Working with Fractions
Is the product always bigger?
Find out whether multiplying by a fraction always makes a number bigger.
With whole numbers, multiplying makes things bigger. Is that still true with fractions? (Leave out 1: × 1 changes nothing.)
3 × 5 = 15: bigger than both. But 1/4 × 8 = 2: bigger than 1/4, but smaller than 8! And 3/4 × 2/5 = 3/10 (0.3), smaller than both 3/4 (0.75) and 2/5 (0.4).
It depends on whether each number is between 0 and 1 or more than 1:
| Case | Example | Product is ... |
|---|---|---|
| both more than 1 | 4/3 × 4 = 16/3 | bigger than both |
| both between 0 and 1 | 3/4 × 2/5 = 3/10 | smaller than both |
| one of each | 3/4 × 5 = 15/4 | in between them |
Two short rules sum it up:
- Multiplying by a number between 0 and 1 makes the other number smaller (it shrinks).
- Multiplying by a number more than 1 makes it bigger (it grows).
Multiplying by a number between 0 and 1 shrinks; multiplying by a number greater than 1 grows.
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