Problem 2 · 1994 AJHSME
Easy
Fractions, Decimals & Percents
sum-fractions
110 + 210 + 310 + 410 + 510 + 610 + 710 + 810 + 910 + 5510=
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Answer: D — 10.
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Hint 1 of 2
Every fraction already shares the bottom 10 — so don't fight the fractions, just collect all the tops into one big numerator.
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Hint 2 of 2
Pair the small numerators to add fast: 1+2+…+9 is four pairs of 10 plus the leftover 5 = 45. (This pairing trick is how you sum any run of counting numbers.)
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Approach: add numerators over the common 10
- The bottoms are all 10, so the whole thing is one fraction: (1+2+3+…+9+55)/10.
- Add the tops smartly: 1+2+…+9 pairs up as (1+9)+(2+8)+(3+7)+(4+6)+5 = 45. Then 45 + 55 = 100.
- So the sum is 100/10 = 10. Sanity check: 55/10 alone is 5.5, and the other nine terms average about 0.5 each (≈4.5 total), landing right at 10.
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