Problem 6 · 2015 Math Kangaroo
Medium
Fractions, Decimals & Percents
fraction-to-decimal
Which of the following fractions is smaller than 2?
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Answer: E — \(\frac{23}{12}\)
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Hint 1 of 3
Notice that a fraction equals exactly 2 when the top is double the bottom.
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Hint 2 of 3
So "smaller than 2" just means the top number is less than two times the bottom number.
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Hint 3 of 3
Go down the list and compare each top with double its bottom.
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Approach: compare each numerator to twice its denominator
- A fraction is smaller than 2 exactly when its top number is less than double its bottom number (because doubling the bottom is what makes the fraction equal 2).
- Compare each one: 19 vs 16, 20 vs 18, 21 vs 20, 22 vs 22, 23 vs 24 — in the first four the top is as big or bigger, so those are 2 or more.
- Only \(\frac{23}{12}\) has its top smaller than the doubled bottom (23 < 24), so the answer is E.
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