Question

How are unit rates written?

Answer 1

see explanation

Explanation:

Depends upon which you are applying the unit measurement

For example, consider the following example of a right triangle

`("Amount of up")/("Amount of along")-> 1/2`

And this is the same as `(1-:2)/(2-:2) = 0.5/1`

The bottom number is the unit (1 off) compared against and the rate is the `0.5`

`color(magenta)("So the unit rate in this instance is "0.5)`

`color(brown)("So unit rate is comparing quantities against a standardised quantity")` `color(brown)("of 1 of something else.")`

If you consider the trigonometric ratio of tangent `->tan(theta)`

For the same triangle:

`tan(theta)=("amount of up")/("amount of along")=1/2 = 0.5/1`

So `tan(theta)=0.5`