Question

A man owned 3
/8

of a business and sold 2
/3

of his shares, what part of the entire business did he sell?

Answer 1

To better understand this problem, start by thinking about what would happen if the man owned $\frac{1}{2}$ of the business and then sold half of his shares to another party. In this case, the man would have sold $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ of the entire business  to someone else.

Similarly, when the man owns  $\frac{3}{8}$ of the business, if he sells $\frac{2}{3}$ of the business, he will have sold $\frac{2}{3}\times \frac{3}{8}= \frac{6}{24} =\frac{1}{4}$ of the entire business.

Another way to think about this problem is initially he owns 3 pieces of a whole that is made up of 8 parts. When he sells 2 of those pieces, he is selling the new owner two  of the three pieces of a whole that is made up of 8 parts. The fraction of the whole that he sells is $\frac{2}{8} =\frac{1}{4}$.

He sells of $\frac{1}{4}$ of the original business.