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

1 Answer
Sep 11, 2015

Answer:

#4/15#

Explanation:

A trick question: The obvious, but wrong answer is #1/4#.

Actually #1/4# is called the harmonic mean of #1/3# and #1/5# - being the reciprocal of the average of the reciprocals.

To find the number halfway between #a# and #b#, calculate #1/2(a+b)# ...

#1/2(1/3+1/5) = 1/2(5/15+3/15) = 1/2(8/15) = 4/15#

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