Percents. Fractions Decimals Percents How do you convert a fraction to a decimal? - divide the numerator by the denominator Example: ½ = 1 ÷ 2 = 0.5.

Percents

Fractions Decimals Percents

How do you convert a fraction to a decimal?- divide the numerator by the denominator

Example: ½ = 1 ÷ 2 = 0.5

Fractions Decimals Percents

How do you convert a decimal to a fraction?- Write it the way you say it

- Then simplify

Example: 0.8 is read “eight tenths”

8/10 simplifies to 4/5

Fractions Decimals Percents

How do you convert a decimal to a percent?- Multiply the number by 100 OR move the decimal point two spaces to the right

Example: 0.25 x 100 = 25%

Fractions Decimals Percents

How do you convert a percent to a decimal?- Divide the number by 100 OR move the decimal point two spaces to the left

Example: 35% ÷ 100 = 0.35

Fractions Decimals Percents

1/3

0.25

100%

2/5

0.45

62.5%

2 4/5

1.45

0.5%

Fractions Decimals Percents

1/3 0.33 33%

1/4 0.25 0.25

1/1 1 100%

2/5 0.4 40%

9/20 0.45 45%

5/8 .625 62.5%

2 4/5 2.8 280%

1 9/20 1.45 145%

1/200 .005 0.5%

What is a percent?

Percents are….

ratios that compare a number out of 100

How to find a Percent:

______ _____ OR _______ ______Percent

100

Part

Whole=

is

of= Percent

100

Can you find the percent?

1. What percent of 92 is 66? (Round to the nearest whole)

Step 1: Set up a proportion

______ ______

Step 2: Cross Multiply

92x = 100(66)

x100

6692

=

Can you find the percent?

Step 3: Solve for your variable

92x = 100(66)

x = 71.739

72%

66 is 72% of 92!

More Examples…

2. Emma walks 2 miles to school. If Rachel’s walk is 80% of the length of Emma’s walk, find the length of Rachel’s walk.

_____ _____

80(2) = 100x160 = 100x 100 100

x = 1.6Rachel walked 1.6 miles!

80

100

x

2=

More Examples…

3. A jacket is on sale for 60% off its original price. The original price was $30. What is the sale price?

_____ _____

60(30) = 100x1800 = 100x 100 100

x = $18 is the amount off the original

$60 - $18 = $12

60

100

x

30=

The sale price was

$12

More Examples…

4. Jon earns $36,000 yearly. Of that he pays $1,020 per month for his mortgage. What percent of his yearly earnings goes to the mortgage?

$1,020 x 12 = 12,240 (yearly mortgage amount)

_____ _____

12240(100) = 36,000x

1,224,000 = 36000x

36,000 36,000

x = 34

34% of his earnings goes to the mortgage!

x

100

12240

36000=

Percent Change

Percent Change: The ratio comparing the amount change to the original amount.

Percent Increase: Describes how much the original amount increases.

Percent Decrease: Describes how much the original amount decreases.

amount of change

original amount percent change =

Examples…1. According to the US Census, 72.3 million

children lived in the United States in 2004. It is estimated that there will be 80.3 million children in 2020. What is the percent increase, to the nearest percent?

80.3 million - 72.3 million = 8

Percent Change = 0.1106 = 11.06%

11%

8

72.3

percent change =

More Examples…2. Anthony buys a LCD monitor for his new

computer. The price tag says the original price is $750 but it’s on sale for $487.50. What is the percent decrease?

$750.00 - $487.50 = $262.50

Percent Change = 0.35

The LCD monitor was 35% off!

262.50

750.00

percent change =

More Examples…3. Ms. Breier bought a house for $125,000. It has

increased in value by 7% in the past two years. Mr. Frommann bought a house for $135,000. His house decreased in value by 4%. Who’s house is currently worth more? How much more?

Ms. Breier: Mr. Frommann:

___ ___ ___ ___

x = 8750 x = 5400$125000 – $8750 = $133750 $135000 - $54000 = $129600.

$133,750 – $129,600 = $4,150

Ms. Breier’s house is worth $4,150 more than Mr. Frommann’s

7 x

125000 100100= =

x4

135000

More Examples…4. You see a house for sale down the road from you.

The house is listed for $294,600. You are very interested and decide to put an offer down. You offer $287,000 for the home. What is the percent decrease of the offer to the listing price? Round to the nearest tenth

$294,600 - $287,000 = $7600

Percent Change = 0.0257

2.6% Decrease!

7600

294600 percent change =

Percent ErrorPercent Error: A ratio that compares the

inaccuracy of an estimate, or amount of error, to the actual amount.

Finding percent error is similar to finding the percent change.

→ Instead of finding the amount of increase or decrease , you will find the amount an estimate is greater than or less than the actual amount.

amount of error

actual amount percent error =

Steps for Calculating Percent Error

Steps to Calculate Percent Error:1. Determine the error – subtract the estimate form

the actual amount.

