Pre-algebra variable expressionsDate: 09/01/99 at 20:04:16 From: Vanessa Subject: Pre-algebra variable expressions Can you please send me step-by-step instructions on how to do variable expressions problems? Date: 09/10/99 at 22:28:40 From: Doctor Maureen Subject: Re: Pre-algebra variable expressions Dear Vanessa, Thanks for your question. Let me start with the "expressions" part of your question. I am going to explain mathematical expression by comparing it to something you probably understand from studying English or grammar in school. When we write, we use sentences to write a complete thought, and in a sentence there must be a noun and verb, and often there are extras like describing words. In mathematics, we also frequently write in sentences, but we use numbers and symbols to convey a thought. A complete mathematical sentence includes an equals sign or an inequality sign (< or >) and at least one number on either side. For instance: 5 + 3 = 8 is a mathematical sentence, called an equation; 9 < 100 is an inequality. When you study English, you may have talked about phrases, which are groups of words, but are not always complete sentences, like "just do it" or "good sport." In mathematics, we have phrases called expressions, which can be just one number or several numbers and some symbols; however, there is no equals sign or inequality sign. For example, 8 is an expression, and so is 5+3 or 4/3. Some expressions include letters, called variables, which are symbols that represent numbers. These kinds of expressions are used every day in all kinds of situations. Here is an example: let's say that you have a car and it can travel 15 miles for every gallon of gas in the tank. Then you could represent the total miles you can drive based on how much gas you put into the tank using the expression 15g, where g stands for the numbers of gallons you put in the tank. Once you put gas into your tank, you can figure out how far you will be able to go by replacing g with the number of gallons you purchased and pumped into your tank. Another example involving cars is determining your travel time using a variable for distance. If you are driving down a highway at a steady rate of 50 miles per hour, then you can determine how long it will take you to get to your destination by representing the time as an expression m/50 where m represents the number of miles you have to drive to reach your destination. If your destination is 250 miles away, then by replacing m with 250 miles, you can calculate that the travel time will be 250/50, or 5 hours. If your trip is 525 miles, it will take 10 1/4 hours. How long will it take if the trip is 775 miles? One more example: Let's say you baby-sit and you charge $4 per hour. Then you could express your total earnings in a week as 4h where h is the number of hours you baby-sit. Maybe you work for a health club and you are paid $25 per week to be available when the club needs you and then $4 per hour to actually baby-sit children while club members work out. We could express your weekly pay as 25 + 4h, where again h = hours worked. Now for solving problems using variable expressions. You can only solve problems involving variable expressions if you are given a value for the variable. For instance, in the travel time example above, you cannot actually determine a travel time until you are given a value for distance. If you are told that the distance is 250 miles, then you substitute 250 for the variable, m, and solve the expression: 250/50 = 5 hours. In the babysitting examples, you can only determine a weekly pay total if you know how many hours you worked. I suggest to my students that they first substitute, then compute the arithmetic, then check their work. For instance, if you worked 4 hours for the health club, then you would substitute 4 for h in the expression 25 + 4h. It would look like this: 25 + (4)(4) = 41. Solving variable expressions is like using a formula. The expression is like a formula and the value you are given is to be substituted into the formula. I hope this explanation helps. Write back if you need more explanation. Maybe you could give an example of a problem with which you are having difficulty. - Doctor Maureen, The Math Forum http://mathforum.org/dr.math/ |
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