# What fraction is between #1/3# and #1/2# ?

##### 5 Answers

There are infinitely many possibilities, but the midpoint between

#### Explanation:

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#

#### Explanation:

First, make the denominators equal:

Now figure out the middle number between the numerators:

Since

Check the answer:

so

There are many ... but

#### Explanation:

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.

#### Explanation:

The fraction

**Proof:**

Assuming that

The middle term

That means

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.