Problem 13 · 2016 Math Kangaroo
Medium
Fractions, Decimals & Percents
proportion
Which of the following fractions is closest to \(\tfrac12\)?
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Answer: C — \(\tfrac{29}{57}\)
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Hint 1 of 2
A fraction is close to 1/2 when its numerator is close to half its denominator.
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Hint 2 of 2
Compare 2 times the numerator with the denominator for each option.
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Approach: compare twice the numerator with the denominator
- A fraction n/d equals 1/2 exactly when 2n = d; the closer 2n is to d, the closer to 1/2.
- For 29/57, 2 × 29 = 58, differing from 57 by only 1 — closer than every other option.
- So 29/57 is closest to 1/2.
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