2. Divide the error by the actual value (it will be a decimal).

3. Convert the decimal to a percent by multiplying by 100.

Example…1. Suppose you guess there are 300 gumballs

in the gumball jar, but there are actually 400. Calculate the percent error.

400 – 300 = 100

Percent Error = 0.25

The percent error was 25%!

100

400 percent error =

More Examples…2. CJ wants to practice free-throws. He

estimates the distance from the free-throw line to the hoop and marks it with chalk. CJ’s estimate was 13.5 feet. The actual distance should be 15 feet. Find the percent error.

15 – 13.5 = 1.5

Percent Error = 0.1The percent error was 10%!

1.5

15 percent error =

More Examples…3. Did you know? Measuring instruments are not

exact! For example if you measure a plant to be 80 cm high (to the nearest cm). This means you could be up to 0.5 cm wrong (the plant could be between 79.5 and 80.5 cm high). Calculate the percent error. Round to the nearest tenth of a percent.

Percent Error = 0.0625

The percent error was 0.6%!

0.5

80 percent error = Since we don’t

know the actual amount we have

to use the measured value

instead.

More Examples…4. You thought 70 people would turn up at

Iroquois’ Winter concert, but in fact 80 did. Calculate the percent error.

80 – 70 = 10

Percent Error = 0.125

The percent error was 12.5%!

10

80 percent error =

More Examples…5. What is the percent error in using as an

approximation for . Give your answer to the nearest 0.01%.

– = 0.001264489

Percent Error = 0.004

The percent error was 0.04%!

0.001264489 percent error =

7

22

7

22

Commission

A fee paid to a person who makes a sale.

** Its is usually a percent of the selling price.

Commission Rate: The percent of the sale.

commission rate sales = commission

Examples…

1. Julie is paid a monthly salary of $2,100 plus commissions. Last month she sold one care for $39,500, earning a 4% commission on the sale. How much was her commission? What was her total pay for the month?

Commission: $1,580

Monthly Pay: $3,680

0.04 $39,500 = commission

Examples

2. A furniture sales associate earned $960 in commission in May. If his commission is 12% of his sales, how much were his sales in May?

x = $8,000

He had $8,000 worth of sales in May.

0.12 sales = $960

Examples…

3. The realtor you hired in order to buy your home made $6,796 in commission. You bought your home for $169,900. What was the realtor’s commission rate?

x = .04

The commission rate is 4%!

commission rate $169,900 = $6,796

Sales Tax

Sales tax is the tax on the sale of an item or service.

** Sales tax needs to be rounded to the nearest penny!

Sales tax rate price = sales tax

Examples…1. I bought a pair of jeans at the store. They

were $39.99. I had to pay 8.75% sales tax. How much did I have to pay in sales tax? How much were the jeans with sales tax?

Sales Tax: $3.50

How much were the jeans with the sales tax?

$39.99 + $3.50 = $43.49

I spent $43.49 total!

0.0875 $39.99 = sales tax

Examples…

2. If the sales tax rate is 7.75%, how much sales tax would Michael have to pay in sales tax if he bought a portable DVD player for $59.99 and two DVD’s for $17.99 each?

Sales Tax: $7.44

What is the total amount the Michael owes?

$95.97 + $7.44 = $103.41

0.0775 ($59.99+2($17.99)) = sales tax

0.0775 $95.97 = sales tax

Examples…3. Explain whether adding 6% sales tax to a total gives

you the same result as finding 106% of the total.

*Let’s use an example!

-Say our total is $20.50

Sales Tax: $1.23

$20.50 + $1.23 = $21.73

What is 106% of $20.50?

Sale Price: $21.73

0.06 $20.50 = sales tax

1.06 $20.50 = sale price

They’re the same!

Examples…

4. Explain how to find the price of an item if you know the total cost after 5% sales tax.

Let x = the price of your item

Let 0.5x = the sales tax

x + 0.5x = total cost

Examples…5. Explain whether the sales tax on a $20 item would be

double the sales tax on a $10 item. Justify your answer.*Lets use an example!

-Say our sales tax is 8.75%.

Sales Tax: $1.75

Sales Tax: $0.88 (rounded)

$1.75/2 = $0.875

0.0875 $20 = sales tax

0.0875 $10 = sales tax

Examples…

6. You just bought your first home at a sale price for $249,500. New York state sales tax is 8.75%. How much did he pay in sales tax?

Sales Tax: $21,831.25

How much did you pay for your home total?

$249,500 + $21,831.25 = $271,331.25

0.0875 $249,500 = sales tax

Tips, Markups, & Discounts

Tip or Gratuity: is the small amount of money in return for a service

Markup: the amount of increase from what the store bought the time for to what the store sells the item for.

