When multiplying makes it smaller
3/4 of a 20-metre rope is 15 metres. That is less, not more.
Step 1 of 4
- A line marks 20 metres.
- 20 × 3/4 = 15: shorter.
- 20 × 4/4 = 20: the same.
- 20 × 5/4 = 25: longer.
Look at the multiplier alone
A top below the bottom shrinks the amount. A top above it grows the amount. A matching pair leaves it alone.
That holds for any starting amount above zero.
Why? 3/4 is less than 1. So it takes only part of the amount. 5/4 is more than 1, so it takes more than the whole.
Half of a half is an easy example. 1/2 × 1/2 is 1/4, since 1 × 1 = 1 and 2 × 2 = 4. On the number line, 1/4 is closer to 0 than 1/2.
Tap Smaller, Same or Bigger in the lab. Then look at the bars.
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