# Question #b2995

##### 1 Answer

One is half of 2

#### Explanation:

A fraction has two parts, the top and bottom number. I want you to think of the top number as the count and the bottom number as an indicator of size. Proper names are

Consider the fraction

The number of 5 means that we need 5 of them to make a whole of something. Suppose you have a plank of wood and split it into 2 equal lengths. We have a count of 2 but the size is also 2 so we have

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I am using the sign

Remember that half is

But for all of something we need the count part of

To change the count of 1 into a count of 2 we have 1+1

It is the same with fractions

To change the count of 1 (of size 2) we add another 1 (of size 2)

That is

If we have doubled the right hand side of

Then we need to double the left as well

So

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 is