Slide 1 / 194 Percents Slide 2 / 194 Table of Contents Ratios as Percents Decimals as Percents Percents as Decimals Fractions as Percents Percents as Fractions Fractional Parts and Equivalent Names Relating Fractions, Decimals and Percents Three types of Percent Problems Percent of Change Applied Percent of Decrease Applied Percent of Increase Real-life Application Problems Slide 3 / 194 Slide 4 / 194 Ratios as Percents What fraction of each grid is shaded? Return to table of contents Slide 5 / 194 Slide 6 / 194 What is the ratio of shaded boxes to total boxes? to to to The fractions and ratios can also be written as percentages. Percent means per. Fraction: 10 Ratio: 10 to Fraction: Ratio: Fraction: Ratio: Percent: 10% Percent: Percent:
Slide 7 / 194 Slide 8 / 194 What percent of the grid is shaded? Use the green stylus to shade 20% of the grid. How many squares will you shade? Use the black stylus to shade 5% of the grid. How many squares will you shade? Slide 9 / 194 Slide 10 / 194 1 1% of the grid is shaded. True False Use the red stylus to shade % of the grid. How many squares will you shade? % of something represents how much? 2 % of the grid is shaded. Slide 11 / 194 Slide 12 / 194 3 What percent of the grid is shaded? True False
Slide 13 / 194 4 6 to is the same as what percent? A 600% B 60% C 6% D % Slide 14 / 194 5 15 is the same as what percent? A 150% B % C 15% D 5% Slide 15 / 194 Slide 16 / 194 6 Express the ratio as a percent. 57 out of 7 Express the ratio as a percent. 67 lacrosse team members in students Slide 17 / 194 8 Express the ratio as a percent. $18 per $ 0 Slide 18 / 194 Writing Decimals as Percents Return to table of contents decimals percents
Slide 19 / 194 Writing decimals as percents... Multiply by and add the percent symbol. Example 1: 0.75 0.75 75% Remember To multiply a # by, move the decimal two places to the RIGHT. Slide 20 / 194 Writing decimals as percents... Multiply by and add the percent symbol. Example 2: 0.09 0.09 9% Remember To multiply a # by, move the decimal two places to the RIGHT. 0.09 0.75 Slide 21 / 194 Writing decimals as percents... Multiply by and add the percent symbol. Example 3: 0.007 0.007 0.7% Remember To multiply a # by, move the decimal two places to the RIGHT. 0.007 Slide 22 / 194 Writing decimals as percents... Multiply by and add the percent symbol. Example 4: 0.4 0.4 40% Remember To multiply a # by, move the decimal two places to the RIGHT. 0.4 Slide 23 / 194 Writing decimals as percents... Multiply by and add the percent symbol. Example 5: 1.49 1.49 149% Remember To multiply a # by, move the decimal two places to the RIGHT. 1.49 Slide 24 / 194 Writing decimals as percents... Multiply by and add the percent symbol. Example 6: 8 8 800% Remember To multiply a # by, move the decimal two places to the RIGHT. 8
9 Write the decimal as a percent: 0.45 Slide 25 / 194 Slide 26 / 194 10 Write the decimal as a percent: 1.3 130% 45% Slide 27 / 194 11 Write the decimal as a percent: 0.008 Slide 28 / 194 12 Write the decimal as a percent: 5.8% 500% Slide 29 / 194 Slide 30 / 194 13 Write the decimal as a percent:.2 20% Writing Percents as Decimals Return to table of contents percent decimal
Slide 31 / 194 Writing percents as decimals... Divide by and remove the percent symbol. Example 1: 28% 28% 0.28 Remember To divide a # by, move the decimal two places to the LEFT. 28% Slide 32 / 194 Writing percents as decimals... Divide by and remove the percent symbol. Example 2: 8% 8% 0.08 Remember To divide a # by, move the decimal two places to the LEFT. 8% Slide 33 / 194 Writing percents as decimals... Divide by and remove the percent symbol. Example 3: 0.4% 0.4% 0.004 Remember To divide a # by, move the decimal two places to the LEFT. 0.4% Slide 34 / 194 Writing percents as decimals... Divide by and remove the percent symbol. Example 4: 375% 375% 3.75 Remember To divide a # by, move the decimal two places to the LEFT. 375% Slide 35 / 194 Writing percents as decimals... Divide by and remove the percent symbol. Slide 36 / 194 14 Write the percent as a decimal: 2% Example 5: 0.235 Remember To divide a # by, move the decimal two places to the LEFT..02
