Question

How do you divide `6\div \frac { 1} { 3}`?

Answer 1

`6/(1/3)=18`

Explanation:

We know this rule for dividing fractions:
`(a/b)/(c/d)=a/b*d/c`

If we write the `6` as `6/1` we can use this rule:

`6/(1/3)=(6/1)/(1/3)=6/1*3/1=18/1=18`

Answer 2

We can divide by a fraction by multiplying by the fraction's reciprocal.

Explanation:

A number's reciprocal can be thought of as flipping it upside down, i.e. The reciprocal of `1/2` is `2/1`, and the reciprocal of `4/2` is `2/4`.
Using this logic we can determine that the reciprocal of `1/3` is `3/1`, or simply `3` .
Once we have found the reciprocal, it is simply a matter of multiplying out the the numbers: `6 * 3`.
Therefore, `6 -: 1/3 = 18`.

Another Example:
`5 -: 1/8 = 5 * 8/1 = 5 * 8 = 40.`