Discount (Markdown): The amount of decrease that the original item is reduced. The sale price is the regular price minus the discount.

The selling price is the amount the customer pays for an item

Examples…

1. Tessa went to Hoch’s Hair Styling to get a haircut. The bill was $58 and Tessa wanted to leave a 20% tip. How much did Tessa leave for a tip? What was the total cost of Tessa’s bill (before sales tax)?

$58 0.2 = $11.16

$58 + $11.16 = $69.60

Tessa left $11.16 for a tip and paid a total of $69.60 for her haircut

Examples…

2. Rachel took Mrs. Long (her favorite teacher) out to breakfast. The bill came to $28.75. Find the total cost if the tax is 6.25% and a 20% tip is left on the amount before tax.

$28.75 0.2 = $5.75

$28.75 0.0625 = $1.80

The total breakfast bill was $36.30

$28.75 + 1.80 + 5.75 = $36.30

Examples…

3. Brad needs to sell his hockey painting with a 45% markup. If the painting cost Brad $450, what will the selling price of the painting be?

$450 0.45 = $202.50

$450 + 202.50 = $652.50

The selling price of the painting will be $652.50

Examples…

5. A cell phone is on sale for 30% off. If the sale price is $239.89, what was the original price?

Sale Price is 100% - 30% 70% of the original price

The original price of the cell phone was $342.70

_____ ________

239.89(100) = 70x23989 = 70x 70 70

70100

239.89x

Examples…6. Brandon needed a new pair of skates for hockey.

He found a great pair of Reebok skates at Great Skate on sale for $90. If this price represents a 9% discount from the original price, what was the original price to the nearest cent?

Sale Price is 100% - 9% so 91% of the original price

The original price of the skates were $98.90

_____ ________

90(100) = 91x9000 = 91x 91 91

91

100

90

x

Examples…7. Colton, Chris, and Luca were so excited about these great

deals they got on backpacks, that they couldn’t stop giggling. Colton’s backpack was originally $65 and it was on sale for 25% off. Chris’ backpack was originally $75 but he used his 30% coupon. Luca’s backpack was also $75 but it was on sale for 20% off and he had a 15% coupon. Which backpack was the better buy? Explain.

Chris: $75 0.3 = $22.50$75 - $22.50 = $52.50

Colton: $65 0.25 = $16.25$65 - $16.25 = $48.75

Colton got the better buy

because his backpack was the

cheapest

Luca: $75 0.2 = $15$75 - 15 = $60$60 0.15 = $9$60 - $9 = $51

Simple Interest

Interest is money paid to the bank when you borrow the bank’s money OR it is money paid to you when you deposit money into a savings account.

Simple Interest is a type of interest paid for the use of money.

Simple Interest Rate of interest is the percent charged or earned

Time that the money is borrowed or invested (in years)

I = P r t

Principal is the amount of money borrowed or invested

Examples…

1. Tristan borrowed $14,500 from his brother and promised to pay him back over 5 years at an annual simple interest rate of 7%. How much interest will he pay if he pays off the entire loan at the end of the fifth year?

I = $5,075

What is the total amount he will repay?

$14,500 + $5,075 = $19,575

I = 14,500 0.07 5

Examples…

2. Jamie invested $3,500 in a mutual fund at a yearly rate of 6%. He earned $945 interest. For how long was the money invested.

4.5 = t

The money was invested for 4.5 years!

945 = 3,500 0.06 t

Examples…

3. Emily invested $2000 in a simple interest account for three years. At the end of the three years she had earned $150 in interest. What was the simple interest rate of the account?

0.025 = r

The simple interest rate was 2.5%!

150 = 2,000 r 3

Examples…

4. If Tracey deposits $720 in the bank for 3 months and earns 4.25% interest, how much will be in her bank account at the end of the three months?

$7.65 = I

Tracey’s bank account will have $727.65!

I = 720 0.0425 0.25

Examples…5. You are in the process of buying a home. You take out a

mortgage loan for the sale price (including sales tax) of your house, which is $309,938. Since you are a first time home owner and plan on living in the house for the next 20 years, you will get a mortgage rate of 4.5%. How much interest will you pay on the entire loan?

I = 278,944.20

You will pay $278,944 in interest!

I = 309,938 0.045 20

#5 Continued…

What will your monthly mortgage be, including interest?

$309,938 + $278,944 = $588,882

- There are 12 months in a year, so how many months are in 20 years?

20(12) = 240 months

$588,882 / 240 months

Your monthly mortgage payment will be $2,453.68!

Examples…

6. The average cost for a vacation is $1,050. If a family borrows the money for the vacation at an interest rate of 11.9% for 6 months, what is the total cost of the vacation including the interest rate on the loan?

$62.48 = I

The total cost of the vacation is $1,112.48!

I = 1,050 0.119 0.5