Problem 1 · 1994 AJHSME
Easy
Fractions, Decimals & Percents
common-denominator
Which of the following is the largest?
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Answer: D — 5/12.
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Hint 1 of 2
You can't compare fractions by eye when the bottoms are all different — first give them a shared yardstick.
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Hint 2 of 2
Rewrite every fraction over one common denominator (24 fits all of them). Once the bottoms match, the fraction with the biggest top wins.
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Approach: compare over a common denominator
- All five bottoms (3, 4, 8, 12, 24) divide 24, so 24 is the natural common yardstick. Rewrite each: 1/3 = 8/24, 1/4 = 6/24, 3/8 = 9/24, 5/12 = 10/24, 7/24 = 7/24.
- Now the bottoms all match, so just read off the biggest top: 10 wins, so 5/12 is largest.
- Why this works: a fraction's size is 'how many pieces' (top) of 'a fixed piece-size' (bottom). Only when the piece-size is the same can you compare by counting pieces. You'll reuse this every time you add, subtract, or order fractions.
Another way — compare each to a benchmark:
- Notice 1/3, 1/4, 7/24 are all below 1/3 ≈ 0.33, while 3/8 = 0.375 and 5/12 ≈ 0.417 are bigger.
- Between the two big ones, 5/12 > 3/8 (10/24 vs 9/24), so 5/12 is largest — no full common denominator needed if you only care about the top contenders.
Mark:
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