Associated Topics || Dr. Math Home || Search Dr. Math

### Density Equation Family

```
Date: 03/27/2002 at 20:07:04
From: Mary
Subject: Mass = ?

I know that density = mass/volume, but I need to know how to solve for
mass using volume and density.
```

```
Date: 03/28/2002 at 09:12:15
From: Doctor Rick
Subject: Re: Mass = ?

Hi, Mary.

This sort of formula occurs a lot. You have probably seen the Rate
Equation:

Rate = Distance / Time

The Rate Equation has two other equivalent forms:

Distance = Rate * Time

Time = Distance / Rate

One way to think of this is just like "fact families" (if you learned
multiplication and division this way). Every multiplication or
division problem is part of a "family" that uses the same numbers, for
instance:

2 * 5 = 10
5 * 2 = 10
10 / 2 = 5
10 / 5 = 2

The three forms of the Rate Equation are just three members of the
same fact family, except that we have names instead of particular
numbers. (We leave out one because Distance = Time * Rate isn't any
better than Distance = Rate * Time.)

The other way to think about it is the "algebraic" way. If two
quantities are the same, and you multiply them by the same amount,
then the new quantities are also the same. If Rate is equal to
Distance divided by Time, then when I multiply both by Time, they are
still the same:

Distance * Time = Rate / Time * Time

But this can be rearranged:

Distance * Time = Rate * (Time / Time)

Whatever Time is, Time divided by Time will always be 1, and 1 times
Rate will always be Rate. Thus our new formula is

Distance * Time = Rate

That's another member of the "Rate Equation Family."

Now, I hope you see that your formula, Density = Mass / Volume, is
just the same as the Rate Equation, Rate = Distance / Time, except
that the names have been changed. Can you see how to write two other
members of the Density Equation Family?

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search