Question

How do you find the unit rate of 405 rotations in 5 minutes?

Answer 1

The unit rate is 81 revolution per minute

Explanation:

`color(blue)("Initial thoughts")`

Unit rate is where there is only 1 of the reference units of measurement. In this case the reference units are minutes.

The word 'per' means for 'one of'

So as a ratio we have: rotations per minute is: `->("rotation count")/("1 minute")`
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`color(blue)("Answering the question")`

Initial condition:`->(" 405 rotations")/("5 minutes")`

As we need 1 minute we need to change the 5 into 1 so we divide 5 by 5.

To maintain proportionality (for multiply and divide) what we do to the bottom we do to the top.

Divide top and bottom by 5

`(" 405 rotations")/("5 minutes") -=(405-:5)/(5-:5)=81/1`

The `-=` means 'equivalent to'

So for 1 minute we have 81 revolutions.

The unit rate is 81 revolution per minute