Slide 37 / 194 15 Write the percent as a decimal: 658% Slide 38 / 194 16 Write the percent as a decimal: 0.019% 6.58.00019 Slide 39 / 194 17 Write the percent as a decimal: 4.3% Slide 40 / 194 18 Write the percent as a decimal:.5%.043 0.005 19 Write the percent as a decimal: Slide 41 / 194 Slide 42 / 194 20 Write the percent as a decimal: 0.725 0.2975
Slide 43 / 194 Slide 44 / 194 Writing fractions as percents... Writing Fractions as Percents Return to table of contents percents fractions Write an equivalent fraction with a denominator of. Example 1: 3 4 x 3 4 25 x 25 75 75% Slide 45 / 194 Slide 46 / 194 Writing fractions as percents... Writing fractions as percents... Write an equivalent fraction with a denominator of. Write an equivalent fraction with a denominator of. Example 2: 4 5 x 4 5 20 x 20 80 Example3: 9 4 x 9 4 25 x 25 225 80% 225% Slide 47 / 194 Writing fractions as percents... Slide 48 / 194 21 Write the fraction as a percent: Write an equivalent fraction with a denominator of. 19 20 Example 4: 3 600 x 3 600 x 6 6 0.5 95% 0.5%
Slide 49 / 194 22 Write the fraction as a percent: 9 0 Slide 50 / 194 23 Write the fraction as a percent: 8.9% 8% Slide 51 / 194 24 Write the fraction as a percent: 5 2 Slide 52 / 194 25 Write the fraction as a percent: 3 500 250%.6% To write any fraction as a percent: Slide 53 / 194 METHOD 1: Express the fraction as a decimal and then express the decimal as a percent. Example 5: To write any fraction as a percent: Slide 54 / 194 METHOD 2: Write a proportion with the fraction as the first ratio and as the denominator of the second ratio. Solve using cross products. Example 5: 7 8 8 0.875 7.000 0.875 87.5%
To write any fraction as a percent: Slide 55 / 194 METHOD 1: Express the fraction as a decimal and then express the decimal as a percent. Example 6: 12 9 9 1.333 12.000 1.333 To write any fraction as a percent: Slide 56 / 194 METHOD 2: Write a proportion with the fraction as the first ratio and as the denominator of the second ratio. Solve using cross products. Example 6: 133.3% 1 133 3 % Slide 57 / 194 Slide 58 / 194 To write any fraction as a percent: METHOD 1: Express the fraction as a decimal and then express the decimal as a percent. Don't forget to add the whole number! Example 7: 5 3 3 8 8 0.625 5.000 3.625 362.5% Slide 59 / 194 26 Write the fraction as a percent: 5 8 Slide 60 / 194 27 Write the fraction as a percent. Round to the nearest whole percent. 4 7 62.5% 57%
Slide 61 / 194 28 Write the fraction as a percent: 3 3 5 Slide 62 / 194 29 Write the fraction as a percent: 2 500 360%.4% Slide 63 / 194 Slide 64 / 194 30 Write the fraction as a percent: 9 2 Writing Percents as Fractions percents 450% Return to table of contents fractions Slide 65 / 194 Slide 66 / 194 Writing percents as fractions... Express the % as a fraction with a denominator of, then simplify. Writing percents as fractions... Express the % as a fraction with a denominator of, then simplify. Example 1: 75% 75 3 4 Example 2: 120% 120 1 1 5
Slide 67 / 194 Writing percents as fractions... Express the % as a fraction with a denominator of, then simplify. Example 3: 0.3% 0.3 3 0 Slide 68 / 194 Writing percents as fractions... Express the % as a fraction with a denominator of, then simplify. Example 4: 2 1 4 9 % 4 2.25 225 10,000 Multiply by to eliminate the decimal 9 400 Multiply by 10 to eliminate the decimal Slide 69 / 194 Writing percents as fractions...another way Express the % as a fraction with a denominator of, then simplify. Slide 70 / 194 Example 4: Convert the percent to a fraction. Divide the numerator by the denominator (). Simplify. Slide 71 / 194 31 Write the percent as a fraction in simplest form: 40% Slide 72 / 194 32 Write the percent as a fraction in simplest form: 110% 2 5 11 10
