Hi Bridget,
I am going to show you two ways to solve this problem, one method just uses a diagram and the other uses addition and multiplication of fractions.
Method 1.
I drew a rectangle to represent a whole stock and coloured Sam's half orange and Mary's half green.
Sam then divided his half sock into three equal parts and sold two of them to Mary.
![stock](bridget2.2.gif)
If Mary divides her original half stock in three as Sam did you can easily see how much she now owns.
![](bridget2.3.gif)
The stock is divided into six equal sized pieces and Mary owns five of them so she owns 5/6 of a stock.
Method 2.
Sam owns 1/2 a stock and he sells 2/3 of his stock to Mary. 2/3 of 1/2 is 2/3 × 1/2 = 1/3. Mary already owned 1/2 a stock so now she owns
1/2 + 1/3 = 3/6 + 2/6 = 5/6 of a stock.
Penny
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