What fraction is halfway between 1/3 and 1/5?

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What fraction is halfway between 1/3 and 1/5?

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Answer 1 · 2015-09-11T17:55:52

$\frac{4}{15}$ $4/15$

Explanation:

A trick question: The obvious, but wrong answer is $\frac{1}{4}$ $1/4$ .

Actually $\frac{1}{4}$ $1/4$ is called the harmonic mean of $\frac{1}{3}$ $1/3$ and $\frac{1}{5}$ $1/5$ - being the reciprocal of the average of the reciprocals.

To find the number halfway between $a$ $a$ and $b$ $b$ , calculate $\frac{1}{2} (a + b)$ $1/2(a+b)$ ...

$\frac{1}{2} (\frac{1}{3} + \frac{1}{5}) = \frac{1}{2} (\frac{5}{15} + \frac{3}{15}) = \frac{1}{2} (\frac{8}{15}) = \frac{4}{15}$ $1/2(1/3+1/5) = 1/2(5/15+3/15) = 1/2(8/15) = 4/15$

Note that to add the fractions $\frac{1}{3}$ $1/3$ and $\frac{1}{5}$ $1/5$ we first give them a common denominator $15$ $15$ by multiplying them by $\frac{5}{5}$ $5/5$ and $\frac{3}{3}$ $3/3$ respectively. Once we have a common denominator, then we can just add the numerators.

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What fraction is halfway between 1/3 and 1/5?

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