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Unit 5

Unit 5. PERCENTS. PERCENTS. Indicates number of hundredths in a whole Decimal fraction can be expressed as a percent by moving decimal point two places to right and inserting percent symbol Express 0.375 as a percent: Move decimal point two places to right Insert percent symbol

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Unit 5

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  1. Unit 5 PERCENTS

  2. PERCENTS • Indicates number of hundredths in a whole • Decimal fraction can be expressed as a percent by moving decimal point two places to right and inserting percent symbol • Express 0.375 as a percent: • Move decimal point two places to right • Insert percent symbol 0.375 = 37.5%Ans

  3. FRACTIONS TO PERCENTS • To express a common fraction as a percent: • Divide the numerator by the denominator to get the decimal fraction • Convert the answer to a percent by moving the decimal point two places to the right

  4. FRACTIONS TO PERCENTS EXAMPLE • Express each of the following as percents = 625% Ans

  5. PERCENTS TO FRACTIONS • Decimal Fractions: • To express percent as decimal fraction: • Drop percent symbol • Move decimal point two places to left • Express 25.4% as a decimal 25.4% = .254Ans

  6. PERCENTS TO FRACTIONS • Common Fractions: • To express percents as common fractions: • First convert percent to decimal fraction • Express 64.5% as a common fraction

  7. PERCENT TERMS DEFINED • All simple percent problems have three parts: • Rate is percent (%) • Base represents whole or a quantity equal to 100% • Word “of” generally relates to the base • Part (Percentage in Book) is part or quantity of percent of base • Word “is” generally relates to the percentage

  8. PERCENT TERMS DEFINED • Identify base, rate, and percentage What percent of 64 is 8? • Problem is asking for rate (percent) • 64 represents whole and is identified by word “of,” so it is the base • 8 represents part and is identified by word “is,” so it is the percentage

  9. FINDING THE PERCENTAGE • Proportion formula for all three types of percentage problems: Where • B is the base or the starting/original value • P is the percentage or part of the base • R is the rate or percent

  10. FINDING THE PERCENTAGE • Find 7.5% of 120? • Rate: 7.5% • Base: 120 • Problem is asking for percentage (part) • Multiply 120 x 75 • Divide the answer by 100 Calculate using cross-products and division. P = 9 Ans

  11. FINDING THE RATE • What percent of 76 is 49.4? • Rate: Find the rate • Base: 76 • Percentage (part): 49.4 • Multiply 49.4 x 100 • Divide the answer by 76 Calculate using cross-products and division. R = 65% Ans

  12. FINDING THE BASE • 17.5 is 12.5% of what amount? • Percentage: 17.5 • Rate: 12.5% (.125 as a decimal) • Problem is asking for base Calculate using cross-products and division. B = 140Ans

  13. Application Problem Examples • A tank has a capacity of 300 gallons. It is 35% full. How many gallons are in the tank? • Part ->?? Base-> 300 Rate-> 35% • 105 gallons

  14. Application Problem Examples • A tank has a capacity of 300 gallons. It is 35% full. How many are needed to fill it? • We found it had a 105 gallons in it in the last part. So one way is to figure that and subtract from 300….195 gallons to fill • Another way is to see that percentages always add up to 100% so the tank is 35% full or 65% empty…so change the rate.

  15. PRACTICE PROBLEMS 1. Express each of the following as a percent. 2. Express each of the following as a decimal fraction. a. 1.46% b. 100% c. 0.05% 3. Express each of the following as a common fraction or mixed number. a. 14.4% b. 2.5% c. 138%

  16. PRACTICE PROBLEMS (Cont) 4. Round to two decimal places whenever necessary: • What is 12% of 150? • What percent of 234 is 86? • 14.5 is 45% of what number? • What is 8 ¾% of 640? • What percent of 50 is 75?

  17. PRACTICE PROBLEMS (Cont) 4. Round to two decimal places whenever necessary: • What is 125% of 75? • 200 is 37 ½% of what number? • What percent of 1375 is 350? • 135 is 150% of what number?

  18. Applications • A carpenter has 1350 nails. He uses 23% on a job and then uses 34% of the remaining nails at his second job. How many nails are left? • A mixture requires 20% of compound A, 30% of compound B, and 50% of compound C. If there is 250 pounds of compound B, how much should there be of compound A?

  19. Percents 130% 40% 62.5% Decimals .0146 1 .0005 Fractions A B C Problems 18 36.75% 32.22 56 150% 93.75 533.33 25.45% 90 686 nails 166.67 pounds Solutions

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