Multiplication and division of measurements: Decide whether each proposed multiplication or division of measurements is possible. If it is possible, write the result in the last column of the table.

Question

Decide whether each proposed multiplication or division of measurements is possible. If it is possible, write the result in the last column of the table.

9.0 kg^2 / 1.0 kg = ? is it possible? or not.

50.cm^2 / 0.10 m = ? is it possible? or not.

(9.0 kg) * (2.0 m^3) = ? is it possible or not.

Answer 1

Hi Zara,

It looks like you're learning about multiplying and dividing numbers with units, which we often do in science classes like chemistry and physics! When we divide or multiply using units, we are usually either "combining "or "cancelling" units.

For example: 9.0 kg² / 1.0 kg. Both kg² and kg are the same base measurements (kg), and because they're the same, we can "cancel" one unit from the top and bottom of the equation. It looks like this: 9.0 kg² / 1.0 kg = 9.0 kg / 1.0 = 9.0 kg. So this is possible! Notice that we completely cancelled out all units from the denominator of this equation, so the final answer is in kg.

However, 50.0 cm² / 0.1 m is not possible as currently written. But why not? What would we have to change? (hint: are both base units the same?) When units don't match, we can often convert them.

For multiplication, we generally multiply units together, or "combine" them. So for example: (10.0 g) * (2.0 m³) = 20 g*m³. However, it isn't always this simple and there are plenty of exceptions! I'd check your class notes and make sure this is what your teacher is talking about.

Here's an easy article on multiplying and cancelling units: https://ccnmtl.columbia.edu/projects/mmt/frontiers/web/chapter_1/6251.html