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Master the four fraction operations and mixed number conversions for every IGCSE Maths paper.
To add or subtract fractions, find the lowest common denominator (LCD), convert, then combine the numerators. To multiply, multiply numerators together and denominators together. To divide, flip the second fraction (take its reciprocal) and multiply. Always convert mixed numbers to improper fractions first, and simplify your final answer.
Source: Edexcel IGCSE Mathematics (9-1) Specification 4MA1
When fractions have the same denominator, simply add or subtract the numerators and keep the denominator. When the denominators are different, you must first find the lowest common denominator (LCD), convert each fraction, then combine the numerators.
Rule: a/b + c/d = (ad + bc) / bd
Example: 2/5 + 1/3 → LCD = 15 → 6/15 + 5/15 = 11/15
Multiply the numerators together and the denominators together. Simplify before or after — cross-cancelling before multiplication makes the numbers smaller and reduces errors.
Rule: a/b × c/d = ac / bd
Example: 3/4 × 2/5 = 6/20 = 3/10
To divide by a fraction, flip the second fraction (take its reciprocal) and multiply. This is often remembered as "Keep, Change, Flip" — keep the first fraction, change ÷ to ×, flip the second fraction.
Rule: a/b ÷ c/d = a/b × d/c
Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8
A mixed number combines a whole number and a fraction (e.g. 3 2/5). An improper fraction has a numerator larger than or equal to its denominator (e.g. 17/5).
Multiply the whole number by the denominator, add the numerator, and place over the original denominator. For example: 3 2/5 → (3 × 5 + 2) / 5 = 17/5.
Divide the numerator by the denominator. The quotient is the whole number part, the remainder becomes the new numerator. For example: 17/5 → 17 ÷ 5 = 3 remainder 2 → 3 2/5.
Key rule: Always convert mixed numbers to improper fractions before multiplying or dividing. For adding and subtracting, you can either convert to improper fractions or work with the whole number and fraction parts separately — but the improper fraction method is more reliable under exam pressure.
Calculate: 2 1/3 + 1 3/4
Step 1 (Convert to improper): 2 1/3 = 7/3 and 1 3/4 = 7/4
Step 2 (Find LCD): LCD of 3 and 4 = 12
Step 3 (Convert): 28/12 + 21/12
Step 4 (Add numerators): 49/12
Step 5 (Convert back): 49 ÷ 12 = 4 remainder 1
Answer: 4 1/12
Calculate: 3 1/2 × 2 2/5
Step 1 (Convert to improper): 3 1/2 = 7/2 and 2 2/5 = 12/5
Step 2 (Multiply): 7/2 × 12/5 = 84/10
Step 3 (Simplify): 84/10 = 42/5
Step 4 (Convert back): 42 ÷ 5 = 8 remainder 2
Answer: 8 2/5
Calculate: 4 1/6 ÷ 1 1/4 − 2/3
Step 1 (Convert to improper): 4 1/6 = 25/6 and 1 1/4 = 5/4
Step 2 (Divide — flip and multiply): 25/6 × 4/5 = 100/30 = 10/3
Step 3 (Subtract 2/3): 10/3 − 2/3 = 8/3
Step 4 (Convert back): 8 ÷ 3 = 2 remainder 2
Answer: 2 2/3
Adding numerators and denominators: Students write 1/3 + 1/4 = 2/7. This is wrong. You must find the LCD first.
Forgetting to convert mixed numbers: Multiplying 2 1/3 × 3 as (2 × 3) + (1/3 × 3) gives the wrong answer. Convert to 7/3 first.
Not simplifying the final answer: If your answer is 6/8, you must simplify to 3/4. Marks are often deducted for unsimplified fractions.
Flipping the wrong fraction when dividing: In a/b ÷ c/d, you flip the second fraction (c/d), not the first.
Cross-cancel before multiplying: Divide a numerator and a denominator by a common factor before you multiply. This keeps numbers small and avoids arithmetic errors.
Show the LCD conversion step: Write out the equivalent fractions with the common denominator. This earns method marks and helps you spot errors.
Leave answers as improper fractions if told to: Read the question — some say "Give your answer as an improper fraction" rather than a mixed number.
Estimate first: Before calculating, estimate the answer. If 2 1/3 + 1 3/4 should be roughly 4, and you get 12, you know something went wrong.
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