Which piece is more?

Two strips are the same length. One is cut into 4 parts. The other is cut into 5. You take 3 parts from each. Which is more?

The rule

The strip cut into 4 gives more: 3/4 is more than 3/5.

Same bottom number: the bigger top is more. The parts are the same size.

Same top number: the smaller bottom is more. A smaller bottom means bigger parts.

Bottoms and tops both differ? Rename both to one bottom number. Then the parts are the same size. Compare the tops.

Renaming keeps the amount the same.

Example

Compare 2/3 and 3/4. Rename both to twelfths, which means 12 parts in the whole.

For 2/3: 3 × 4 = 12, and 2 × 4 = 8. So 2/3 = 8/12.

For 3/4: 4 × 3 = 12, and 3 × 3 = 9. So 3/4 = 9/12.

9 is more than 8, so 3/4 is more.

Try the lab to finish this lesson.