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Unit 17 Percent and Percentage
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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.
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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.
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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.
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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.
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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.
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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:
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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:
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Percents and Percentages Example: What is 150% of 638? Percentage = 150% x 638 Percentage = 1.5 x 638 150% x 638 = 957
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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?
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Practical Problem Set up the problem and solve: Percentage = percent x base Percentage = 22% x 86 = 0.22 x 86 =18.92 86 – 18.92 = 67.08 Tyrone must still lose 67.08 or 67 lbs.
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