Unit 5 PERCENTS

2  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 as a percent: Move decimal point two places to right Insert percent symbol = 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% =.254 Ans

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 P = 9 Ans Calculate using cross- products and division.

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 R = 65% Ans Calculate using cross- products and division.

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 B = 140 Ans Calculate using cross- products and division.

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 5. 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? 6. 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 Solutions 1. Percents a. 130% b. 40% c. 62.5% 2. Decimals a b. 1 c Fractions a. A b. B c. C 4. Problems a. 18 b % c d. 56 e. 150% f g h % i nails pounds