🇺🇸 AMC 8 ⇄ switch contest
1988 AJHSME

Problem 3

Problem 3 · 1988 AJHSME Easy
Fractions, Decimals & Percents simplify-each-fraction

1⁄10 + 2⁄20 + 3⁄30 =

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Answer: D — .3.
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Hint 1 of 2
Before reaching for a common denominator, look at each fraction on its own. What does 2⁄20 reduce to? And 3⁄30?
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Hint 2 of 2
In every fraction here the bottom is exactly ten times the top — so each one is secretly the same value.
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Approach: simplify each term first, then add
  1. Each fraction has a bottom that's 10× its top, so each one equals 1⁄10: 2⁄20 = 1⁄10 and 3⁄30 = 1⁄10.
  2. The sum is just 1⁄10 + 1⁄10 + 1⁄10 = 3⁄10 = 0.3.
  3. Why this transfers: always simplify each fraction before adding. Reducing first can collapse a scary-looking sum into identical pieces, dodging the messy common-denominator step entirely.
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