Question

Question #bc229

Answer 1

`1:1 -> 1/2" and " 0.5.` It is `1/2` because the total count is 2

`3:1-> "the 3 is 75% of the whole which is a count of 4"`
`3:1 ->"the 1 is 25% of the whole which is a count of 4"`
`3:1->"the 3 is 300% of the 1"`

Explanation:

`color(blue)("For 1:1")`

Consider the count of what you are looking at for 1 to 1.

You have 1 of something and 1 of something else. So the total count is 2. Thus as a fraction of the whole one of them is `1/2`

Converting this to the `ul("first decimal place which is 10ths")`

Multiply by 1 but in the form of `1=5/5` giving

`1/2xx5/5" "=" "(1xx5)/(2xx5) = 5/10`

This is the same as `0.5`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("For 3:1 as parts of the whole")`

The count of parts is 3 of one thing and 1 of something else. So we have a total count of 4.

So as a proportion of the whole, 3 is `3/4`

Convert this to the second decimal place of 100ths

Multiply by 1 but in the form of `1=25/25`

`3/4xx25/25" "=" "(3xx25)/(4xx25)" "=" "75/100`

`75/100` is the same as `75%`
'.............................................................

As a proportion of the whole 1 is `1/4`

To change this into 100ths multiply by 1 but in the form of `1=25/25`

`1/4xx25/25" " =" " (1xx25)/(4xx25)" " =" " 25/100`

`25/100` is the same as `25%`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("For 3:1 as direct relationship to each other")`

`300%` in fraction form is `300/100`

So if we multiply the ratio part of 1 by `300/100` we get the other part of the ratio which is 3

So 3 is 300% of 1