What fraction is between #1/3# and #1/2# ?
There are infinitely many possibilities, but the midpoint between
For any two numbers
So to find a fraction between
#1/2(1/3+1/2) = 1/2(2/6+3/6) = 1/2(5/6) = 5/12#
First, make the denominators equal:
Now figure out the middle number between the numerators:
Check the answer:
There are many ... but
There are many fractions between
If you use the LCD you end up with
The values between
However, use a larger value in the denominator:
Now it is easy so see that a fraction exactly between them is
Consider an even bigger value in the denominator:
Now we have the fractions:
You can continue in this using larger and larger values and each time you will find more and more fractions between
There are infinitely many equivalent fractions.
The middle term
In our case the fraction between
It's a nice trick if you need a fraction between fractions quick.
Ford's circles are closely related to that.