Problem 2 · 1988 AJHSME
Easy
Fractions, Decimals & Percents
pair-decimals
The product 8 × .25 × 2 × .125 =
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Answer: C — 1⁄2.
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Hint 1 of 2
Don't multiply left to right. Those decimals are familiar fractions in disguise — 0.25 = 1⁄4 and 0.125 = 1⁄8. Which factor would 'undo' each one?
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Hint 2 of 2
Multiplication can be reordered freely, so hunt for pairs that make a whole number: 8 cancels the eighth, 2 fits the quarter.
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Approach: reorder to make canceling pairs
- 0.125 = 1⁄8 and 0.25 = 1⁄4, so pair each big number with the fraction it cancels: (8 × 0.125) × (2 × 0.25) = 1 × 0.5.
- Product = 1⁄2.
- Why this transfers: because order and grouping don't change a product, scan a long multiplication for factors that pair into 1, 10, or 100 first. Pairing beats grinding through ugly decimals one at a time.
Mark:
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