FLC Ch 7 Math 20 Arithmetic Sec 7.1: Percent,...

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Math 20 Arithmetic Sec 7.1: Percent, Decimals, Fractions

Examples

Ex 1 Write as a percent. In a group of 100 people, 46 people are homeowners. What percent are homeowners? Ex 2 Write each percent as a decimal. Write each decimal as a percent.

Defn Percent means parts per 100. The sign is used to show the number of parts out of 100 parts.

𝑝 =𝑝

𝑝 = 𝑝 ÷

Writing a Percent as a Decimal 𝑃 → 𝐷

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.

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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 _____________________. Ex 4 Write each percent as a fraction or mixed fraction in lowest terms. Write each fraction as a percent. PP PP

𝑝 =𝑝

𝑝 = 𝑝 ÷

Writing a Percent as a Fraction 𝑃 → 𝐹

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.

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Ex 4 (con’t) Write each percent as a fraction or mixed fraction in lowest terms. Write each fraction as a percent.

PP

PP

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Ex 5 Write: a) b) PP c)

d) e) f) PP

g) h)

i) j)

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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? b) 25% of what number is 40? c) 9 is what percent of 50?

OF MULTIPLY

IS EQUALS

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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 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

Percent Proportion

Part is to whole as percent is to 100. That is, 𝑝𝑎𝑟𝑡

𝑤ℎ𝑜𝑙𝑒=

𝑝𝑒𝑟𝑐𝑒𝑛𝑡

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 WHOLE

IS PART

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b) 150 Super Lotto tickets is 25% of what number of tickets? c) PP 292.5 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?

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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?

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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

= 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑎𝑠 𝑎 𝑑𝑒𝑐𝑖𝑚𝑎𝑙

∙ 𝑤ℎ𝑜𝑙𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑖𝑡𝑒𝑚

Sales Tax Formula

𝑝𝑎𝑟𝑡 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡

= 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑟𝑎𝑡𝑒/𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡

∙ 𝑤ℎ𝑜𝑙𝑒 𝑜𝑟𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑖𝑐𝑒

Discount Formula

𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐼𝑛𝑐𝑟𝑒𝑎𝑠𝑒 𝑝𝑎𝑟𝑡

𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 𝑤ℎ𝑜𝑙𝑒 =𝑃𝑒𝑟𝑐𝑒𝑛𝑡

Finding Percent Increase

𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐷𝑒𝑐𝑟𝑒𝑎𝑠𝑒 𝑝𝑎𝑟𝑡

𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 𝑤ℎ𝑜𝑙𝑒 =𝑃𝑒𝑟𝑐𝑒𝑛𝑡

Finding Percent Decrease

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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

$4417.70 7%

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

$29.95 15%

$38 $9.50

$99.80 30%

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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.)

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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

Ex 19 Find the interest.

a) $1000 at 5% for 1 year b) PP $820 at 6% for 1

years

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.

Simple Interest Formula 𝐼 = 𝑃𝑟𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑟𝑎𝑡𝑒 𝑡𝑖𝑚𝑒

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c) $16,800 at 3% for

years d) $28,000 at

1

for 3 months

Ex 20 Find the balance on each account.

a) $3800 at 1

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%

=

= = = =

Balance Formula Using Simple Interest

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Compound Interest (Not In Textbook nor EBook)

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.)

Defn Compound interest is interest paid on principal and past interest. (This is commonly used in savings accounts and most investments.)

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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.

a) $1 at 3% for 6 years b) $1 at 6% for 8 years c) $1 at 1

for 12 years

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Ex 25 Find the compound amount and the interest using the compound interest table.

a) PP $4000 at 3% for 10 years b) $12,600 at 1

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. $10,667.91

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b) What amount of interest will they have earned?

Sec 5.8: The Pythagorean Theorem Review: List perfect squares. Know these perfect squares for test.

Right Triangle A triangle with a ______ degree angle is called a right triangle.

Ex 27 Find the unknown length of each 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 .

𝑎

𝑏 𝑐

16 cm

9 cm

12 cm

9 cm

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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.

FLC Ch 7 Math 20 Arithmetic Sec 7.1: Percent,...

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