Guided Notes Chapter 5 Multiply Or Move the decimal two

Name _________________________________

Guided Notes Chapter 5 Chapter 5 Section 1 – Percents, Fractions, Decimals Percent (%): a __________ that compares a number to _______ Decimals to Percents: 1) Write each decimal as a percent a) 0.759

b) 0.003

Multiply by 100 Or Move the decimal two places to the right

c) 5.187

Percents to Decimals: 2) Write each percent as a decimal

Divide by 100

a) 47.5 %

Or b) 0.06 %

Move the decimal two places to the left

c) 2500 % Fractions to Percents: 3) Write each fraction as a percent a)

b)

c)

17 20

3 9

Rewrite with a denominator of 100 Or Convert to a decimal and multiply by 100

21 40

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Percents to Fractions: 4) Write each percent as a fraction a) 125 %

Rewrite with a denominator of 100 and simplify

b) 3.6 %

c) 0.02 %

Application: 5) In a slice of cheese pizza, 45 calories are from fat. The total number of calories in each slice is 158. About what percent of the calories are not from fat? Round to the nearest tenth of a percent.

Bell Ringer: 6a) Behavorial scientists observed an elephant that slept about 12.5 % of each day. What fraction of each day did the elephant sleep?

6b) An elephant eats about 6 % of its body weight in vegetation each day. Write this as a fraction in simplest form.

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Challenge Your teacher uses different methods of grading quizzes. Your quiz grades are 85%,

16

21

10 20

9

25

, , 92%,

, 79%.

a) Write your quiz grades in order from least to greatest.

b) Find the average percent grade of your quizzes.

Writing in Math Does 0.4 equal 0.4%? Explain.

Closure 1) Write each as a percent. a) 0.523

b) 0.6

2) Order from least to greatest:

c)

3 10

2 3

, , 0.645, 13%

10 5

1

3) Order 0.52, 37%, 0.19, and 40 from least to greatest.

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Bell Ringer: Write each percent as a decimal.

Write each decimal as a percent.

1) 38%

3) 0.26

2) 4.5%

4) 5.7

Write each fraction as a percent.

Write each percent as a fraction.

5)

6)

13

7) 18%

20

1

8) 2.7%

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Chapter 5 Section 2 – Solving Percent Problems Using Proportions

𝑖𝑠 % = 𝑜𝑓 100 1) Find 30% of 280

3) 60% of what number is 126?

𝑝𝑎𝑟𝑡 % = 𝑤ℎ𝑜𝑙𝑒 100 2) 12.5 is what percent of 500?

4) What percent of 75 is 21?

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5) What number is 64% of 75?

6) 120 is 66% of what number?

Application: 7) Mr. Smith spends $150 per week on groceries. This represents 15% of Mr. Smith’s weekly income. How much does Mr. Smith earn each week?

8) You go out with a friend and spend a total of $25 on lunch. You want to tip your waitress 20%. How much should you leave as a tip?

9) Suppose your entertainment budget is 30% of your weekly wages from a job. You plan to spend $10.50 on a movie night. How much will you need to earn at your job in order to stay within your budget.

10) You take a test with 25 questions on it. Your grade on the test is 84%. How many questions did you get right?

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Challenge Rob’s score on a math test was 88% of Cathy’s score. Cathy’s score was 97% of Bill’s score. Bill’s score was 92% of Lynn’s score. Lynn’s score was 94 out of 100. What was Rob’s score?

Is 3% of 96 the same value as 96% of 3?

Closure 1) What percent of 150 is 45?

2) What is 35% of 90?

3) 45% of what number is 117?

Bell Ringer: 1) What number is 36% of 120?

2) 540 is 18% of what number?

3) Your school holds classes from 8:00am to 3:00pm. For what percent of the 24-hour day does your school hold classes? 6

Chapter 5 Section 4 – Applications of Percent Sales Tax: a percent of a _____________________ Sales Tax =

Tip: a percent of a ___________ Tip =

Commission: a percent of the amount of _____________ Commission =

Finding Sales Tax 1) Mrs. Majewski goes to Babies’R’Us and her total bill comes to be $55.50. There is a 6% sales tax at the store. How much tax will she pay on her baby purchases?

How much total will she pay?

