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1985 AJHSME Problems/Problem 10

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Problem

The fraction halfway between \frac{1}{5} and \frac{1}{3} (on the number line) is

unitsize(12);draw((-1,0)--(20,0),EndArrow);draw((0,-.75)--(0,.75));draw((10,-.75)--(10,.75));draw((17,-.75)--(17,.75));label(...

\text{(A)}\ \frac{1}{4} \qquad \text{(B)}\ \frac{2}{15} \qquad \text{(C)}\ \frac{4}{15} \qquad \text{(D)}\ \frac{53}{200} \qq...

Solution

The fraction halfway between \frac{1}{5} and \frac{1}{3} is simply their average, which is \begin{align*}\frac{\frac{1}{5}+\frac{1}{3}}{2} &= \frac{\frac{3}{15}+\frac{5}{15}}{2} \\&= \frac{\frac{8}{15}}{2} \\...

\boxed{\text{C}}

See Also

1985 AJHSME (Problems • Resources)
Preceded by
Problem 9 		Followed by
Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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