Editing Multiplication (section)

==Products of measurements==
{{Main|Dimensional analysis}}
One can only meaningfully add or subtract quantities of the same type, but quantities of different types can be multiplied or divided without problems. For example, four bags with three marbles each can be thought of as:<ref name="Devlin"/>
:[4 bags] × [3 marbles per bag] = 12 marbles.

When two measurements are multiplied together, the product is of a type depending on the types of measurements. The general theory is given by [[dimensional analysis]]. This analysis is routinely applied in physics, but it also has applications in finance and other applied fields.

A common example in physics is the fact that multiplying [[speed]] by [[Time in physics|time]] gives [[distance]]. For example:
:50 kilometers per hour × 3 hours = 150 kilometers.
In this case, the hour units cancel out, leaving the product with only kilometer units.

Other examples of multiplication involving units include:
:2.5 meters × 4.5 meters = 11.25 square meters
:11 meters/seconds × 9 seconds = 99 meters
:4.5 residents per house × 20 houses = 90 residents