Consider the density of an object, which is a function of mass and volume. Being a function of mass and volume means that the density depends on mass and volume. Specifically the density is found by dividing the mass by the volume. If the letter d stands for density, the letter m stands for mass, and the letter V stands for volume, then the functional relationship could be written d = m/V. The mass, m, and the volume, V, are said to be variables of density. They can change, but knowing their values allows calculation of density, d.
If m = 2 and V = 4, then d = m/V = 2/4 = 0.5
When doing physical calculations it is important to express the units being used. Throughout this section units will be used, even though they are not discussed in any detail. One common unit of mass is the kilogram which is abbreviated kg. A common unit for volume is the liter, abbreviated L. One common unit for density, therefore, is kg/L. The above calculation is more appropriately given as
If m = 2 kg and V = 4 L, then d = m/V = 2 kg/4L = 0.5 kg/L
The idea of using a symbol for a variable should already be familiar. The words we use to communicate with each other are just symbols (cow is a symbol for a four legged animal that produces milk). It should also be clear that the context of the symbol is important and that the same symbol could mean two different things (turn right, you are right). An example of that in science is that g could mean grams (a unit of mass) or it could mean the acceleration due to gravity (a number, usually about 9.8 meters per second squared or 9.8 m/s2). The context will tell. If an object has a mass of 2.4 g, you would assume it means 2.4 grams. If, on the other hand, the symbol g is found in a mathematical equation, like PE = mgh (potential energy equals mass times g times height), you would assume it to be the constant 9.8 m/s2.
So far this example has only dealt with arithmetic and calculating density given mass and volume. Sometimes density and volume might be known and it is necessary to calculate mass. This is possible by rearranging the formula d = m/V as m = d*V. There are several ways to explain how this rearrangement is done, but it is expected that one of them is already familiar to the reader. The relationship to find volume would be V = m/d.
Here is a review sheet that I have prepared. It may also help with the Practice and Homework for this section.