# How do you simplify 6 / (2/3)?

Apr 7, 2016

$9$

#### Explanation:

To divide a number by a fraction, you can multiply it by the inverse of the fraction.

Think of dividing something by $\frac{1}{2}$. There are two halves in every whole, so the number of halves in, say, $3$ will be $3 \times 2 = 6$. So we can see that $\frac{3}{\frac{1}{2}} = 3 \times \frac{2}{1} = 3 \times 2 = 6$

So, we can put this into action with our calculation:

$\frac{6}{\frac{2}{3}} = 6 \times \frac{3}{2} = 6 \times 1.5 = 9$

Hope this helps; let me know if I can do anything else:)

Apr 7, 2016

$\frac{6}{\frac{2}{3}} = 9$

#### Explanation:

Using the shortcut rule of: to divide turn the divisor upside down (invert) and multiply.

We have $\frac{6}{\frac{2}{3}}$ which is the same as$\text{ } 6 \div \frac{2}{3}$

Applying the rule

$6 \times \frac{3}{2}$

It is perfectly correct to write 6 as $\frac{6}{1}$. It just not very common to see it.

$6 \times \frac{3}{2} \text{ " ->" " 6/1xx3/2" " ->" } \frac{6 \times 3}{1 \times 2} = \frac{18}{2}$

But $\frac{18}{2} = 9$

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$\textcolor{b l u e}{\text{EDIT By Tarik:}}$
Any number written as a whole number is actually a fraction: so 6 is $\frac{6}{1}$. Accordingly, let me rewrite the task:

$\frac{\frac{6}{1}}{\frac{2}{3}} =$
Now, multiply inner part with inner part and external part with external part:

When multiplied, the product of multiplication of external parts will stay as nominator, and the product of multiplication of inner parts will stay as denominator.

$\frac{\frac{6}{1}}{\frac{2}{3}} = \frac{18}{2} = 9$
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$\textcolor{b l u e}{\text{Additional comment by Tony B}}$

$\textcolor{red}{\text{I will leave Tarik's edit in place as it sometimes useful to see a different approach!}}$

Using Tarik's terminology; multiplying the inner numbers together and then the outer numbers together is the same process as inverting and then multiplying.