Question

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

Answer 1

`9`

Explanation:

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

Think of dividing something by `1/2`. There are two halves in every whole, so the number of halves in, say, `3` will be `3xx2=6`. So we can see that `3/(1/2) = 3xx2/1 = 3xx2 = 6`

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

`6/(2/3) = 6xx3/2 =6xx1.5 = 9`

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

Answer 2

`6/(2/3)= 9`

Explanation:

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

We have `6/(2/3)` which is the same as`" " 6 -: 2/3`

Applying the rule

`6xx3/2`

It is perfectly correct to write 6 as `6/1`. It just not very common to see it.

`6xx3/2" " ->" " 6/1xx3/2" " ->" " (6xx3)/(1xx2) = 18/2`

But `18/2 =9`

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`color(blue)("EDIT By Tarik:")`
Any number written as a whole number is actually a fraction: so 6 is `6/1`. Accordingly, let me rewrite the task:

`(6/1)/(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.

`(6/1)/(2/3)=18/2=9`
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`color(blue)("Additional comment by Tony B")`

`color(red)("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.