# Just need to verify if this one needs to be subtracted or no.

#### jaytheseer

##### New member
Mr. Gates owns 3/8 of Macrohard. After selling 1/3 of his share, how much more of Macrohard does Mr. Gates still own?

#### MarkFL

Staff member
Yes, I would view the subtraction in the form:

If Mr. Gates sold 1/3 of his share, how much of his share does he have left?

What portion of Macrohard is Mr. Gates' remaining share?

#### jaytheseer

##### New member
My solution so far:

3/8 = 9/24 and 1/3 = 8/24
9/24 - 8/24 = 1/24

But my book says a totally different thing which confuses me:

3/8 x 1/3 = 1/8.3/8 - 1/8 = 2/8 =1/4

#### Deveno

##### Well-known member
MHB Math Scholar
Mr. Gates owns 3/8 of Macrohard. This means that for every 8 shares of Macrohard out there, he owns 3 of them.

1/3 of 3, is of course, 1.

So if he sells 1/3 of his shares, he now only owns 2 shares out of every 8, which is 2/8 = 1/4.

When we take a fraction OF something, it means: "multiply".

So 1/3 OF 3/8 means:

MULTIPLY (1/3)*(3/8), from which we get: (1/3)*(3/8) = 1/8 <---how much he sold.

If we want to know how much he has LEFT, then we SUBTRACT, so:

3/8 - 1/8 = ...?

#### MarkFL

Staff member
The way I look at it he has 2/3 of his shares left after selling 1/3. So the portion of Macrohard he still owns is:

$$\displaystyle \frac{2}{3}\cdot\frac{3}{8}=\frac{1}{4}$$

#### Prove It

##### Well-known member
MHB Math Helper
The OP is not realising that it is not 1/3 of the block which is being sold, but 1/3 of HIS PART of the block. So 1/3 of 3/8 = 1/3 x 3/8 = 1/8.

So what Mr Gates still owns is what's left after 1/8 of the entire block is removed from his 3/8 of the block, so 3/8 - 1/8 = 2/8 = 1/4.

#### jaytheseer

##### New member
3/8 - 1/8 = ...?

=2/8
=1/4

Very clear and simple to understand. Thank you!