions first.

Example: 1 1/2 + 2 1/3

Solution:

1. Convert: 1 1/2 = 3/2 and 2 1/3 = 7/3
2. LCM of 2 and 3 is 6
3. Convert: 3/2 = 9/6 and 7/3 = 14/6
4. Add: 9/6 + 14/6 = 23/6 = 3 5/6

Answer: 3 5/6

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Understanding Percentages: The Basics

A percentage is a fraction with denominator 100.

Notation: % means “out of 100”

Key conversions:

• 1% = 1/100 = 0.01
• 50% = 50/100 = 1/2 = 0.5
• 100% = 100/100 = 1 (the whole)

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Percentage Calculations

Finding a Percentage of a Quantity

Method: Convert percentage to decimal, then multiply.

Formula: Percentage of quantity = (Percentage/100) × Quantity

Example 1: Find 25% of 80

Solution: 25% of 80 = 0.25 × 80 = 20

Answer: 20

Example 2: Find 15% of 240

Solution: 15% of 240 = 0.15 × 240 = 36

Answer: 36

Expressing One Quantity as a Percentage of Another

Method: Divide the first quantity by the second, then multiply by 100.

Formula: Percentage = (Part/Whole) × 100

Example 1: Express 15 as a percentage of 60

Solution: (15/60) × 100 = 0.25 × 100 = 25%

Answer: 25%

Example 2: Express 8 as a percentage of 32

Solution: (8/32) × 100 = 0.25 × 100 = 25%

Answer: 25%

Percentage Increase

Method: Find the increase, then express it as a percentage of the original.

Formula: Percentage Increase = (Increase/Original) × 100

Example: A price increases from $50 to $65. Find the percentage increase.

Solution:

1. Increase: $65 - $50 = $15
2. Percentage increase: (15/50) × 100 = 30%

Answer: 30%

Percentage Decrease

Method: Find the decrease, then express it as a percentage of the original.

Formula: Percentage Decrease = (Decrease/Original) × 100

Example: A price decreases from $80 to $64. Find the percentage decrease.

Solution:

1. Decrease: $80 - $64 = $16
2. Percentage decrease: (16/80) × 100 = 20%

Answer: 20%

Finding the Original Value After a Percentage Change

Example: After a 20% increase, a price is $120. Find the original price.

Solution:

1. After 20% increase, the price is 120% of original
2. 120% of original = $120
3. Original = $120 ÷ 1.20 = $100

Answer: $100

Alternative method: If increased by 20%, new value = 1.20 × original So: Original = New value ÷ 1.20 = $120 ÷ 1.20 = $100

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Step-by-Step Method for Fraction/Decimal/Percentage Problems

1. Identify what you need - Conversion, operation, or calculation?
2. Choose the appropriate method - Use the rules above
3. Work systematically - Show all steps clearly
4. Simplify your answer - Always give answers in simplest form
5. Check your answer - Does it make sense?

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Worked Examples

Example 1: Fraction Operations

Calculate: 2/3 + 1/4 - 1/6

Solution:

1. LCM of 3, 4, and 6 is 12
2. Convert: 2/3 = 8/12, 1/4 = 3/12, 1/6 = 2/12
3. Calculate: 8/12 + 3/12 - 2/12 = 9/12 = 3/4

Answer: 3/4

Example 2: Percentage of a Quantity

A shirt costs $45. There’s a 15% discount. Find the sale price.

Solution:

1. Discount: 15% of $45 = 0.15 × $45 = $6.75
2. Sale price: $45 - $6.75 = $38.25

Answer: $38.25

Alternative method: After 15% discount, pay 85% of original 85% of $45 = 0.85 × $45 = $38.25

Example 3: Percentage Change

A population increases from 5000 to 5750. Find the percentage increase.

Solution:

1. Increase: 5750 - 5000 = 750
2. Percentage increase: (750/5000) × 100 = 15%

Answer: 15%

Example 4: Reverse Percentage

After a 25% discount, a book costs $30. Find the original price.

Solution:

1. After 25% discount, pay 75% of original
2. 75% of original = $30
3. Original = $30 ÷ 0.75 = $40

Answer: $40

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Common Examiner Traps (and How to Dodge Them)

• Adding fractions without common denominator - Always find LCM first
• Forgetting to simplify - Always reduce fractions to lowest terms
• Percentage increase/decrease confusion - Always use original value as denominator
• Reverse percentage errors - Remember: if increased by x%, divide by (1 + x/100)
• Decimal place errors - Be careful with decimal conversions
• Mixed number operations - Always convert to improper fractions first

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IGCSE Fractions, Decimals and Percentages Practice Questions

Question 1: Fraction Operations

Calculate: a) 3/4 + 2/5 b) 5/6 - 1/3 c) 2/3 × 3/8

Solution: a) LCM of 4 and 5 is 20: 15/20 + 8/20 = 23/20 = 1 3/20 b) LCM of 6 and 3 is 6: 5/6 - 2/6 = 3/6 = 1/2 c) (2 × 3)/(3 × 8) = 6/24 = 1/4

Answers: a) 1 3/20 b) 1/2 c) 1/4

Question 2: Conversions

Convert: a) 3/8 to decimal and percentage b) 0.625 to fraction and percentage c) 37.5% to fraction and decimal

Solution: a) 3/8 = 0.375 = 37.5% b) 0.625 = 625/1000 = 5/8 = 62.5% c) 37.5% = 0.375 = 375/1000 = 3/8

Answers: a) 0.375, 37.5% b) 5/8, 62.5% c) 3/8, 0.375

Question 3: Percentage Calculations

a) Find 18% of 250 b) Express 42 as a percentage of 140 c) A car’s value decreases from $20,000 to $16,000. Find the percentage decrease.

Solution: a) 18% of 250 = 0.18 × 250 = 45 b) (42/140) × 100 = 30% c) Decrease: $20,000 - $16,000 = $4,000 Percentage: (4000/20000) × 100 = 20%

Answers: a) 45 b) 30% c) 20%

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Frequently Asked Questions About IGCSE Fractions, Decimals and Percentages

How do I add fractions with different denominators?

Find the Lowest Common Multiple (LCM) of the denominators, convert each fraction to have this common denominator, then add the numerators.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75.

How do I find a percentage of a quantity?

Convert the percentage to a decimal and multiply. Example: 25% of 80 = 0.25 × 80 = 20.

What’s the difference between percentage increase and decrease?

• Increase: (New - Original)/Original × 100
• Decrease: (Original - New)/Original × 100

How do I find the original value after a percentage change?

If increased by x%, divide the new value by (1 + x/100). If decreased by x%, divide by (1 - x/100).

How do I multiply fractions?

Multiply numerators together and denominators together, then simplify. Example: 2/3 × 3/4 = 6/12 = 1/2.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Ratios and Proportions: Complete Guide - Master ratio simplification and proportion problems
• IGCSE Directed Numbers: Complete Guide - Master positive and negative numbers
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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