Why Fractions Matter More Than You Think
Fractions appear in almost every IGCSE Maths topic. Obvious places include number questions, ratio problems, and probability calculations. But they also appear in algebra (algebraic fractions), trigonometry (exact values like sin 30° = 1/2), geometry (fractional lengths and areas), and statistics (proportional calculations).
Students who are slow or unreliable with fractions struggle across the entire syllabus. Students who handle fractions fluently have a significant advantage. The investment in mastering fraction operations pays dividends far beyond the number chapter.
Adding and Subtracting Fractions
To add or subtract fractions, you need a common denominator — the same number on the bottom of both fractions.
Step 1: Find the lowest common multiple (LCM) of the denominators. Step 2: Convert each fraction to an equivalent fraction with that denominator. Step 3: Add or subtract the numerators. Keep the denominator the same. Step 4: Simplify if possible.
Example: 2/3 + 3/4
- LCM of 3 and 4 is 12
- 2/3 = 8/12 (multiply top and bottom by 4)
- 3/4 = 9/12 (multiply top and bottom by 3)
- 8/12 + 9/12 = 17/12 = 1 5/12
Common mistake: Adding both numerators and denominators (2/3 + 3/4 = 5/7). This is wrong. You must find a common denominator first.
Multiplying Fractions
Multiplying fractions is the simplest operation. Multiply the numerators together and multiply the denominators together.
Step 1: Multiply the numerators. Step 2: Multiply the denominators. Step 3: Simplify if possible.
Example: 3/5 × 4/7 = 12/35
Speed tip: Cancel common factors before multiplying. This keeps the numbers small and avoids needing to simplify afterwards.
Example: 4/9 × 3/8
Cancel: 4 and 8 share a factor of 4 (giving 1 and 2). 3 and 9 share a factor of 3 (giving 1 and 3).
Result: 1/3 × 1/2 = 1/6
This is much easier than computing 12/72 and then simplifying.
Dividing Fractions
To divide by a fraction, multiply by its reciprocal (flip the second fraction).
Step 1: Keep the first fraction as it is. Step 2: Change the division to multiplication. Step 3: Flip the second fraction (reciprocal). Step 4: Multiply and simplify.
Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Memory aid: “Keep, change, flip” — keep the first fraction, change ÷ to ×, flip the second fraction.
Working with Mixed Numbers
Mixed numbers (like 2 3/4) must usually be converted to improper fractions before you can perform operations.
Converting mixed to improper: Multiply the whole number by the denominator and add the numerator. Place the result over the original denominator.
2 3/4 = (2 × 4 + 3)/4 = 11/4
Converting improper to mixed: Divide the numerator by the denominator. The quotient is the whole number; the remainder is the new numerator.
17/5: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5
Example: Full Mixed Number Calculation
Calculate 2 1/3 − 1 3/4.
Step 1: Convert to improper fractions. 2 1/3 = 7/3 1 3/4 = 7/4
Step 2: Find common denominator (LCM of 3 and 4 = 12). 7/3 = 28/12 7/4 = 21/12
Step 3: Subtract. 28/12 − 21/12 = 7/12
Fractions on the Calculator
On calculator papers, your scientific calculator can handle fractions directly. Learn to use the fraction button (usually labelled a b/c or □/□).
Entering a fraction: Press the fraction button, enter the numerator, press the down arrow, enter the denominator.
Entering a mixed number: Some calculators have a mixed number button. Others require you to enter the improper fraction.
Converting between forms: Most calculators have an S⇔D button that switches between fractions and decimals.
Even when a calculator is available, knowing how to work with fractions by hand is important for Paper 1 (non-calculator) and for algebraic fractions where calculators cannot help.
Fraction of a Quantity
To find a fraction of a quantity, multiply the quantity by the fraction.
Example: Find 3/5 of 40. 3/5 × 40 = 3 × 40 ÷ 5 = 120 ÷ 5 = 24
Tip: It is often easier to divide by the denominator first, then multiply by the numerator. This keeps the numbers smaller.
3/5 of 40: divide 40 by 5 to get 8, then multiply by 3 to get 24.
Fractions in Algebra
Algebraic fractions follow exactly the same rules as numerical fractions.
Adding algebraic fractions: Find a common denominator.
1/x + 2/(x+1) = (x+1)/(x(x+1)) + 2x/(x(x+1)) = (x + 1 + 2x)/(x(x+1)) = (3x + 1)/(x(x+1))
Simplifying algebraic fractions: Factorise numerator and denominator, then cancel common factors.
(x² − 9)/(x + 3) = (x + 3)(x − 3)/(x + 3) = x − 3
Comparing Fractions
To compare fractions, convert them to the same denominator, then compare numerators. Alternatively, convert to decimals.
Which is larger: 5/8 or 7/11?
Method 1 (common denominator): 5/8 = 55/88, 7/11 = 56/88. So 7/11 is larger.
Method 2 (cross-multiply): 5 × 11 = 55, 7 × 8 = 56. Since 56 > 55, 7/11 is larger.
Common Exam Errors with Fractions
- Forgetting to find a common denominator before adding or subtracting
- Not converting mixed numbers to improper fractions before multiplying or dividing
- Cancelling terms instead of factors in algebraic fractions (e.g., cancelling the x in (x+3)/x — this is wrong)
- Not simplifying the final answer when the question asks for the simplest form
- Incorrectly flipping the first fraction instead of the second when dividing
Practice Strategy
The best way to build fraction fluency is daily practice:
- Week 1: Focus on adding and subtracting fractions with different denominators
- Week 2: Focus on multiplying and dividing, including mixed numbers
- Week 3: Practise fraction word problems (fraction of a quantity, comparing fractions)
- Week 4: Tackle algebraic fractions
Do 10 questions per day. Time yourself after the first few days and work on improving your speed while maintaining accuracy.
Summary
Fractions are a fundamental skill that supports success across the entire IGCSE Maths syllabus. Master the four operations, practise with mixed numbers, learn to use your calculator efficiently, and develop the fluency to handle fractions quickly and accurately. The effort invested in fractions pays off in every topic you study.
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