Cancel before you multiply
A gardener waters 4 flower beds. Each bed gets 3/8 of a bucket. How much water is that?
- One bed gets 3 of the 8 pieces.
- Four beds get 4 × 3 = 12 pieces.
- Group the pieces in fours. Both 12 and 8 split into fours.
- 12/8 = 3/2, which is 1 1/2 buckets.
Cancel first
The water is 1 1/2 buckets.
Adding 3/8 four times gives 12/8. That is 4 × 3/8.
Before multiplying, divide a top and a bottom by the same number. The answer stays the same.
This is cancelling. The product's top and bottom shrink by the same number.
Write 4 as 4/1. The top 4 and the bottom 8 both divide by 4. 4 ÷ 4 = 1 and 8 ÷ 4 = 2. So 4/1 × 3/8 = 1/1 × 3/2 = 3/2.
Try 9/10 × 5/12. Divide 9 and 12 by 3: they become 3 and 4. Divide 5 and 10 by 5: they become 1 and 2. Now the product is 3/2 × 1/4 = 3/8.
Watch out!
Cancel a top against a bottom. Two tops do not cancel. In 4/9 × 6/10, halving both tops gives 2/9 × 3/10, which is 1/15. The true answer is 4/15.
Tap the pair that can cancel in the lab. Then check the product.
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