Question

What is one-half of one and two thirds?

Answer 1

`r = 2/3`

Explanation:

We can rewrite this problem as

What is `1/2` of `1 1/3`?

When dealing with fractions the word "of" means "times" or "to multiply".

Also, let's call the value we are looking for `r`:

So we can again rewrite this as:

`r = 1/2 xx 1 1/3`

To complete this problem we need to convert the mixed fraction to an improper fraction. We do this by multiplying the integer by the proper form of `1` and then adding it to the fraction:

`r = 1/2 xx ((color(red)(3/3) xx 1) + 1/3)`

`r = 1/2 xx (color(red)(3/3) + 1/3)`

`r = 1/2 xx (3 + 1)/3`

`r = 1/2 xx 4/3`

`r = (1 xx 4)/(2 xx 3)`

`r = 4/6`

`r = (2 xx 2)/(2 xx 3)`

`r = (2/2) xx (2/3)`

`r = 1 xx 2/3`

`r = 2/3`