CH
CalcHub
← Back to Guides
SATsGCSE

Fractions Made Easy

Understand fractions from scratch — adding, subtracting, multiplying, dividing, simplifying, and converting mixed numbers. With pizza, cake and real-world examples.

Fractions are just a way of describing parts of a whole. If you can share a pizza fairly, you already understand fractions.

What Does a Fraction Mean?

A fraction has two parts: the numerator (top number — how many pieces you have) and the denominator (bottom number — how many equal pieces the whole thing is split into).

If a pizza is cut into 8 slices and you take 3, you have 3/8 of the pizza.

Adding & Subtracting Fractions

Rule: You can only add or subtract fractions when they have the same denominator (same size slices).

If they don't, you need to find a common denominator — a number both denominators divide into.

Worked Example 1 — Adding 1/3 + 1/4

  1. Find a common denominator: 3 × 4 = 12
  2. Convert: 1/3 = 4/12 and 1/4 = 3/12
  3. Add the tops: 4 + 3 = 7
  4. Answer: 7/12

Think of it like this: you can't add thirds and quarters directly, just like you can't add pounds and dollars without converting first.

Multiplying Fractions

This one is easy: multiply the tops together, multiply the bottoms together.

a/b × c/d = (a×c) / (b×d)

Worked Example 2 — 2/3 × 3/5

  1. Tops: 2 × 3 = 6
  2. Bottoms: 3 × 5 = 15
  3. Answer: 6/15 = 2/5 (simplified by dividing both by 3)

Dividing Fractions — KFC: Keep, Flip, Change

To divide by a fraction: Keep the first fraction, Flip the second fraction upside down, then Change the ÷ to ×.

Worked Example 3 — 3/4 ÷ 2/5

  1. Keep 3/4
  2. Flip 2/5 → 5/2
  3. Change to multiply: 3/4 × 5/2
  4. Tops: 3 × 5 = 15. Bottoms: 4 × 2 = 8
  5. Answer: 15/8 or 1 and 7/8

Simplifying Fractions

Divide both the top and bottom by their highest common factor (the biggest number that goes into both).

Example: 12/18 → both divide by 6 → 2/3.

Mixed Numbers & Improper Fractions

A mixed number is like 2 and 3/4. An improper fraction is when the top is bigger than the bottom, like 11/4.

To convert: multiply the whole number by the denominator, add the numerator. So 2 and 3/4 = (2×4 + 3)/4 = 11/4.

Try It Yourself

  1. Work out 2/5 + 1/3. (Answer: 11/15)
  2. Work out 4/7 × 7/8. (Answer: 1/2)
  3. Convert 3 and 2/5 to an improper fraction. (Answer: 17/5)

Need to check your fraction calculations?

→ Open the Fractions Calculator