Writing a Percent as a Decimal P D

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1 Math 20 Arithmetic Sec 7.1: Percent, Decimals, Fractions Defn Percent means parts per 100. The sign is used to show the number of parts out of 100 parts. Examples Ex 1 Write as a percent. In a group of 100 people, 46 people are homeowners. What percent are homeowners? p = p Writing a Percent as a Decimal P D p = p 1) Drop the sign. 2) Divide by 100 (by moving the decimal twice to the left). Writing a Decimal as a Percent D P 1) Multiply by 100 (by moving the decimal two places to the right). 2) Attach a percent sign. Ex 2 Write each percent as a decimal. Write each decimal as a percent. Page 1 of 18

2 Ex 3 Fill in the blanks. a) 100% of $7.80 is. b) 100% of 24 photographs is. c) 200% of 24 photographs is. d) 300% of 8 miles is. e) 50% of 200 patients is. f) 10% of 240 feet is. g) 1% of 240 feet is. h) 2% of 240 feet is. Writing a Percent as a Fraction P F p = p p = p 1) Drop the sign. 2) Put the number over 100. Writing a Decimal as a Percent F P 1) If possible, multiply top and bottom by the same number to achieve a multiple of 10 in the denominator. This method has more steps but is actually quicker and less prone to mistakes. 2) Convert this to a decimal. 3) Move the decimal two places to the right. 4) Attach a sign. If it is not possible to rewrite the bottom as a multiple of 10, do the following: 1) Divide (the denominator into the numerator) to convert to a decimal. 2) Move the decimal two places to the right. 3) Attach a sign. Ex 4 Write each percent as a fraction or mixed fraction in lowest terms. Write each fraction as a percent. PP PP Page 2 of 18

3 Ex 4 (con t) as a percent. Write each percent as a fraction or mixed fraction in lowest terms. Write each fraction PP PP Page 3 of 18

4 Ex 5 Write: a) b) PP c) d) e) f) PP g) h) i) j) Page 4 of 18

5 k) l) Ex 6 Write the answer as a fraction in lowest terms, as a decimal, and as a percent. A zoo has 125 types of animals, including 25 that are endangered. What portion is not endangered? Ex 7 Convert 11/9 to a percent. Provide the exact answer. Next, round to the answer to the nearest tenth of a percent. This means round to the nearest. Sec 7.2: Solving Basic Percent Problems Ex 8 Translate into an equation to solve each percent problem. a) What number is 42.2% of 125? OF IS MULTIPLY EQUALS b) 25% of what number is 40? c) 9 is what percent of 50? Page 5 of 18

6 d) What number is 10% of 70? 200% of 70? 50% of 70? 1% of 70? 7% of 70? Sec 7.3: General Applications of Percent Percent Proportion Part is to whole as percent is to 100. That is, part = percent whole 100 Note: The percent is the ratio of a part to a whole, where the denominator is 100. Warning: When solving for percent, do NOT move the decimal. For example, if p=125, the answer is 125% not 1.25% OF IS WHOLE PART Ex 9 Translate the words into an equation to solve OR use a percent proportion to solve. a) PP 7% of 2700 miles b) 39% of 1220 meters c) 55% of 10,000 injections d) PP 135% of 60 dosages e) 0.5% of $238 Ex 10 Solve each problem using the method of your choice (translate or percent proportion). Include the set up for each. a) One day on Jacob s mail route, there were 2920 pieces of mail. If 45% were advertising pieces, find the number of advertising pieces. Set Up/Equation Page 6 of 18

7 b) 150 Super Lotto tickets is 25% of what number of tickets? c) PP miles is 37.5% of what number of miles? d) A freeze resulted in a loss of 52% of an avocado crop. If the loss was 182 tons, find the total number of tons in the crop. e) $21 is what percent of $105? Page 7 of 18

8 f) What percent of 320 Internet companies is 48 Internet companies? g) The service department set a goal of 360 service calls this week. If they made 504 service calls, find the percent of their goal that they completed. Ex 11 Translate the words then solve. Include the set up for each. a) PP 15% of 880 policyholders b) 0.5% of 1200 test tubes c) PP 67.5 containers is 27% of what number of containers? Page 8 of 18

9 d) 1 of what number of policies is 66 policies? e) PP What percent of 35 monitors is 7 monitors? f) 9 world-class runners is what percent of 1125 runners? part amount of sales tax Sales Tax Formula = percent tax rate as a decimal Finding Percent Increase Amount of Increase part Original Value whole whole cost of item = Percent part amount of discount Discount Formula = percent rate/percent of discount Finding Percent Decrease Amount of Decrease part Original Value whole = Percent whole orginal price Page 9 of 18

