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 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%

______ _____ OR _______ ______ What is a percent? Percents are…. ratios that compare a number out of 100 How to find a Percent: ______ _____ OR _______ ______ Part is Percent Percent = = Whole 100 of 100

Can you find the percent? What percent of 92 is 66? (Round to the nearest whole) Step 1: Set up a proportion ______ ______ Step 2: Cross Multiply 92x = 100(66) x 66 = 100 92

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) = 100x 160 = 100x 100 100 x = 1.6 Rachel walked 1.6 miles! 80 x = 2 100

x = $18 is the amount off the original 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) = 100x 1800 = 100x 100 100 x = $18 is the amount off the original $60 - $18 = $12 x 60 = 100 30 The sale price was $12

More Examples… = _____ _____ x 12240 100 36000 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 12240 = 100 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… 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 =

The LCD monitor was 35% off! 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 x 7 x 4 = = 100 125000 100 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 Error Percent 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: Determine the error – subtract the estimate form the actual amount. Divide the error by the actual value (it will be a decimal). Convert the decimal to a percent by multiplying by 100.

Example… 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 = 0.1 The 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%! Since we don’t know the actual amount we have to use the measured value instead. 0.5 80 percent error =

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 =

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… 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

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

The commission rate is 4%! 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… 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 They’re the same! 1.06 $20.50 = sale price

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

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

The total breakfast bill was $36.30 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 $28.75 + 1.80 + 5.75 = $36.30 The total breakfast bill was $36.30

The selling price of the painting will be $652.50 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

The original price of the cell phone was $342.70 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 _____ ________ 239.89(100) = 70x 23989 = 70x 70 70 70 239.89 100 x The original price of the cell phone was $342.70

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 91 90 _____ ________ 90(100) = 91x 9000 = 91x 91 91 100 x The original price of the skates were $98.90

Colton got the better buy because his backpack was the cheapest 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. Colton: $65  0.25 = $16.25 $65 - $16.25 = $48.75 Chris: $75  0.3 = $22.50 $75 - $22.50 = $52.50 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… 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

The money was invested for 4.5 years! 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

The simple interest rate was 2.5%! 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

Tracey’s bank account will have $727.65! 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

You will pay $278,944 in interest! 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

Your monthly mortgage payment will be $2,453.68! #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!

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