Slide 73 / 194 33 Write the percent as a fraction in simplest form: 0.5% Slide 74 / 194 34 Write the percent as a fraction in simplest form: 8% 1 200 2 25 Slide 75 / 194 35 Write the percent as a fraction in simplest form: 1 5 % 3 Slide 76 / 194 36 Write the percent as a fraction in simplest form: 3 9 % 8 4 75 3 32 Slide 77 / 194 Slide 78 / 194 37 Write the percent as a fraction in simplest form: 54 4 % 7 191 350 Fractional Parts and Equivalent Names Return to table of contents
Slide 79 / 194 Common Equivalents you should know like the back of your hand! Slide 80 / 194 Common Equivalents you should know like the back of your hand! 1 5 2 3 3 4 1 2 1 3 1 4 0.2 0.666... 0.75 20% 66.6% 75% 0.5 0.3333... 0.25 50% 33.3% 25% Slide 81 / 194 Slide 82 / 194 Relate Fractions, Decimals & Percents...Tying it all together! Return to table of contents Slide 83 / 194 Slide 84 / 194 Helping you remember... Fill in each box below with an example of the process described. % to a fraction % to a decimal fraction to a % decimal to a % Order the numbers from least to greatest. 0.15 12.5% 0.095 In order to do this, they must all be in the same form. Let's turn them all into percents: 15% 12.5% 16% 9.5% So least to greatest: 9.5% 12.5% 15% 16% 0.095 12.5% 0.15
Slide 85 / 194 Slide 86 / 194 38 Find the lowest value 39 Find the greatest value A 5% B 1/2 C.5% D.05 A 120% B 1.02 C.2% D 1.19 Slide 87 / 194 Slide 88 / 194 40 Find the greatest value 41 Find the lowest value A 6% B.6 C 60 D 6 A 2% B.2 C.02 D.2% Slide 89 / 194 Slide 90 / 194 42 Find the lowest value A 50% B 500% C 50.0 D 50.01
Slide 91 / 194 Express each fraction as a percent: 1) 2) 3) 43 Express as a fraction. Slide 92 / 194 Click to Reveal Click to Reveal Click to Reveal 44 Express as a decimal. Slide 93 / 194 45 Express as a percent. Slide 94 / 194 46 Express as a decimal. Slide 95 / 194 47 Express as a percent. Slide 96 / 194
Slide 97 / 194 Slide 98 / 194 48 Express as a percent. Three Types of Percent Problems Return to table of contents Slide 99 / 194 Remember, percents are "parts of a whole". The part is the numerator and the whole is the denominator. 17% means 17 parts per or We are going to solve problems involving percents. There are 3 types of problems: 1. Find the part What number is 54% of 34? 2. Find the whole 4 is 60% of what number? 3. Find the percent 18 is what percent of 28? Slide / 194 Two words that will occur in these types of problems are "is" and "of". These words have specific meanings in math. "Is" means equals () "Of" means multiply To solve a percent problem, translate the words into an equation. Change the following: 1. Percent into a decimal 2. "is" to "" 3. "of" to " " 4. Unknown to "x" Then, solve the equation. Slide 101 / 194 Slide 102 / 194 Examples: Find 40% of 60 Write a mathematical sentence Finding the Part....40 60 24 20% of 90 Write a mathematical sentence.20 90 18
Slide 103 / 194 Slide 104 / 194 What is 10% of 88? Write a mathematical sentence X.10 88 X 8.8 Try these: Find 12% of 70 What is 40% of 28? Slide 105 / 194 Slide 106 / 194 Let's try these examples again, but solve them with a proportion this time! Examples: Find 40% of 60.40 60 24 20% of 90.20 90 18 Slide 107 / 194 Slide 108 / 194 What is 10% of 88? X.10 88 49 Find 30% of 45 X 8.8 Try these: Find 12% of 70 What is 40% of 28?
50 What is 15% of 90? Slide 109 / 194 51 Find the greater value. Slide 110 / 194 A 20% of 16 B 10% of 90 C 25% of 40 D % of 7 52 Find the greater value. A 2% of 0 B 5% of 500 C 10% of 300 D 15% of Slide 111 / 194 Slide 112 / 194 53 Identify any values that are equal. A What is 40% of 80? B 60% of 70 C 25% of 128 D 200% of 16 Slide 113 / 194 Slide 114 / 194 Remember, you can solve this by: 1. Translating into an equation 2. Setting up a proportion Finding the Whole... 40% of what number is 50?.40 X 50 X 50.40 X 125
Try This: is 20% of what number? Slide 115 / 194 54 What is 70% of 80? Slide 116 / 194.20 X X.20 X 500 Slide 117 / 194 55 12% of 50 is what number? Slide 118 / 194 56 65% of what number is 10? Slide 119 / 194 57 What number is 150% of 18? Slide 120 / 194 58 1% of what number is 12?
