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# Math Basics: Using Percents

13 Mar Posted by in Math Fundamentals, Pre-Algebra | Comments Off

Overview:  What Are Percents?
A percent is a special ratio that literally means “per 100.”  Therefore 5% is 5/100 or .05, 25% is 25/100, or .25, 200 % is 200/100 or twice as much, and so on.  In grade school students learn they can think of percent as how many cents of a dollar when calculating the amount of money.

Using Proportions to Find Percents
In order to find a percent of a known number, students can use a proportion.  Suppose the question is “What is 15% of \$60.00?”   That can also be written as ” What proportion of n/60 equals 15/100?  To set up the equation in mathematical terms n/60 = 15/100.  By cross multiplying, 100n = 15X60, or 100n = 900.  To solve for n, 100n/100 = 900/100, or n=9.

Using Equations to Find Percents
When the percentage is an even number, the proportion method is easy to see.  The equation method can also be used in the above problem as 0.15 X 60 = n.  Multiplying 0.15 X 60, solving for n equals 9.  That’s using the definition of what the percent means and expressing it as a decimal.  It also makes sense if the problem asks for something like, What’s “12 1/2% of 25? “  0.125 X 25 = 3.125.

When the Percent Is Not Known
Sometimes the percentage is what is unknown.  For example, the example problem could be written as, “9 is what percentage of 60?”  That can be written as x/100 = 9/60 .  Using cross products , 60x =9 (100), or 60x = 900.  Dividing both sides of the equation by 60, X = 900/60 or 15.

How Percentages Are Used in Everyday Life
Because money is based on the decimal system, most problems involving money involve percents.  For example, giving tips at a restaurant was once 15%, and now is 20%.  If one has a meal and wants to know how much to give as a 20% tip, multiply the price of the meal by 20%.  More usually, sale prices are a certain percentage and the customer wants to know how much money is actually saved on the purchase.  (In addition, sometimes the customer wants to know if the price of an item is mentioned, how much the sale price actually saved.  If the price has been increased before the sale, sometimes the amount of the markup and the “sale price” are equal.)

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