Question

How do you find a fraction between `1/2 and 4/5?`

Answer 1

There are many more than one fraction in the middle

Explanation:

There are an infinite number of fractions in between `1/2` and `4/5`. We'll find first the middle point between these two, and then we'll show that you can find as many as you like in between `1/2` and `4/5`.

The middle point between `a` and `b` is `(a+b)/2`.

So the middle point between `1/2` and `4/5` is `(1/2+4/5)/2= ((5+8)/10)/2=13/20`

But you can do the same now and find the middle point between `1/2` and `13/20`, and also the middle point between `13/20` and `4/5`, and so on. You can find as many points as you want between `1/2` and `4/5`

Answer 2

There are infinitely many - change to a common denominator for comparison.

Explanation:

Before you can do any comparison between fractions, change them to the same denominator.

`1/2 < ? < 4/5`

There are infinitely many fractions between these two fractions.

`5/10 < color(blue)(?) < 8/10`

Now we can see that a fraction between these can be
`color(blue)(6/10" or " 7/10)`

However, you can use any common denominator, not only the lowest.

For example:`" "15/30 < color(red)(?) < 24/30`

You could use `color(red)(16/30," "17/30," "18/30," "18/30," "19/30," "20/30," "21/30," "22/30," "23/30)`

And so on .....

The fraction exactly halfway would be: `((6+7)/2)/10 = 6.5/10 = 13/20`