Problem 10 · 1985 AJHSME
Medium
Fractions, Decimals & Percents
average-two-fractions
The fraction halfway between 1⁄5 and 1⁄3 (on the number line) is
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Answer: C — 4⁄15.
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Hint 1 of 2
'Halfway between' two points on the number line is exactly their midpoint — and the midpoint of two numbers is just their average. So this isn't a special fraction trick; it's add-and-halve.
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Hint 2 of 2
To average fractions, give them a common bottom first (fifteenths work for 5 and 3), add the tops, then halve. Halving is the same as dividing the answer by 2.
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Approach: average the two fractions
- The midpoint is the average: add the two fractions, then halve. Common denominator 15: 1⁄5 = 3⁄15 and 1⁄3 = 5⁄15, so the sum is 8⁄15.
- Halve it: 8⁄15 ÷ 2 = 8⁄30 = 4⁄15.
- Sanity check: 1⁄5 = 3⁄15 and 1⁄3 = 5⁄15, and 4⁄15 sits exactly between 3⁄15 and 5⁄15 — right in the middle, as a midpoint should be.
Mark:
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