1985 AJHSME Problem 10

Problem

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

$[asy] unitsize(12); draw((-1,0)--(20,0),EndArrow); draw((0,-.25)--(0,.25)); draw((10,-.25)--(10,.25)); draw((17,-.25)--(17,.25)); label("$0$",(0,-.5),S); label("$\frac{1}{5}$",(10,-.5),S); label("$\frac{1}{3}$",(17,-.5),S); [/asy]$

$\text{(A)}\ \frac{1}{4} \qquad \text{(B)}\ \frac{2}{15} \qquad \text{(C)}\ \frac{4}{15} \qquad \text{(D)}\ \frac{53}{200} \qquad \text{(E)}\ \frac{8}{15}$

Solution

$\frac{1}{5} = \frac{3}{15}$ and $\frac{1}{3} = \frac{5}{15}.$ The fraction in between is $\boxed{\text{(C)} \quad \frac{4}{15}}.$

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1985 AJHSME Problem 10

Problem

Solution