Problem 15 · 1988 AJHSME
Hard
Fractions, Decimals & Percents
add-fractions-then-flip
The reciprocal of (1⁄2 + 1⁄3) is
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Answer: C — 6⁄5.
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Hint 1 of 2
'Reciprocal of (a sum)' means you must finish the sum first, getting one single fraction, before you flip anything. So: what is 1⁄2 + 1⁄3 as one fraction?
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Hint 2 of 2
Add over a common denominator of 6, then flip the result top-for-bottom.
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Approach: add into one fraction, then flip
- First combine: 1⁄2 + 1⁄3 = 3⁄6 + 2⁄6 = 5⁄6. Reciprocal flips a single fraction over, so the answer is 6⁄5.
- Trap to avoid: you cannot flip each piece separately. Flipping gives 2 + 3 = 5 (choice E), which is wrong — the reciprocal of a sum is not the sum of the reciprocals.
- Why this transfers: 'reciprocal of (…)' is one operation on the *whole* finished value. Always collapse what's inside the parentheses to a single number first, then take the reciprocal once.
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