What is Algebra?
Date: 07/20/2001 at 13:43:47 From: Jason Subject: Algebra What is algebra?
Date: 07/20/2001 at 15:45:08 From: Doctor Ian Subject: Re: Algebra Hi Jason, Algebra is like arithmetic, but some of the numbers have names instead of values. For example, if I ask you something like 3 + 4 * 5 - 6 / 3 = ? you can just apply the operations in the correct order to get 3 + 4 * 5 - 6 / 3 = ? 3 + 20 - 6 / 3 = ? 3 + 20 - 2 = ? 23 - 2 = ? 21 = ? Now, suppose that instead, I ask you something like (x + 3) * (x + 4) = 42 Now you can't really apply the operations, because you don't know the values of the numbers. What's x + 3? It depends on what the value of x is, doesn't it? In this case, you might start guessing possible values for x that would make the equation true: x = 1? (1 + 3) * (1 + 4) = 4 * 5 = 20 (No.) x = 2? (2 + 3) * (2 + 4) = 5 * 6 = 30 (No.) x = 3? (3 + 3) * (3 + 4) = 6 * 7 = 42 (Yes!) However, suppose the problem changes to (x + 3) * (x + 4) = 35.75 Now it becomes a lot harder to guess an answer. What 'algebra' gives you is a set of tools for figuring out the answers to problems like this, without having to guess. This becomes more and more important as you start using more complicated equations, involving more than one variable. So why should anyone care about this stuff? Take a look at the Dr. Math archives: What Are Variables For? http://mathforum.org/dr.math/problems/cindy.02.09.01.html to see what makes variables so useful. Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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