Adding Fractions · Hook

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Ever wondered how to share a pizza fairly?

You and your friend order a pizza cut into 4 equal slices. You eat 1 slice. Your friend eats 2 slices. How much of the pizza is gone? That's adding fractions — and you already do it without noticing!

Revision notes

📒 Adding Fractions: lesson notes

Add fractions with the same and different denominators — and see why it works.

You and your friend order a pizza cut into 4 equal slices. You eat 1 slice. Your friend eats 2 slices. How much of the pizza is gone? That's adding fractions — and you already do it without noticing!

What a fraction tells you

The bottom number — the denominator — tells you how many equal parts the whole is cut into.

The top number — the numerator — tells you how many of those parts you have.

So 14 means: cut into 4 equal parts, take 1.

🔑 Key idea: You can only add parts that are the SAME size.

Worked example 1

27 + 37

  1. Step 1: Check the denominators

    Both are 7 — the pieces are the same size (sevenths).

  2. Step 2: Add the numerators only

    2 + 3 = 5

    27 + 37 = 57

    Why? The denominator names the size of the pieces. Adding pieces doesn't change their size.

Answer: 57

Worked example 2

12 + 13

  1. Step 1: Find a common denominator

    The LCM of 2 and 3 is 6.

    Why? We need halves and thirds cut into the same size pieces: sixths.

  2. Step 2: Rewrite both fractions

    12 = 36 (× 3 top and bottom)

    13 = 26 (× 2 top and bottom)

  3. Step 3: Add the numerators

    36 + 26 = 56

Answer: 56

Summary

  • Same denominator → keep it, add the numerators.
  • Different denominators → change both to a common denominator (use the LCM) first.
  • Never add the denominators.
  • Simplify your answer if you can: 44 = 1, 36 = 12.

Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.