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6: Percents

• • Contributed by OpenStax
• Mathematics at OpenStax CNX

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When you deposit money in a savings account at a bank, it earns additional money. Figuring out how your money will grow involves understanding and applying concepts of percents. In this chapter, we will find out what percents are and how we can use them to solve problems.

• 6.1: Understand Percent
A percent is a ratio whose denominator is 100. Since percents are ratios, they can easily be expressed as fractions. Remember that percent means per 100, so the denominator of the fraction is 100. To convert a percent to a decimal, we first convert it to a fraction and then change the fraction to a decimal. To convert a decimal to a percent, remember that percent means per hundred. If we change the decimal to a fraction whose denominator is 100, it is easy to change that fraction to a percent.
• 6.2: Solve General Applications of Percent
We will solve percent equations by using the methods we used to solve equations with fractions or decimals. Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.
• 6.3: Solve Sales Tax, Commission, and Discount Applications
Sales tax and commissions are applications of percent in our everyday lives. To solve these applications, we follow the same strategy we used in the section on decimal operations. The sales tax is a percent of the purchase price which is calculated as the product of the tax rate and the purchase price. A commission is a percentage of total sales as determined by the rate of commission. A discount is a percent off the original price while a mark-up is the amount added to the wholesale price.
• 6.4: Solve Simple Interest Applications
To use the simple interest formula, I = Prt, we substitute in the values for variables that are given, and then solve for the unknown variable. Applications with simple interest usually involve either investing money or borrowing money. To solve these applications, we continue to use the same strategy for applications that we have used earlier in this chapter. The only difference is that in place of translating to get an equation, we can use the simple interest formula.
• 6.5: Solve Proportions and their Applications (Part 1)
A proportion states that two ratios or rates are equal. The proportion is read “a is to b, as c is to d”. If we compare quantities with units, we have to be sure we are comparing them in the right order. For any proportion of the form a/b = c/d, where b ≠ 0, d ≠ 0, its cross products are equal. So, cross products can be used to test whether a proportion is true. To find the cross products, we multiply each denominator with the opposite numerator (diagonally across the equal sign).
• 6.5: Solve Proportions and their Applications (Part 2)
Percent equations can also be solved by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A percent proportion is an equation where a percent is equal to an equivalent ratio. The amount is to the base as the percent is to 100 in the equivalent ratio. Sometimes, restating the problem in the words of a proportion will make it easier to set up the proportion.
• 6.E: Percents (Exercises)
• 6.S: Percents (Summary)

Figure 6.1 - Banks provide money for savings and charge money for loans. The interest on savings and loans is usually given as a percent. (credit: Mike Mozart, Flickr)