Date:



Name: ______________________________________________________

Percents

Date: ___________

Percents, Decimals, and Fractions

Percent (%): Percent means “per hundred.” P percent is the same as [pic].

Usually there are three ways to write a number: a percent, a fraction, and a decimal. .

Ex: 16% [pic] 0.16

Writing Percents as Fractions in Simplest Form

Example 1: 37% =

Example 2: 24% =

Your Turn: Write 12% as a fraction in simplest form.

Your Turn: Write 55% as a fraction in simplest form.

Writing Percents as Decimals Decimal ↔ Percent

• Divide by 100 OR Move the decimal two places to the LEFT

EXAMPLE 3: Write 9% as a decimal.

EXAMPLE 4: Write 0.5% as a decimal.

EXAMPLE 5: Write 250% as a decimal.

Your Turn: Write 27% as a decimal.

Your Turn: Write 3.4% as a decimal.

Writing Decimals as Percents D ↔ P

• Multiply by 100 OR Move the decimal two places to the RIGHT

EXAMPLE 6: Write 0.13 as a percent.

EXAMPLE 7: Write 0.027 as a percent.

Your Turn: Write 0.04 as a percent.

Your Turn: Write 0.578 as a percent.

Writing Fractions as Percents

EXAMPLE 8: Write [pic] as a percent.

EXAMPLE 9: Write [pic] as a percent.

Your Turn: Write [pic] as a percent.

Your Turn: Write [pic] as a percent.

Your Turn: Fill in the chart by converting between a fraction, decimal, and percent. Show your work in the space below.

|Fraction |Decimal |Percent |

| | |350% |

| |.025 | |

|[pic] | | |

Date: ___________

Part of a Whole as Percent – Using the Percent Equation

Solving Percent Problems

• The whole is 100%.

• When given two terms out of three from the part, whole, and percent use the formula: Part = Percent • Whole

Identifying the Part, Percent, and Whole

|Problem |Part |Percent |Whole |

|40% of the students on the field trip love the museum. If there | | | |

|are 20 students on the field trip, how many love the museum? | | | |

|40% of the students on the field trip love the museum. If 20 | | | |

|students love the museum, how many are on the field trip? | | | |

|20 students on the field trip love the museum. If there are 40 | | | |

|students on the field trip, what percent love the museum? | | | |

Using the Formula to Find a Part, Given a Percent of the Whole

• Part = Percent • Whole

EXAMPLE 1: In Ty’s math class, 20% of students earned an A on a test. If there were 30 students in the class, how many got an A?

|Part |Percent |Whole |

| | | |

|How many students got an A? |20% |30 total students in the class |

Part = Percent • Whole Part = ________________

Check your solution:

[pic]

Your Turn: A bag of candy contains 300 pieces of which 28% are red. How many pieces are red?

|Part |Percent |Whole |

| | | |

Part = Percent • Whole Part = _______________

Check your solution:

[pic]

Finding the Whole

EXAMPLE 3: Zoey inflated 24 balloons for the school dance. If Zoey inflated 15% of the balloons that are inflated for the dance, how many balloons are there in total?

|Part |Percent |Whole |

| | | |

|24 balloons |15% |Total # of balloons for the dance |

Part = Percent • Whole Whole = _______________

Check your solution:

[pic]

[pic]

|Part |Percent |Whole |

| | | |

Part = Percent • Whole Whole = _______________

Check your solution:

[pic]

Finding the Percent

EXAMPLE 4: Haley is making passports for the “Night in Paris” school dance. So far she has made 112 passports, and her plan is to make 320 passports. What percent of the passports has Haley produced so far?

|Part |Percent |Whole |

| | | |

|112 passports |? |320 passports |

Part = Percent • Whole Percent = ______________

Check your solution:

[pic]

Solving the Percent Equation with Verbal Sentences

Part = Percent • Whole

Remember in math “is” means equals, “of” means to multiply, and an unknown number we use a variable.

EXAMPLE 5: What number is 20% of 110? ( What number is 20% of 110?

Check solution: [pic]

EXAMPLE 6: 117 is 45% of what number? ( 117 is 45% of what number

Check solution: [pic]

EXAMPLE 7: What percent of 150 is 90? ( What percent of 150 is 90?

Check solution: [pic]

Date: ___________

Percent of Change

Percent of Change: indicates how much a quantity increases or decreases with

respect to the original amount.