10 Ex 12 Find the commission earned or rate of commission. Round money answers to the nearest cent if necessary. Sales Rate of Commission Commission $660 10% $7800 $1170 $ % Ex 13 PP Find the amount or rate of discount and the sale price after the discount. Round money answers to the nearest cent if necessary. Original Price Rate of Discount Amount of Discount Sale Price $ % $38 $9.50 $ % Page 10 of 18

11 Ex 14 A personal computer and monitor priced at $698 are marked down 8%. If the sales tax is also 8%, find the cost of the computer and monitor including sales tax. Before we begin, would you expect the answer to be less than, greater than, or equal to $698? Ex 15 Attendance at the homecoming game decreased from 6820 fans last year to 5797 fans this year. Find the percent decrease. (Do not round.) Ex 16 Our mail carrier, Norm, saw his route expand from 850 residential stops to 918 residential stops. Find the percent increase. (Do not round.) Page 11 of 18

12 Ex 17 (#25) The force of gravity on Mars is only 38% of the force of gravity on earth. If you weigh 150 pounds on earth, how much will you weigh on Mars? 57 lb Ex 18 (#37) Each year, Americans throw out an average of about 1,600 pounds of waste per person. Aracata, CA resident Michael Winkler only uses one trash bag every year totaling at most 40 pounds. Find the percent of average annual waste per person Mr. Winkler throws out to a tenth of a percent. 2.5% Sec 7.5: Interest Defn Interest is a fee paid or a charge made for lending or borrowing money. The amount of money borrowed is the principal. The charge for interest is often given as a percent, called the interest rate or rate of interest. I = Prt Simple Interest Formula interest = principal rate time Ex 19 Find the interest. a) $1000 at 5% for 1 year b) PP $820 at 6% for 1 years Page 12 of 18

13 c) $16,800 at 3% for years d) $28,000 at 1 for 3 months Balance Formula Using Simple Interest = = = = = Ex 20 Find the balance on each account. 1 a) $3800 at for 6 months b) $2400 at 11% for years c) $2400 at 1 for 7 months Ex 21 (#47) The balance on a 4-year loan is $5,720. If the principal borrowed was $4,400, what was the simple interest rate (as a percent)? 7.5% Page 13 of 18

14 Compound Interest (Not In Textbook nor EBook) Defn Compound interest is interest paid on principal and past interest. (This is commonly used in savings accounts and most investments.) Ex 22 Suppose you make a deposit of $1000 into your savings that earns 5% per year. How much would you have at the end of 3 years if interest is compounded annually? Compare this to what you would ve earned if interest accrued only on the principal. (Do not use table but a calculator is ok.) Page 14 of 18

15 Ex 23 Find the compound amount given the following deposits. Round to the nearest cent if necessary. (Do not use the table but a calculator is ok.) a) $500 at 4% for 2 years b) $2000 at 7% for 3 years Ex 24 Find the compound amount using the compound interest table. Round to the nearest cent. 1 a) $1 at 3% for 6 years b) $1 at 6% for 8 years c) $1 at for 12 years Page 15 of 18

16 Ex 25 Find the compound amount and the interest using the compound interest table. 1 a) PP $4000 at 3% for 10 years b) $12,600 at for 8 years c) PP $32,700 at 6% for 12 years Ex 26 (As time permits) The River City School PTA Emergency fund deposited at compounded annually. Two years after the first deposit, they deposit another, also at compounded annually. Use the compound interest table to answer the following. a) What total amount will they have in 4 years after their first deposit? Round to the nearest cent. $10, Page 16 of 18

17 b) What amount of interest will they have earned? Review: Sec 5.8: The Pythagorean Theorem List perfect squares. Know these perfect squares for test. Right Triangle A triangle with a degree angle is called a right triangle. Pythagorean Theorem In any right triangle, if c is the length of the hypotenuse and a and b are the lengths of the two legs, then a b = c. b c a Ex 27 Find the unknown length of each triangle. 9 cm 9 cm 12 cm 16 cm Page 17 of 18

18 Ex 28 William drove his car 15 miles north, then made a right turn and drove 7 miles east. How far is he from his starting point? Draw a sketch to illustrate the problem and solve it. Ex 29 (#28) The base of a 30-foot long guy wire is located 9 feet from the base of the telephone pole that is anchoring it. How high up the pole does the guy wire reach? Provide the exact answer. Next, round your answer to the nearest hundredth. Your solution should include a well-labeled sketch. Page 18 of 18