Overview
Applications of percents are widely used in many areas, from figuring sale prices to measurement of increase or decrease. Knowing how to translate words into meaningful equations is an important part of mathematical literacy.
Definition
The definition of percentage and the percent sign % is per 100. It is a fraction or a ratio. Since money in the US and Canada is based upon the dollar, which is divided into fractions of 1/100, percentages are a useful tool. There are key words used in percent equations, such as of, which signals multiplication, is, which signals equation or the equals sign, what, the variable, and the percent sign, which signals multiplication by 0.01. There are three different types of percent problems: finding the amount when the percentage and the base are known, finding the base when the percentage and the amount are known, and finding the percentage when the amount and the base are known.
Figure 1: Percentages are part of everyday life.
Problems of Amount
These are the most straightforward percentage problems, asking what the amount is when the percentage and the base are known. Suppose the problem is, “What is 30% of 75?” Using the key words in the question, let w equal the variable for what, so that the equation is w = .30∙75. After performing the multiplication, w equals 22.50.
Figure 2: Figuring out the amount when the percentage and the base are known.
Problems of Base
These are problems when the amount and the percentage are known. Suppose the problem is, “12 is 30% of what number?” Using the key words in the question, 12 = 30%w can be converted to 12 = 0.30w or 12/.30 = w. After performing the division, w equals 40.
Problems of Percentage
These are problems when both the base and the amount are known. Suppose the problem is, “29 is what percent of 82?” Using the key words in the question, 29 = w82, or 29/82 = w, with one extra step. The fraction 29/82 equals 0.35, which is equal to 35%. For example, Office World has a shredder on sale for 69.99, and its normal price is 99.99, a savings of 30.00. The savings of 30.00 is what percentage of the normal price of 99.99? Using the key words in the question, 30/99.99 = .30 or 30%.
Figure 3: What percentage is saved from the list price?
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