Density Equation FamilyDate: 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/ |
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