Quantity of Increase or Decrease = Percent • Whole (Original Amount)

Finding the Percent of Increase

EXAMPLE 1: Cassandra likes jewelry. She has five rings in her jewelry box.

Cassandra’s aunt said she will buy Cassandra another ring for her

birthday. If Cassandra gets the ring for her birthday, what will be the

percent increase in her ring collection?

Quantity of Increase = Percent • Whole 1 = p • 5

Your Turn: John increased his trading card collection by 5 cards. He originally

had 15 cards. What is the percent of increase?

Quantity of Increase = Percent • Whole

[pic]

EXAMPLE 3: Original: 55

New: 143

Quantity of Increase = Percent • Whole

Your Turn: Original: 20

New: 25

Quantity of Increase = Percent • Whole

Finding the Percent of Decrease

EXAMPLE 4: Ken said that he is going to reduce the number of calories that he eats

during the day. Ken reduced the amount of calories he consumed from

2,500 calories to 2,200 calories per day. What percent did Ken reduce

his calorie intake?

Quantity of Decrease = Percent • Whole

Your Turn: Last month 349 books were checked out from the school library. This

month, 273 books were checked out. Find the percent of decrease in

the number of books checked out. Round to the nearest whole percent.

EXAMPLE 5: Original: 20

New: 15

Quantity of Decrease = Percent • Whole

Your Turn: Original: 75

New: 35

Quantity of Decrease = Percent • Whole

Finding the Original Amount

EXAMPLE 6: The population of cats in a rural neighborhood has declined in the past

year by roughly 30%. Residents hypothesize that this is due to wild

coyotes preying on the cats. The current cat population in the

neighborhood is estimated to be 12. Approximately how many cats

were originally in the neighborhood?

• Do we know the part or the whole? ____________________________________

________________________________________________________________

• Is this a percent increase or decrease? How do you know? _________________

________________________________________________________________

• If there was about a 30% decline in the cat population, then what percent of cats

remain? _______________________________________________________

• How do we write an equation to model this situation?

Part = Percent • Whole

EXAMPLE 7: Jessica’s math level on her achievement test in 7th grade was a level

650. Her math teacher told her that her test level went up by 25%

from her 6th grade test score level. What was Jessica’s test score

level in 6th grade?

• Is this a percent increase or decrease? How do you know? _________________

________________________________________________________________

• If Jessica’s 6th grade test score level represents the whole, then what percent

represents the 7th grade level? _______________________________________

• How do we write an equation to model this situation?

Part = Percent • Whole

Date: ___________

Percent of Error

Absolute Error: The difference of the exact value, x, and the approximate value, a.

[pic]

Percent of Error: a ratio that compares the inaccuracy of an estimate, or amount of

error, to the actual amount

Percent of Error Equation: [pic]

[pic]

EXAMPLE 1: The length of the diagonal of a computer monitor’s screen tells the screen’s size. The diagonal of the computer monitor is 15 inches. Three students were selected to measure the diagonal of the 15-inch screen with their ruler. Below is a table of measurements each student recorded.

Do you believe that the stated size of the screen, printed on the box, is the actual size

of the screen? ________________________________________________________

_____________________________________________________________________

Using the table, find the absolute error of each student’s measurement.

Taylor Kellen John

Explain what the absolute error means in the context of the problem.

Taylor: _______________________________________________________________

Kellen: ______________________________________________________________

John: _______________________________________________________________

Using the table, find the percent error of each student’s measurement. Explain what the percent error means in the context of the problem.

Taylor Kellen John

Explain what the percent error means in the context of the problem.

Taylor: _______________________________________________________________

_______________________________________________________________

Kellen: ______________________________________________________________

______________________________________________________________

John: _______________________________________________________________

_______________________________________________________________

What is the purpose of finding the percent error? _____________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

Date: ___________

Markup and Markdown Problems

Markdown rate (discount rate) – the percent of decrease in the price

Original price – the starting price, sometimes called the cost or wholesale price

Markdown – the amount of decrease in a price

Sale price – the original price minus the markdown

Finding a Sale Price

[pic]

• What was the total markdown of the jeans?

33% of $55 (

• What was the sale price?

• Use the equation, Quantity = Percent • Whole, to solve this problem.

Your Turn:

[pic]

• What was the total markdown of the sandals?

• What was the sale price?

