Page 178 - Science Coursebook

Reference

Working with equations
In science, we often use equations to show how two or more quantities are related
to each other. You need to be able to use equations. Sometimes you will have to
rearrange an equation before you can calculate the quantity you are interested in.

Here is an equation from Unit 9:
mass
density =
volume
This equation tells us how we can calculate the density of a substance. We need
to know two quantities:
• the mass of a sample of the substance
• the volume of the sample.
Then we calculate the density of the substance by dividing mass by volume.

Remembering an equation
You may be able to memorise an equation simply by repeating it to yourself.
It may be easier if you change the names of the quantities into letters or other
symbols, like this:
mass
density =
volume
M
D =
V
Another way is to think about the meaning of the quantity. Density tells us how
to compare two materials – which is heavier? To make it a fair test, we have to
compare equal volumes. So we compare the masses of 1 cm or 1 m .
3
3
An alternative is to think about units. The unit of density is g/cm , or kg/m .
3
3
This should remind you to divide the mass (in g or kg) by the volume (in cm
3
or m ).
3
Rearranging an equation
The equation for density has density as its subject (the quantity on its own, on the
left). But sometimes, we might want to calculate one of the other quantities. For
example:
3
3
What is the mass of 4 cm of mercury? The density of mercury = 13.5 g/cm .
We need to rearrange the equation to make mass M its subject. To do this,
multiply both sides by volume V:

D × V = M

So
M = D × V = 13.5 × 4 = 54 g

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