2) Alyssa goes to the Montgomery Mall and spends $139.00. She paid 7% sales tax on her total purchases. How much money total did Alyssa spend at her shopping spree at the Mall?

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Estimating a Tip 3) You and your friends go to Friendly’s. The total bill comes to $45.90. You want to leave a 20% tip. How much tip should you leave?

4) Kris and Emma go to Chili’s for lunch. The meal comes to $25.50. They leave a 15% tip. What is the total bill that Kris and Emma must pay?

Finding a Commission 5) Find the commission on a $500 sale with a commission rate of 12.5%.

6) A sales agent earns a weekly salary of $650, plus a commission of 4% on all sales. His sales this week are $1,250. How much does he earn?

Finding a Registration Fee 7) In one state the fee to register a medium weight truck is 1.5% of its assessed value. What is the fee to register a truck with an assessed value of $14,500?

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Homework: 1) Find the payment for a $75 purchase with a sales tax rate of 5%.

2) Find a 15% tip for a $270.60 bill. And find the estimated tip.

3) Find the commission on $3,580 in sales when commission is paid at 6%.

4) At a local community college, the fee to register for classes is 2.25% of total class tuition. If the total class tuition is $3,300, what is the registration fee?

5) All states charge a fee for using cell phones. In one state, the fee is 1.14% of the bill. What is the monthly fee for a $39.00 bill?

6) Your neighbor pays $40 to have her lawn mowed and always adds a 15% tip. You and your friend decide to mow the lawn together and split the earnings evenly. How much will each of you make?

7) A store pays a 6% commission on the first $500 in sales and 8% on sales over $500. Find the commission on an $800 sale.

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Challenge 1) Ben’s weekly salary is $850. He also earns a 6% commission on sales. Last week, his total salary with commission was $959.80. What were Ben’s sales?

2) Kate went to Kohl’s and saw that shirts were on sale for 25% off. She picked out a shirt that was originally listed at $30.99. What would Kate pay as the sale price?

Bell Ringer: 1) Bryan and two friends went to Pizza Hut for lunch. The total bill came to $35.65. Bryan wants to leave a 20% tip. What is the total that Bryan should leave?

2) Your neighbor pays $30 to have her flower garden weeded and always adds a 20% tip. You and your friend decide to weed the garden together and split the earnings evenly. How much will each of you make?

Chapter 5 Section 5 – Simple Interest Principal: the original amount you ___________ or ____________ Simple Interest: interest earned only on the _______________

I = prt

I=

p=

r=

t=

Finding Simple Interest 1) Dan deposited $500 into a savings account at a local bank that earns 2% interest per year. How much interest does he earn in 3 years?

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2) You borrow $300 for 5 years at an annual interest rate of 4%. What is the simple interest you pay in dollars?

3) The Smith’s are looking to buy a new house that costs $250,000. They get a loan for that mount at 5% interest for 30 years. How much interest will they have to pay over the life of the loan?

How much money total will they end up paying for the house?

Graphing Simple Interest 4) You have $500 in an account that earns an annual rate of 5.1%. At the end of each, you withdraw the interest you have earned. Graph the total interest you earn after 1, 2, 3, and 4 years.

Step 1: Make a Table Time (yr)

Step 2: Draw a Graph

Interest ($)

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Comparing Loans 6) You need to borrow $1,000. You can borrow it for 3 years at 8% simple interest or for 2 years at 11% simple interest. Which loan will cost more? 3 Year Loan

2 Year Loan

Challenge 1) You invest $2,000 in a simple interest account. The balance after 8 years is $2,720. What is the interest rate?

2) A college student takes out a 4-year loan at 6.25% simple interest. When the loan is due, she has to pay $30,000. What was her original loan amount, and how much interest did she end up paying?

3) How long would it take Steven to earn $200 at an interest rate of 3.5% if his original deposit was $1,500?

4) Barbara wants to borrow $2,000. She can get a loan of $2,000 at 7% simple interest for 3 years or 11% simple interest for 2 years. Which loan will cost her less?

Closure 1) What is simple interest? 2) What is principal? 3) Find the simple interest earned on $500 at 4.5% for 4 years 4) You borrow $500 at 18% simple annual interest. You make no payments for 6 months. How much do you owe after 6 months 12

Bell Ringer: 1) Find the simple interest on $500 invested at a 3% annual interest rate for 4 years.

