Hi Bridget.

Each of them owns half the stock to start out:

Then Sam sells 2/3 of his stock to Mary. (Let's say Sam is the portion on the right hand side.) So he has to divide his half into three pieces first.

Using fractions, this is like dividing 1/2 (the original) by three: 1/2 ÷ 3 = 1/6. There are three pieces and each one is 1/6 of the stock, that makes 3/6 that Sam owns.

Now Sam gives 2 of the pieces to Mary:

So what fraction (portion) of the company does Mary own? You have to add the amount Sam gave her (2 pieces each worth 1/6 of the company) to the amount she already had (1/2 of the company):

Can you finish the problem now? You have to make a common denominator in order to add fractions, Bridget.

Hope this helps,
Stephen La Rocque.