Add, subtract, multiply, and divide fractions with step-by-step solutions. Simplify, compare, and convert between mixed numbers and improper fractions. Perfect for GCSE and KS3 maths revision.
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A fraction represents a part of a whole. It is written as two numbers separated by a line: the numerator (top number) tells you how many parts you have, and the denominator (bottom number) tells you how many equal parts the whole is divided into.
numerator (parts you have) / denominator (total equal parts)
Fractions are one of the most important topics in GCSE maths. They appear in everything from recipes (half a cup) to probability (1 in 4 chance) to algebra (solving equations with fractional coefficients).
Numerator is less than the denominator. Value is less than 1.
Numerator is greater than the denominator. Value is more than 1.
A whole number plus a proper fraction. Same as 7/4.
Each operation has its own rules. The key thing to remember: addition and subtraction need common denominators, but multiplication and division do NOT.
Find a common denominator (the LCM of both denominators), convert each fraction, then add the numerators. The denominator stays the same.
Same process as adding — find the common denominator, convert, then subtract the numerators instead.
The simplest operation! Multiply the numerators together and the denominators together. No common denominator needed.
2/3 × 3/5 = 6/15 = 2/5
Cross-cancel first to keep numbers small
Use the "Keep, Change, Flip" method: Keep the first fraction, Change ÷ to ×, Flip the second fraction. Then multiply.
These are the most common conversions you need to know for GCSE maths. Memorise the key ones — they come up in almost every exam.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.3% |
| 2/3 | 0.666... | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
How to convert: Fraction → Decimal: divide numerator by denominator. Decimal → Percentage: multiply by 100. Percentage → Fraction: put over 100 and simplify.
Fractions have several traps that catch out even confident students. Watch out for these:
When adding 1/3 + 1/4, students often write 2/7. This is wrong! You cannot add denominators. You must find a common denominator first.
1/3 + 1/4 = 4/12 + 3/12 = 7/12 (not 2/7).
Leaving 6/8 as the final answer when it should be 3/4. Always check if numerator and denominator share a common factor.
Find the GCD of your numerator and denominator. If it is greater than 1, divide both by it.
In 2/3 ÷ 4/5, some students flip the FIRST fraction instead of the second. The rule is: flip the fraction you are dividing BY.
Remember "Keep, Change, Flip": Keep 2/3, Change ÷ to ×, Flip 4/5 to 5/4.
Multiplication does NOT need a common denominator. Some students waste time finding the LCM before multiplying — this is unnecessary.
For multiplication: just multiply tops together and bottoms together. Simple!
You cannot add 2½ + 1¼ directly. You must first convert to improper fractions: 5/2 + 5/4.
Always convert mixed numbers to improper fractions before performing any operation.
Master fraction operations with these step-by-step examples:
Step 1: Find LCM(5, 4) = 20
Step 2: Convert: 2/5 = 8/20 and 3/4 = 15/20
Step 3: Add numerators: 8 + 15 = 23
Step 4: Result = 23/20
= 1 3/20 (as a mixed number)
Step 1: Keep 3/4, Change ÷ to ×, Flip 2/3 to 3/2
Step 2: 3/4 × 3/2
Step 3: Multiply: (3×3)/(4×2) = 9/8
= 1 1/8 (as a mixed number)
Step 1: Convert to improper fractions
2 1/3 = (2×3+1)/3 = 7/3
1 1/2 = (1×2+1)/2 = 3/2
Step 2: LCM(3, 2) = 6
Step 3: 7/3 = 14/6 and 3/2 = 9/6
Step 4: 14/6 − 9/6 = 5/6
= 5/6
Step 1: Find GCD(48, 60)
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
GCD = 12
Step 2: Divide both by 12
48 ÷ 12 = 4, 60 ÷ 12 = 5
= 4/5
Leaving an unsimplified fraction can cost you marks. Check that the GCD of numerator and denominator is 1.
Before any calculation, convert mixed numbers to improper fractions. Convert back at the end if the question asks for a mixed number.
Write out the LCM calculation, the conversion, and each step. Method marks are available even if your final answer is wrong.
When multiplying fractions, cancel common factors across the fractions before multiplying. This keeps numbers small and reduces errors.
Quick check: convert your fractions and answer to decimals. If 1/3 + 1/4 = 7/12, verify: 0.333 + 0.25 = 0.583 ≈ 7/12.
Does it ask for "simplest form", "mixed number", or "improper fraction"? Give the answer in the requested format.
Find the LCM of both denominators, convert each fraction to have that common denominator, then add the numerators. Simplify the result.
Dividing by a fraction is the same as multiplying by its reciprocal. "Keep, Change, Flip" converts division into multiplication.
Always simplify your final answer. A fraction is fully simplified when the GCD of the numerator and denominator is 1.
They are equivalent! An improper fraction (like 7/4) has a larger numerator than denominator. A mixed number (1¾) shows whole number + fraction. Convert by dividing numerator by denominator.
List multiples of each number and find the smallest shared one. Or use: LCM(a,b) = (a×b) ÷ GCD(a,b).
No! Only addition and subtraction need common denominators. For multiplication, just multiply tops together and bottoms together.
A shortcut for multiplication: cancel common factors between a numerator and denominator of different fractions before multiplying. Keeps numbers small.
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions give recurring decimals: 1/3 = 0.333...
Write the decimal as a fraction over 1, then multiply top and bottom by 10 for each decimal place. Then simplify. E.g., 0.75 = 75/100 = 3/4.
Yes! It's 100% free and mirrors the working out required by GCSE exam boards. Learn mode walks you through each step interactively.
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