Slide 121 / 194 Slide 122 / 194 Remember, you can solve this by: 1. Translating into an equation 2. Setting up a proportion What percent of 80 is 24? Finding the Percent... x 80 24 X 24 80 X.30 X 30% Slide 123 / 194 Slide 124 / 194 60 is what percent of 15? 59 What percent of 3 is 12? 60 X 15 60 X 15 4 X 400% X 60 30 is what percent of 36? Slide 125 / 194 Slide 126 / 194 61 What percent of 18 is 180?
62 2 is what percent of 1? Slide 127 / 194 63 What percent of 25 is 20? Slide 128 / 194 Slide 129 / 194 You have just studied three different types of percent problems. Try all 3 types: What number is 40% of 60? 42 is what percent of 840? PU Slide 130 / 194 64 Find the largest value. A What is 50% of 50? B What number is 45% of 60? C 30 is 60% of what number? D 25% of what number is 150? What is 30% of 45? Slide 131 / 194 65 Find the greatest percentage value. A What percent of 30 is 18? B 60 is what percent of 90? C What percent of 70 is 210? D 1,000 is what percent of? 66 Find 20% of 78. Slide 132 / 194
67 8 is what percent of 28? Slide 133 / 194 Slide 134 / 194 68 What number is 3% of 17? 69 Find 27% of 54. Slide 135 / 194 Slide 136 / 194 70 23 is what percent of 200? 71 What percent is 35 of 20? Slide 137 / 194 Slide 138 / 194 72 56% of what number is 40?
Slide 139 / 194 73 45 is 30% of what number? Slide 140 / 194 74 62% of 40 is what number? A 24.8 B.0155 C 24.8% D 15.5 Slide 141 / 194 Slide 142 / 194 Percent of Change: The ratio of the amount of increase or decrease to the original amount Percent of Change It is an increase when the new amount is larger than the original and a decrease when the new amount is smaller than the original. To find the percent of change, use the following proportion: Return to table of contents Percent of change: Amount of increase or decrease % Original Amount Slide 143 / 194 Find the percent of change (be sure to label your answer as an increase or decrease). Examples: Original amount: 20 Original amount: 40 New amount: 30 New amount: 10 Slide 144 / 194 Identify the percent of change as an increase or decrease. Then find the percent of change. 1. Original: 45 New: 75 Percent of change Percent of change 2. Original: New: 42 3. Original: 58 New: 75
Slide 145 / 194 Slide 146 / 194 Try This! A CD's original price was $12.99. It is now on sale for $10.99. What is the percent of change? Try This! A student's first test grade was 60. The second test grade was an 85. What was the percent of change? Slide 147 / 194 75 In 2005, the price of a McDonald's hamburger was $0.89. In 2010, the price of a McDonald's hamburger was $1.19. What was the percent of change? Slide 148 / 194 76 Original Amount: 500 New: 700 Find the percent of change. Slide 149 / 194 77 Original Amount: 52 New: 17 Find the percent of change. Slide 150 / 194 78 The number of students who attended FHS in 2010 was 1405. In 2011, 1380 students attended FHS. What was the percent of change in student enrollment?
Slide 151 / 194 79 Find the percent of change. Original price: $120 Sale price: $75 Slide 152 / 194 80 Find the percent of change. Original price: $80 Sale price: $50 Slide 153 / 194 Slide 154 / 194 81 A stereo, originally priced at $360, is on sale for $200. What is the percent of change? Applied Percent of Decrease Return to table of contents Slide 155 / 194 There are situations when the percent of change is going to be a decrease. Examples are: Discounts Sales Reduction in Population Slide 156 / 194 When finding a discount, there are two different methods you can use. Method 1: Find the percent of the original price (discounted amount in $) Subtract the discount from the original price. Method 2: Subtract the percent from % (percent you are paying) Find the percent of the original price.
Slide 157 / 194 Slide 158 / 194 Slide 159 / 194 Slide 160 / 194 Slide 161 / 194 Slide 162 / 194 82 A $710 computer is to be discounted 30%. What will be the sale price?
