# Unit 5 PERCENTS PERCENTS Indicates number of hundredths

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Unit 5 PERCENTS

PERCENTS Indicates number of hundredths in a whole p Decimal fraction can be expressed as a percent by moving decimal point two places to right and inserting percent symbol p Express 0. 375 as a percent: p n n Move decimal point two places to right Insert percent symbol 0. 375 = 37. 5% Ans 2

FRACTIONS TO PERCENTS p To express a common fraction as a percent: n n 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 3

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

PERCENTS TO FRACTIONS p Decimal Fractions: p To express percent as decimal fraction: n n p Drop percent symbol Move decimal point two places to left Express 25. 4% as a decimal 25. 4% =. 254 Ans 5

PERCENTS TO FRACTIONS Common Fractions: p To express percents as common fractions: p n p First convert percent to decimal fraction Express 64. 5% as a common fraction 6

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

PERCENT TERMS DEFINED p Identify base, rate, and percentage What percent of 64 is 8? n n n 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 8

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

FINDING THE PERCENTAGE p Find 7. 5% of 120? n n n Rate: 7. 5% Base: 120 Problem is asking for percentage (part) Multiply 120 x 75 Divide the answer by 100 Calculate using crossproducts and division. P = 9 Ans 10

FINDING THE RATE p What percent of 76 is 49. 4? n n n Rate: Find the rate Base: 76 Percentage (part): 49. 4 Multiply 49. 4 x 100 Divide the answer by 76 Calculate using crossproducts and division. R = 65% Ans 11

FINDING THE BASE p 17. 5 is 12. 5% of what amount? n n n Percentage: 17. 5 Rate: 12. 5% (. 125 as a decimal) Problem is asking for base Calculate using crossproducts and division. B = 140 Ans 12

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

Application Problem Examples p A tank has a capacity of 300 gallons. It is 35% full. How many are needed to fill it? n 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 n 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. 14

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% 15

PRACTICE PROBLEMS (Cont) 4. Round to two decimal places whenever necessary: n n n 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? 16

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

Applications 5. 6. 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? 18

Solutions 1. Percents a. b. c. 2. b. c. . 0146 1. 0005 d. e. f. Fractions a. A b. B c. C Problems a. Decimals a. 3. 130% 40% 62. 5% 4. g. h. i. 5. 6. 18 36. 75% 32. 22 56 150% 93. 75 533. 33 25. 45% 90 686 nails 166. 67 pounds 19