Question

Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert untis of measurement?

Answer 1

Well, units divide and multiply just like numbers. That's why Area is in units of  distance squared (cm × cm = cm²) and volume is cubic distance (m × m × m = m³).

Likewise other mathematical operations can be performed on them, including division where they can cancel out of the equation.

For instance, a rate, speed, slope or conversion factor is usually one unit divided by another unit. Like so...

speed = 5 meters per second
$= \frac{5m}{1sec}$

If you are given a distance traveled, let's say 100 meters and asked to solve for time it takes to get there. You would divide by the speed so that meters cancel leaving only time.

** Of course to divide by a fraction is to flip and multiply so really you're just multiplying by it, making sure the same units are diagonal and cancel out like so:

$100 m * \frac{1sec}{5m} = 20 sec$


Hope this helps!