Problem 2 · 1993 AJHSME
Easy
Fractions, Decimals & Percents
simplify-fraction
When the fraction 4984 is expressed in simplest form, the sum of the numerator and the denominator will be
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Answer: C — 19.
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Hint 1 of 2
The numerator 49 is 7×7, and that's the clue — does 7 also divide 84? If so the fraction isn't in lowest terms yet.
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Hint 2 of 2
'Simplest form' means top and bottom share no common factor. Cancel the shared 7, THEN add — never add before reducing, or you'd get 49+84=133 (a trap answer).
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Approach: reduce first, then add
- 49 = 7×7, and 84 = 7×12, so they share a factor of 7. Divide both by 7: 49/84 = 7/12. Now 7 and 12 share nothing, so it's in simplest form.
- 7 + 12 = 19.
- Trap to dodge: the question asks for the sum after simplifying. Adding the original 49+84 gives 133 (choice E) — that's the bait for anyone who skips the reduce step.
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