Question

What is `5` divided by `1/4`?

Answer 1

`20`

Explanation:

The question is how many `1/4`ths can be derived from `5`?

It is clear that there are four `1/4`ths in `1`
`5` is made up of `5` times `1` of `5 xx 4 = 20`

A more mathematical way is to actually do this as a division problem of two fractions

`5 = 5/1`

so divide `5/1` by `1/4`

`( 5/1)/ (1/4)`

This is a complex fraction make it simpler by multiplying both sides by the inverse of 1/4 which is 4/1. This will cause the bottom fraction 1/4 to become 1

`{(5/1) xx ( 4/1)}/ {(1/4) xx (4/1)} = (5/1) xx ( 4/1)`

Multiplying both the top and the bottom by the same number is the fairest doctrine it is the same as multiplying by 1 it doesn't change anything,

This leaves

`5/1 xx 4/1 = 20/1`

`20` divided by `1` is `20` so the answer is

`20`

Answer 2

`5 xx 4/1 =20`

Explanation:

Remember that `1` is made up of `4/4`

`1/4+1/4+1/4+1/4 = 4/4 =1`

So for every whole number there are four quarters.

`1 div 1/4 =4`

`2 div 1/4 = 8` and so on.

The question `5 div 1/4` is asking how many quarters can be obtained from `5`.

`5` is five times as many as `1`.

Therefore in `5` whole there will be `5 xx 4 =20` quarters

This can also be obtained from normal fraction division:

`5 div1/4`

`= 5/1 xx 4/1" "larr` multiply by the reciprocal

`=20`