• Use the equation, Quantity = Percent • Whole, to solve this problem.

Your Turn:

[pic]

Finding a Selling Price or Retail Price

Markup rate – the percent increase in the price

Original price – the starting price, sometimes called the cost or wholesale price

Markup – the amount of increase in a price

Selling price (retail price) – the original price plus the markup

EXAMPLE 2:

[pic]

• What was the total markup of the skateboard?

150% of $40 (

• What is the selling price or retail price of the skateboard?

• Use the equation, Quantity = Percent • Whole, to solve this problem.

Your Turn:

[pic]

• What was the total markup of the guitar?

• What is the selling price or retail price of the skateboard?

• Use the equation, Quantity = Percent • Whole, to solve this problem.

[pic]

Date: ___________

Multi-Step Percent Problems

Method 1 Method 2

Method 1 Method 2

Method 1 Method 2

Method 1 Method 2

Date: ___________

Finding the Original Price

[pic] (100% + Markup percent) ( Wholesale price = Retail Price

[pic]

(100% - Discount percent) ( Original Price = Sale Price

[pic]

Date: ___________

Simple Interest Day 1

Interest (I): the amount earned or paid for the use of money

Principal (P): the amount of money deposited or borrowed

Simple Interest: interest that is earned or paid only on the principal

Annual Interest Rate (r): the percent of the principal earned or paid per year

Balance (A): the sum of the interest and the principal (Interest + Principal = Balance)

Simple Interest Formula

I = Prt

• P is the amount deposited or borrowed

• r is the annual interest rate (written as a decimal)

• t is the time in years

Finding Simple Interest

EXAMPLE 1: George puts $1,560 into a savings account. The account pays 2.5% simple interest. How much interest will he earn in 3 years?

I = Prt P = ____________ I = _________________________

r = ____________ I = _________________________

t = ____________

Answer: George will earn $117 in interest after 3 years.

Your Turn: Suppose a bank is offering its customers 3% interest on savings accounts. If a customer deposits $1500 in the account, how much interest does the customer earn in 5 years?

I = Prt P = ____________ I = _________________________

r = ____________ I = _________________________

t = ____________

EXAMPLE 2: If you deposit $500 into an account that earns 6% simple annual interest, how much interest will you earn after 10 months?

I = Prt P = ____________ I = _________________________

r = ____________ I = _________________________

t = ____________

I = Prt P = ____________ I = _________________________

r = ____________ I = _________________________

t = ____________

Finding a Balance

[pic]

I = Prt P = ____________ I = _________________________

r = ____________ I = _________________________

t = ____________ A = ________________________

Answer: Tim’s total amount (balance) that he will owe his parents in 1 year is $105.

[pic]

I = Prt P = ____________ I = _________________________

r = ____________ I = _________________________

t = ____________ A = ________________________

Date: ___________

Simple Interest Day 2

Finding an Interest Rate

[pic]

P = __________________ I = Prt

A = __________________

I = __________________

r = __________________

t = __________________

Answer: The simple annual interest rate is 6%.

Example 2: You deposit $1000 into a 3 month certificate of deposit. After 3 months the balance is $1005. Find the simple annual interest rate.

P = __________________ I = Prt

A = __________________

I = __________________

r = __________________

t = __________________

Your Turn: Mrs. Educate borrows $6,300 from the bank for a new car. When she pays off the loan in 2 years, her balance is $7,056. Find the simple annual interest rate.

P = __________________ I = Prt

A = __________________

I = __________________

r = __________________

t = __________________

Find an Amount of Time

[pic]

P = _________________ I = Prt

I = _________________

r = ________________

t = ________________

Answer: It will take 5 years to earn $150 in interest.

Your Turn: Suppose Ann has $300 in a savings account that earns 1.75% simple annual interest. In how many years will she have $21 in interest?

P = _________________ I = Prt

I = _________________

r = ________________

t = ________________

-----------------------

Your Turn: In a survey, 105 teenagers said surfing was their favorite water sport. If 20% of teenagers said that surfing was their favorite water sport, how many total teenagers were surveyed?

EXAMPLE 2: In 1970 the price of gas was $1.70. In 2010, the price of gas was $2.95. Find the percent of change in the cost of gasoline from 1970 to 2010. Round to the nearest tenth.

|Student |Measurement |

|Taylor |[pic][pic] |

|Kellen |[pic] |

|John |[pic] |

|Student |Measurement |

|Taylor |[pic][pic] |

|Kellen |[pic] |

|John |[pic] |

EXAMPLE 2: You guess that there are 300 gum balls in a jar, but there are actually 400 gum balls. Find the percent of error.