2) You can invest $200 at 4.5% simple interest for 6 years or at 8% for 3 years. Which investment earns you more money? How much is the interest?

Chapter 5 Section 6 – Finding Percent of Change Percent of Change: the ___________ a quantity increases or decreases from its ____________ amount

𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡 100

Find a Percent of Increase/Decrease 1) South Carolina had 6 seats in the U.S. House of Representatives in the 2000s. After the 2010 census, South Carolina had 7 seats. Find the percent of increase in the number of representatives.

2) A football player gained 1,200 yd last season and 900 yd this season. Find the percent of change. State whether the change is an increase or decrease.

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Markup: the difference between the _________________ and the ______________________________

𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡

=

𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 100

Finding a Percent of Markup 3) An electronics store orders sets of walkie-talkies for $14.85 each. The store sells each set for 19.90. What is the percent of markup?

4) Find the percent of markup for a $17.95 headset marked up to $35.79.

Discount: the difference between the _____________________ and ___________________________-

𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡

𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 = 100

Finding Percent of Discount 5) During a clearance sale, a keyboard that normally sells for $49.99 is discounted to $34.99. What is the percent of discount?

6) Find the percent of discount of a $24.95 novel on sale for $14.97.

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Homework: Round to the nearest percent. Find each percent of increase. 1) 60 to 75

2) 88 to 99

3) 135 to 200

4) 12 to 18

Find each percent markup. 5) $22 marked up to $33

6) $15 marked up to $60

Find each percent of discount. 7) $70 discounted to $63

8) $9 discounted to $4

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Percent Error: used to assure that products meet specifications

Percent Error =

8) The supervisor at a shoelace factory checks the length of 1 shoelace out of every 500 made. If shoelaces are not within 0.5% of the specified length, they will be rejected. A 36-inch shoelace she just checked was 7 35 8 in long. Does she reject this shoelace?

9) At a sporting good factory, a quality control technician checking the weights of baseball bats measures a 1 bat that should weigh 26oz at 264 oz. If a bat is not within 0.6% of its specified weight, it is rejected. Why does this bat pass or fail this test?

Classwork / Homework: Find each percent of increase. Round to the nearest percent. 1) 2 to 7

2) 12 to 63

3) 120 to 240

4) 15 to 35

5) A worker earning $5.15/hour receives a raise. She now earns $6/hour. Find the percent of increase in her hourly rate of pay.

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Find each percent of markup. Round to the nearest percent. 6) $13.50 marked up to $25

7) $40 marked up to $59.75

8) Find the percent of markup for a shirt that a store buys for $3.25 and sells for $7.50.

Find each percent of discount. Round to the nearest percent. 9) $10 discounted to $7

10) $480 discounted to $300

11) A package of poster board usually sells for $8.40. This week the package is on sale for $6.30. What is the percent of discount?

12) The annual precipitation for a city dropped from 65 cm to 47 cm over the course of 5 years. What is the average percent of change in the amount of precipitation for 1 year?

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More than One Way: A jacket goes on sale with a discount of 40% off the original price. The original price of the jacket is $42.95. What is the sale price of the jacket? Anna’s Method:

Kris’ Method:

Choose a Method: You get a discount of 20% on a $27.50 ticket. How much will your ticket cost? Describe your method.

Find the price of each item. 13) originally $35.75, 65% markup

14) originally $82, 35% discount

15) originally $19.50, 43% markup

16) originally $299, 15% discount

17) A TV goes on sale with a discount of 28%. The original price of the TV is $942. What is the sale price of the TV?

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Challenge A storeowner buys a case of 144 pens for $28.80. Tax and shipping cost an additional $8.64. He sells the pens for $0.59 each. What is the markup per pen?

What is the percent of markup?

Error Analysis The number of students enrolled in a school has increased from 1,938 to 2,128. A student calculates the percent of increase. His work is shown to the right. Explain the student’s mistake. Then find the correct answer.

Closure 1) What is the percent of change formula?

2) Find the percent of change and round to the nearest tenth. State whether it is an increase or decrease. a) 10 to 25

b) 95 to 76

3) Find the percent markup for a car that a dealer buys for $10,590 and sells for $13,775.

4) Find the percent of discount for a $74.99 tent that is discounted to $48.75. 19