Unit 17 Percent and Percentage

Basic Principles of Percent and Percentage Percent means number of parts per one hundred. Twenty percent, written as 20%, means 20 parts out of 100 parts or 20/100. To solve some mathematical problems, you may need to convert a percent to a common fraction or decimal fraction.

Converting Percent and Decimal Fractions To express a percent as a decimal fraction, divide by 100 or move the decimal point two places to the left and drop the percent sign. Change a decimal fraction to a percent by multiplying by 100 or by moving the decimal point two places to the right and adding a percent sign.

Converting a Percent to a Common Fraction To change a percent to a common fraction: –Change the percent to a decimal fraction. –Put the decimal fraction over the appropriate multiple of 10 represented by the decimal fraction. –Reduce the common fraction to lowest terms. Another method of converting a percent to a common fraction is to replace the percent symbol with 100 as the denominator of the fraction and then reduce the fraction to lowest terms.

Converting a Common Fraction to a Percent To convert a common fraction to a percent, change the common fraction to a decimal fraction by dividing the numerator by the denominator. If a mixed number is involved, change the mixed number to an improper fraction first.

Percentage Percentage is the term used to describe the part of the whole number. –Do not confuse percentage with percent, which has the symbol % attached to it. –A formula frequently used is: Percentage (part) = Percent (rate) x Base (whole) –The percent (rate) is written as a decimal. –The base is the whole from which a part will be described as a percentage.

Calculating Percent or Rate When a problem asks for a rate, it is asking for a percent. –To find the rate, divide the percentage by the base. –Convert the quotient to a percent by multiplying by 100 or moving the decimal point two places to the right and adding the % symbol:

Calculating the Whole or Base To find the base (whole) when the percent (rate) and percentage (part) are known, first change the percent to a decimal fraction. Then divide the percentage by the percent. Use the formula:

Percents and Percentages Example: What is 150% of 638? Percentage = 150% x 638 Percentage = 1.5 x % x 638 = 957

Practical Problem Tyrone Daniel’s doctor has suggested he lose 86 pounds. In 3 months, he has lost 22% of his goal. How many more pounds must he lose to reach his goal?

Practical Problem Set up the problem and solve: Percentage = percent x base Percentage = 22% x 86 = 0.22 x 86 = – = Tyrone must still lose or 67 lbs.