Working with Fractions
When dividing makes things bigger
Find out when dividing can make a number bigger instead of smaller.
With whole numbers, dividing makes things smaller: 6 ÷ 3 = 2.
But 6 ÷ 1/4 = 6 × 4 = 24: four times bigger! And 1/8 ÷ 1/4 = 1/8 × 4 = 1/2, also bigger than 1/8.
When is the answer bigger, and when smaller? Remember, dividing = multiplying by the reciprocal. So look at the reciprocal of the divisor:
| Divisor | Its reciprocal | Effect | Answer |
|---|---|---|---|
| more than 1 (like 3) | between 0 and 1 (1/3) | shrinks | smaller than the dividend |
| between 0 and 1 (like 1/4) | more than 1 (4) | grows | bigger than the dividend |
It makes sense: 6 ÷ 1/4 asks how many quarters fit into 6? Lots of small pieces fit, so the answer is big.
Dividing by a number between 0 and 1 makes the quotient bigger than the dividend, because its reciprocal is greater than 1.
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