MTH 232

Section 7.4Percent

Overview

• It is nearly impossible to live in today’s society and not be aware of the notion of percent.

• For students in Grades K – 2, the emphasis should be on the relationship between percents and “common” fractions (for example, 50% = ½). These relationships can be modeled relatively easily.

• In Grades 3 and 4, students begin to explore the relationship between fractions, decimals, and percents.

• Finally, in Grades 5 and 6 students learn to solve percent problems (usually by the proportion method).

A Percent Is A Ratio

• “percent”, when translated from the Latin per centum, means “per hundred”

• This application of ratio measures the relative size of a part (the percent) to a whole (100):

100%

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Modeling Percents

Percents and Decimals

• To change a percent to a decimal, drop the percent sign and move the decimal two places to the left.

• To change a decimal to a percent, move the decimal two places to the right and add a percent sign.

Percents and Fractions

• To change a percent to a fraction:1.Drop the percent sign and write the percent

over 100.2.Be prepared to simplify and/or reduce.• To change a fraction to a percent:1.First change the fraction to a decimal. Then

change the decimal to a percent, or2.Set up a proportion.

Three Basic Types of Percent Problems

1. Calculating the Percentage of a Number2. Calculating a Number of Which a Given

Number is a Given Percentage3. Calculating What Percentage One Number Is

of AnotherThese types of problems can all be solved by

either an equation (with decimals) or a proportion (with diagram)

Examples

1. Sarah and her friends go out to eat. The total bill is $55. How much money should they leave if they want to leave a 15% tip?

2. Bill took a test and scored 85%. If he got 17 questions right, how many questions were on the test?

3. Juan made 25 out of 30 free throws. Anna made 33 out of 40 free throws. Who had the higher percentage?