[pic]

[pic]

Your Turn: Sean wants to practice free-throws in his drive way. He estimates the distance from the free-throw line to the hoop and marks it with chalk. Jake’s estimate was 13.5 feet. The actual distance is 15 feet. Find the percent of error.

Your Turn: Izzy estimates the weight of her Cavapoo to be 17 pounds. The actual weight of her dog is 20.75 pounds. Find the percent of error.

[pic]

EXAMPLE 1: You buy a pair of jeans that is 33% off the original price of

$55.

• What is the markdown rate or discount rate? _________

• What is the original price? _____________

A store is selling all sandals at 20% off their original price. What is the sale price of a pair of sandals originally priced at $20?

• What is the markdown rate or discount rate? ____________

• What is the original price? ___________________

A store is selling DeMarini baseball bats at 15% off their original price. What is the sale price of the bat originally priced at $199.95?

Tilly’s buys skateboards from a manufacturer at a wholesale price of $40. The store’s markup is 150%. What is the retail price?

• What is the markup rate? _____________

• What is the wholesale price? _____________

• What is the markup rate? ____________________________

• What is the wholesale price? __________________________

Hix’s buys acoustic guitars from a manufacturer at a wholesale price of $125. The store’s markup is 200%. What is the retail price?

Your Turn: At Friday’s, you order a meal that costs $12 including tax. You leave a 20% tip. What is the total cost of the meal?

EXAMPLE 1: Best Buy is selling their Solo Beats for 10% off the original price of $199.99. If there is a 7% tax rate, how much would it cost to buy a pair of Beats?

[pic]

[pic]

EXAMPLE 2: At Chili’s, you order a meal that costs $8. The sales tax is 7.5% and you leave a 20% tip. What is the total cost of the meal?

[pic]

EXAMPLE 3: Last week Jamie went to Forever 21 and there was a shirt she loved for $12.99. When she went back this week, the shirt was 15% off. She also had a coupon that would take an extra 5% off the sale price. How much would Jamie have to pay for the shirt?

EXAMPLE 4: Sports Authority buys stocking caps from a manufacturer at a wholesale price of $14. The store’s markup is 90%. In March, they put the stocking caps on sale for 45% off. What is the retail price?

[pic]

EXAMPLE 1: Home Goods marks up the wholesale price of a decorative lamp by 40%. The retail price is $35. What is the wholesale price (original price)?

Your Turn: Game Stop marks up the wholesale price of a video game by 60%. The retail price is $60. What is the wholesale price?

EXAMPLE 2: You have a coupon for 10% off a pair of shoes at Dick’s Sporting Goods. With the 10% discount, your shoes cost $89.10. What is the original price of the shoes?

[pic]

Your Turn: The iPhone 5 is on sale for 20% off. If the sale price is $239.20, what is the original price?

Your Turn: Mr. Smith purchased a $7000 wedding ring with his credit card that has an interest rate of 6%. How much simple interest will Mr. Smith owe if it takes him 18 months to pay off the ring?

[pic]

EXAMPLE 3: Tim’s parents lend him $100 so he can buy a radio-controlled airplane. They charge Tim 5% simple annual interest. What will be the total amount (balance) that Tim will owe his parents in 1 year?

Your Turn: Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4% interest. How much interest will she earn in 4 years? What will be in Kelly’s account at the end of four years?

EXAMPLE 1: =?@BJKY`bcw‹?™š¥ßà÷øöìÞØÒ̸®¤š?„wk[kH%jn¾V[pic]h7`CJOJ[?]QJ[?]U[pic]V[pic]^J[?]jh7`CJOJ[?]QJ[?]U[pic]^J[?]h7`CJOJ[?]QJ[?]^J[?]hLU>*[pic]CJOJ[?]QJ[?]^J[?]hLUCJOJ[?]QJ[?]^J[?]hLUOJ[?]QJ[?]^J[?]hþbÂOJ[?]QJ[?]^J[?]h&N You deposit $600 into a savings account. After 6 months the balance is $618. Find the simple annual interest rate.

EXAMPLE 3: You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You received a check for the interest at the end of each year. How long will it take to earn $150 in interest?

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