Simplifying Using the Distributive Property
Date: 09/07/99 at 17:57:42 From: Christina Subject: Math - Distributive Property How do you actually work out this kind of problem? Directions: Simplify each expression. 12(c+3d+4e)+2(2c+d+6e) This is really confusing, when I have those big math problems. This one is kind of hard too: 9ab+8ab-7ab Thank you very much.
Date: 09/12/1999 at 21:12:21 From: Doctor Jody Subject: Re: Math - Distributive Property Hi Christina, I can see how it can be confusing. There's a lot to do. Let's try to break it down into simpler tasks - then it might seem less confusing. The first thing I would do is put some space between the different parts of the expression: 12(c + 3d + 4e) + 2(2c + d + 6e) It seems less cluttered to me when I write it like this, and that helps unclutter my thinking. It looks as if we have some multiplying and some adding to do. You have to do multiplication in two parts of the problem, and then add those results together. Let's look at just one part of the problem where you have to do multiplication: 12(c + 3d + 4e) We can't add the items in the parentheses to each other. Do you know why? Here, the only thing I can think of to do is multiply the 12 by each of the items inside the parentheses (applying the distributive property over addition.) After multiplying 12 by each of the items in the parentheses, we get: 12c + 36d + 48e We can't add these items together, either. So it's as simple as it can get. Now it's time to look at the other part of the problem: 2(2c + d + 6e) It looks as if we need to do the same thing to it, for the same reasons, so: 4c + 2d + 12e Do you see how I did that? Looking back at the original problem, it shows that these two parts of the problem need to be added together. Let's put them side by side again, with an addition sign between them, to make it clear: 12c + 36d + 48e + 4c + 2d + 12e Because they are all plus signs, it doesn't matter if there are parentheses, and we can add them in any order we like, as long as it makes sense. In this case, the thing to do is add the terms that share the same variable, also called "like terms." So, 12c + 4c = 16c 36d + 2d = 38d 48e + 12e = 60e Giving us: 16c + 38d + 60e Can you simplify this expression any more? Try the second problem that you wrote above, doing it the same way as I did the last part for the first problem. You will probably see what to do. Here's a nice explanation of the distributive property from the Dr. Math archives, if you need more help with it: What is the Distributive Property? http://mathforum.org/dr.math/problems/distribute.html Write back if you have any more questions, and please try to explain exactly where your problem is. I can help you much more that way. - Doctor Jody, The Math Forum http://mathforum.org/dr.math/
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