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Grade 5 · Maths · Lessons
Different bottoms
🍕pizza✂️cut to match➕add➖take away
Different bottoms.
The big ideaPieces must be the same size to add or take away. Cut both fractions to match, then work with the tops.

How it works

Pieces must be the same size to add or take away.

Cut both fractions to match, then work with the tops.

5/8 − 1/4: 1/4 is 2/8, so 5/8 − 2/8 = 3/8.

1/3 + 1/2• 1/3 = 2/6• 1/2 = 3/6Add• 2/6 + 3/6 = 5/6
Match the bottoms.

Example 1: Take away

  1. 5/8 − 1/4 = ?
  2. 1/4 is the same as 2/8.
  3. 5/8 − 2/8 = 3/8.
  4. So the answer is 3/8.

Example 2: Mixed numbers

  1. 1 1/3 + 2 1/2 = ?
  2. 1/3 is 2/6 and 1/2 is 3/6.
  3. Wholes: 1 + 2 = 3. Parts: 2/6 + 3/6 = 5/6.
  4. So the answer is 3 5/6.

Example 3: A bigger bottom

  1. 3 3/4 + 2 1/6 = ?
  2. 3/4 is 9/12 and 1/6 is 2/12.
  3. Wholes: 3 + 2 = 5. Parts: 9/12 + 2/12 = 11/12.
  4. So the answer is 5 11/12.

Words to know

common denominator
A bottom number both fractions share.
equivalent
A fraction that is the same size.

Watch out

Try it

  1. 5/6 − 1/3 = ?
  2. 1/4 + 5/8 = ?
  3. 1 1/2 + 4 4/5 = ?
Answers: 1. 1/2 · 2. 7/8 · 3. 6 3/10
For grown-upsFold two paper strips differently and line them up to see why bottoms must match.
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