Percent Graphic

Chapter 9.1 – Percents and Fractions Chapter 9.3 – Percents and Decimals Percent – ratio whose denominator is 100. Example #1 – Writing percents as decimals (move 2 jumps to the left) Example #1 – Writing percents as fractions 37% = 37/100 (reduce when you can) Example #2 – Writing fractions as percents 4/5 means 4 ÷ 5 = 0.8 0.8 x 100 = 80% Example #3 – Finding a percent of a number 9% = 0.09 Example #2 – Writing decimals as percents (move the decimal 2 jumps to the right) 0.135 = 13.5% Example #3 – Writing fractions as percents (divide the fraction) 60% of 75 = ? To solve… 60% x 75 = 45 OR 0.60 x 75 = 45 OR 3/5 x 75 = 45 ¾ = 0.75 Chapter 9.2 – Percents and Proportions Chapter 9.4 – The Percent Equation p a = (a = part, b = whole, p = percent) b 100 To solve: Substitute, cross multiply, and solve for the missing value! Example #1 – (Finding a percent) What percent of 3 is 1? p 1 p a = → = → 3p = 100 → P = 33 1/3 b 100 3 100 Example #2 – (Finding a part of a base) What number is 76% of 25? a 76 = → 100a = 1900 → a = 19 25 100 Example #3 – (Finding a base) 42 is 30% of what number? 42 30 = → 30b = 4200 → b = 140 b 100 Example #4 – Using percents less than 1% (convert percent to a decimal and multiply by the number) What is 0.005% of 20,000 0.00005 x 20,000 = 1Chapter 9.2 – Percents and Proportions Set up as equivalent fractions with numbers on one side and fractions on the other. Cross multiply and solve for the variable. Example #1 – What percent of 150 is 90? # % 90 = x 150 100 150x = 9000 x = 60 Example #2 – What number is 20% of 110? # % x = 20 110 100 100x = 2200 x = 22 Example #3 – The number 117 is 45% of what number? # % 117 = 45 x 100 45x = 11700 x = 260 Example #4 – A shoe salesman receives a 9% commission on the sale of a $125.00 pair of shoes. How much did he earn? # % x = 9 125 100 100x = 1125 x = $11.25 Chapter 9.5 – Circle Graphs Example #1 – Making a circle graph when given the percentage. How big will the piece of a circle graph be if I wanted to represent 20%? 1) Take the percentage and x by 360°. 2) Use a protractor to draw the angle. 20% x 360 = 72° Example #2 – Making a circle graph given data Favorite Exercise Aerobics Jogging Cycling Weightlifting People 8 22 6 12 Chapter 9.7 – Discounts, Markups, Sales Tax, and Tips Example #1 – Finding a sale price What is the sale price of a $29 pair of jeans that is 33% off? 1) Find the amount of discount 33% x 29 = $9.57 2) Subtract discount from the original price 29.00 – 9.57 = $19.43 Example #2 – Finding a retail price A store buys skateboards for $57 from the retailer and the markup is 150%. What is the retail price? 1) 150% x 57 = $85.50 1) Find how many people were surveyed (48) 2) Create a fraction for each group and multiply by 360° Aerobics – 8/48 x 360 = 60° Jogging – 22/48 x 360 = 165° Cycling = 6/48 x 360 = 45° Weightlifting = 12/48 x 360 = 90° 3) Draw and label the circle graph Example #3 – Finding sales tax and tips Chapter 9.6 – Percent of Increase % Decrease Chapter 9.8 – Simple Interest Percent of change – shows how much a quantity has increased or decreased in comparison with the original amount Interest - the amount earned or paid for borrowed money Principal – the amount of money deposited or borrowed (P) Simple interest rate – when interest is earned or paid on the principal (I) Percent of change = Amount of increase or decrease Original amount Example #1 – Finding a percent of increase What is the amount of increase from 8 to 13? 13 − 8 5 = = 62.5% 8 8 Example #2 – Finding the percent of decrease What is the amount of decrease from 49 to 35? 49 − 35 14 = = 28.6% 49 49 Example #3 – Using a percent of change A taco company puts 24 tacos in every box but recently started to put 25% more. How many shells are in a box now? Find the amount of increase = 25% of 24 = 6 Add the increase to the original = 24 + 6 = 30 At a restaurant, you order a meal that costs $12. You leave a 20% tip. The sales tax is 5%. What was the total cost of the meal? 1) Find the tip = 20% x 12 = $2.40 2) Find the sales tax = 5% x 12 = $0.60 3) Add it all up = 12.00 + 0.60 + 2.40 = $15.00 Formula: I = Prt r = rate t = time Annual interest rate – the percent of the principal earned or paid per year (r) Balance – The sum of the interest and the principal Example #1 – Finding a balance Tim’s parent lend him $100. They charge him 5% simple annual interest. What will be the total amount that Tim owes his parents in a year? I = Prt I = 100 x 0.05 x 1 = $105.00 Example #2 – Finding an interest rate You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple interest rate. 1) To find the interest, subtract the principal from the balance (618 – 600 = 18 2) Use the simple interest rate formula and solve for r I = Prt → 18 = 600 x r x 6/12 → 18 = 300r r = 0.06 → 6% Example #3 – Finding an amount of time You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You receive a check for the interest at the end of each year. How long will it take you to earn $150 in interest? I = Prt → 150 = 750 x 0.04 x t → 150 = 30t → t = 5 years