How do you find the fraction between 1/3 and 1/4?

3 Answers

Take the median like that #(1/3+1/4)/2=7/24#

Dec 16, 2015

There are an infinite amount of fractions between the two numbers.

Besides the other ways already mentioned, it's common knowledge that

#1/4=0.25#
and
#1/3=0.33333#

Thus, #1/4=25/100# and #1/3=(33.bar3)/100#.

Fractions between these two fractions can be picked out easily.

#26/100=13/50#

#30/100=3/10#

#31/100#

All of these are found between #1/3# and #1/4#.

You could also take the geometric mean.

#sqrt((1/3)(1/4))=sqrt(1/12)=1/(2sqrt3)=sqrt3/6#

You could also find arbitrary common denominators.

#1/3(52/52)# and #(1/4)(39/39)#

#52/156# and #39/156#

Between these are plenty of fractions...

#50/156=25/78#

#397/1560#

May 11, 2018

The mediant or freshman addition of fractions works great when we need one in between:

#{1 + 1}/{3 + 4} = 2/7#

We're assured

# 1/4 < 2/7 < 1/3 #