Question

Three friends shared `2/3` of a cake equally. What fraction of a cake did each student receive?

Answer 1

`1/3xx2/3=2/9` of the cake.

Explanation:

We've got `2/3` of a cake and we've got three friends who each get an equal piece. So what fraction of the cake did each friend get?

Let's work this problem this way: we can say that there are three friends and each got an equal piece, and so each friend got `1/3` of the cake that was eaten. So had the entire cake been eaten, each friend would have gotten:

`1/3xx1=1/3` of the cake.

So each friend got a `1/3` slice. But not from the full cake. Instead, it's from `2/3` of the cake, so that's:

`1/3xx2/3=2/9` of the cake.

Another way we can work this is to say that the `2/3` of the cake was divided into 3 pieces, so:

`(2/3)/3` and that can be expressed:

`(2/3)/3=2/(3xx3)=2/9`

Answer 2

`2/9`

Explanation:

A fraction consist of `("numerator")/("denominator")->("count")/(" size indicator")`

So we need to convert the count (numerator) into a number we can 'split' into a group of 3 equal parts

`("count")/(" size indicator")" " ->" " color(blue)(2/3xx1)color(green)(" "->" "2/3xx3/3)color(red)(" " =" " 6/9)`

Three people share this so each has :

`(6-:3)/9=2/9` of the whole cake
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Foot note")`

`6/9" " =" " 2/9+2/9+2/9` which is spread evenly over the 3 friends.
`color(white)(.)`
So each has one of these which is `2/9`