Problem 13 · 1994 AJHSME
Medium
Fractions, Decimals & Percents
average
The number halfway between 16 and 14 is
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Answer: C — 5/24.
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Hint 1 of 2
'Halfway between' is just the midpoint — and the midpoint of two numbers is their average. So this is an averaging problem in disguise.
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Hint 2 of 2
To average, add the two fractions then halve. Adding needs a common bottom (12 works for 6 and 4).
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Approach: average the two fractions
- Halfway between = average = (1/6 + 1/4) ÷ 2. Add first: over 12, that's 2/12 + 3/12 = 5/12.
- Now halve 5/12. Halving a fraction is doubling its bottom, so 5/12 → 5/24.
- Sanity check: 1/6 ≈ 0.167 and 1/4 = 0.25, so the midpoint should be near 0.21 — and 5/24 ≈ 0.208 ✓. The answer must land BETWEEN the two given fractions, which rules out tiny choices like 1/10.
Another way — midpoint = jump halfway up the gap:
- The gap from 1/4 to 1/6 is 3/12 − 2/12 = 1/12. Halfway means add half that gap to the smaller one: 2/12 + 1/24 = 4/24 + 1/24 = 5/24.
- Thinking 'start + half the distance' is the same midpoint idea you use on a number line.
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