If a machine part rotates 150 degrees every second how many times does it rotate every minute?

The unit rate for the part is 'rotation unit' per 'time unit.'
To change from degrees per second to rotations per minute, you need to find equivalent measures of time and rotation.

For rotation, there are 360 degrees in one circle, or one rotation. This means that the expression
.
is equal to 1.  Because the expression is equal to 1, that means 360°/1 rotation is a unit conversion rate.

In terms of time, the unit conversion is 60 seconds per 1 minute, or
.

Now we convert the rate of 150° per second to rotations per minute:


To cancel out units, you need to make it so that the unit is in the denominator and numerator, so that means that for degrees you need to put the degrees on the bottom of the unit conversion rate:

The degrees unit cancels out:


Now because the seconds unit is in the denominator, you need to put the seconds unit of the conversion rate in the numerator.

Cancel the seconds unit:


Thus your answer is 25 rotations per minute.