Slide 163 / 194 83 A necklace, priced at $120, is to be marked down 15%. What will be the sale price? Slide 164 / 194 84 The student population of the high school will decrease by 5% next year. The current population is 1407 students. How many students will attend next year? Slide 165 / 194 85 The store is having a 40% off sale. What percent will the customers pay? Slide 166 / 194 86 $80 boots are on sale for 20% off. After the sale, the manager raises the price 20%. What will be the selling price of the boots after the sale? Slide 167 / 194 Slide 168 / 194 There are situations when the percent of change is going to be an increase. Examples are: Applied Percent of Increase Tips Sales Tax Increase in Population Return to table of contents
Slide 169 / 194 Slide 170 / 194 When finding an increase, there are two different methods you can use. Method 1: Find the percent of the original price (increased amount) Add the increase to the original price. Method 2: Add the percent to % (percent you are paying) Find the percent of the original price. Slide 171 / 194 Find the new amount 87 Increase 36 by 25%. Slide 172 / 194 Increase 60 by 10% Increase 68 by 12% 88 Increase 40 by 15% Slide 173 / 194 Slide 174 / 194 Tip: An amount added to a bill for services provided. Customers traditionally tip 18-20% for good service in restaurants and salons. Example: If the restaurant bill is $45 and you want to leave a 20% tip, how much money should you leave? 45 +.20(45) 54 or 45(1.20) 54 The customer will leave $54 on the table. The waitress will receive a $9 tip and the restaurant will receive $45. To calculate the amount of the tip only:.20(45) 9
Calculate a 20% tip on a $75 bill. Slide 175 / 194 What will the customer leave in total? For poor service, my friend will leave a 5% tip. How much less will this waitress earn than the waitress above? Slide 176 / 194 Sales tax: An amount of money that is calculated by applying a percentage rate to the taxable price of a sale. Sales taxes are collected by the buyer from the seller, who turns it over to the government. In NJ the sales tax rate is 7%. To calculate Sales Tax alone find the percent (tax) of the price. That is the amount that you owe in addition to the cost of the item. To find the total cost of an item, you must add the sales tax to the cost. There are 2 ways to do this: 1. Find the percent of the item and add it to the original amount. 2. Find % + tax% of the original amount. Slide 177 / 194 Slide 178 / 194 A car costs $23,500. How much sales tax will the customer pay? 23,500(0.07) $1645 Discuss: How are tips and sales tax alike? What will the customer pay altogether for the car? 23,500 + 1645 25,145 The total cost of the car, including tax, can be calculated as follows: 23,500 +.07(23,500) 25,145 or 23,500(1.20) 25,145 Slide 179 / 194 89 What is the total cost of a $250 stereo in the state of NJ? Slide 180 / 194 90 Calculate the sales tax on a $125 bicycle.
Slide 181 / 194 91 Mike wants to leave a 20% tip. His bill is $35.50. How much is the tip? Slide 182 / 194 92 A $65 restaurant tab is put on the table. The couple plans on leaving an 18% tip. How much should be left altogether? Slide 183 / 194 Slide 184 / 194 93 What is the total cost of a $123 ipod, including tax? Real Life Application Problems Return to table of contents Slide 185 / 194 A store owner pays $12 for a particular bracelet. To cover expenses, the owner will mark up the price by 150%. Find the selling price of the bracelet. Slide 186 / 194 The store is having a 20% off sale on all CD's. With the sale, you pay $12 for a CD. What was the original price? A couple left their waiter a 20% tip in the amount of $18. What was the cost of their meal?
Slide 187 / 194 A group of friends had dinner at a restaurant. The cost of their meals is $62. They want to leave a 15% tip. Calculate the tip. When they arrive at the register the cashier will calculate the sales tax on the meal at a rate of 7%. Determine the sales tax. Calculate the total cost of the meal for each of the 3 friends. Slide 188 / 194 A store is having a 25% off sale on ipods. You want to purchase an ipod with an original price of $249. The sales tax is 7%, which will be applied to the sale price of the ipod. What is the total cost of the ipod? A computer is on sale for 10% off the original price of $325. When it doesn't sell, the manager marks it down another 20% off the sale price. What is the new sale price of the laptop? Is the new sale price the same as it would be had the manager taken 30% off of the original price? Explain. Slide 189 / 194 Slide 190 / 194 94 Wholesale price: $56 Markup percent: 50% New price? 95 Tickets cost $7 at the door. If purchased in advance, the tickets cost $5. What is the percent of discount for purchasing tickets in advance? Slide 191 / 194 96 560 people were surveyed. 25% said they prefer Coke. How many people prefer Coke? Slide 192 / 194 97 Increase 50 by 25%. What is the new amount?
Slide 193 / 194 98 What is the original price on a pair of boots that sell for $72 after a 25% discount? Slide 194 / 194 99 An ipod costs $176. It is on sale for 20% off and will be taxed at a rate of 7% on the sale price. What will be the total cost of the ipod?