Simplifying Expressions with FractionsDate: 9/2/96 at 16:39:19 From: Anonymous Subject: Simplifying Expressions I have tried to do my homework and I don't understand how to work it out. It works with a calculator but I want to do it for myself on paper. One of the problems is: 9(-1/7)(1/3)(-28) I am supposed to simplify it. Please help!!! Thank you, Veronica Date: 9/3/96 at 15:22:42 From: Doctor Mike Subject: Re: Simplifying Expressions Hello Veronica, This is a great problem. It brings up several important points but it is not computationally difficult. Here we go. First of all, since exactly two of the four numbers multiplied together are negative, the result is positive. So, you can safely drop the minus signs as a simplification, getting 9(1/7)(1/3)(28). Second, remember that 9 is the same as (9/1). My next move may not seem like a simplification, and it's really not, but it will help anyway. Change the expression to (9/1)(1/7)(1/3)(28/1). Third, remember the rule for multiplying fractions: (a/b) times (x/y) is (ax)/(by). That is, multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. In your case, it results in a simplification to (9*28)/(7*3). Fourth, you COULD start cancelling. You know, 7 goes into 28 four times and 3 goes into 9 three times, and 4 times 3 is 12. But since I have you as a captive audience for a few minutes, I want to show you WHY cancellation works. You will need to remember just two simple things: (a) multiplication is the same in any order, and (b) the rule for multiplying fractions works also for UN-multiplying them : 9 * 28 28 * 9 28 9 -------- = -------- = ---- * --- = 4 * 3 = 12 7 * 3 7 * 3 7 3 I'm not saying you should not cancel. Far from it. But you should always remember what is really happening when you take the quick cancellation shortcut. Then you will never forget the important rules of when and where cancellation is permitted, and when and where it is not. I hope this helps. Write back if you have more questions. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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