# How do I find the quotient of 3/8 and 2?

Nov 13, 2015

Another perspective!!!

#### Explanation:

When dividing for example 4 by 2 you can do this strait off. So is there a way can do this with fractions?
It takes quite a while to explain what happens but the actual process is very quick once understood

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{g r e e n}{\text{Point 1}}$

The reason $4 \div i \mathrm{de} 2$ can be done strait off is that they are both of the same unit size. The 'unit size $\textcolor{b l u e}{\text{'when viewed this way'}}$ is how many of what you are counting it takes to make a whole.

So if you have $\frac{1}{2}$ then the count is 1 and the unit size is such that it takes 2 of them to make a whole.

If you have $\frac{2}{3}$ then the count is 2 and the unit size is such that it takes 3 of them to make a whole.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{g r e e n}{\text{Point 2}}$

When counting 'the normal way' such as 1, 2 , 3 and so on, you can write them as: $\frac{1}{1} , \frac{2}{1} , \frac{3}{1}$ The bottom number (denominator) is how many of what you are counting it takes to make a whole of something. This is why $4 \div i \mathrm{de} 2$ can be done strait off!!!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{g r e e n}{\text{Using the idea}}$

$\frac{3}{8} \div i \mathrm{de} 2$
Write as:

$\frac{3}{8} \div i \mathrm{de} \frac{2}{1}$

color(blue)("if you make the unit sizes the same you can then divide the counts directly"

When dividing you are doing so with counts. In this case you can not divide the count of 2 directly into the count of 3 as the unit sizes are different. One is of unit size 8 and the other of unit size 1.

Lets look at how to change $\frac{2}{1}$ into the same unit size as $\frac{3}{8}$

If we multiply $\frac{2}{1}$ by 1 we do not change its value. There are many ways of writing 1. Suppose we chose to write it as $\frac{8}{8}$

Then $\frac{2}{1} \times 1 \to \frac{2}{1} \times \frac{8}{8}$

But $\frac{2}{1} \times \frac{8}{8} = \frac{16}{8}$

So we can write

$\frac{3}{8} \div i \mathrm{de} \frac{16}{8}$

This is exactly the same as $3 \div i \mathrm{de} 16 \to \frac{3}{16}$