Percent

= = Writing Ratios Step 1 Step 2 Step 3 1 girls 20 girls 4∙5 girls Write the ratio of girls to boys in simplest form A class has 20 girls to 16 boys. Identify the two quantities being compared Step 1 Step 2 Write as a ratio Step 3 Simplify girls 20 girls 4∙5 girls 5 girls 1 = = boys 16 boys 4∙4 boys 4 boys 5 girls:4 boys 5 girls to 4 boys Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.1 Ratios

Comparing Unit Rates Step 1 Step 2 Step 3 Derrick Louise Derrick’s car travels 360 miles and uses 15 gallons of gas. Louise’s car travels 340 miles and uses 10 gallons of gas. Whose car gets better gas mileage (in miles per gallon)? Identify the two ratios being compared and the units of each ratio Step 1 Step 2 Write each ratio Divide each ratio (make each ratio into a unit rate) and compare! Step 3 miles Derrick 360 mi = 24 miles per gallon gallons 15 gal Louise miles 340 mi = 34 miles per gallon gallons 10 gal Louise’s car gets 10 miles per gallon more than Derrick’s! Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.2 Rates and unit rates

Solving Proportions 1 Solve: Step 1: Cross multiply 3 x =12 5 3x = 60 Step 2: Solve for x 3x = 60 3 3 1 x = 20 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.3 Proportions

Solving Real-life Problems Using Proportions Jason can read 12 pages of a book in 15 minutes. How many pages can he read in 25 minutes? Step 1: Write a ratio using words Pages minutes 12 15 x 25 = Step 2: Set-up a proportion 12 25 = 15 x 300 = 15x 300 = 15x 15 15 Step 3: Cross multiply Step 4: Solve for x x = 20 pages Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.3 Proportions

Solving Real-life Problems Using Proportions Jared is printing a 240 page research paper for his college class. The printer prints the first 60 pages in 4 minutes. How long will it take to print the rest of the paper? Pages Step 1: Write a ratio using words Minutes Step 2: Set-up a proportion How many pages does Jared have left to print? 60 4 180 x 240 ― 60 = 180 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Solving Real-Life Problems Using Proportions (cont.) Jared is printing a 240 page research paper for his college class. The printer prints the first 60 pages in 4 minutes. How long will it take to print the rest of the paper? 60 4 180 x Step 3: Cross multiply and solve for x 3 60x = 4•180 It will take 12 minutes to print the rest of the paper! 1 60 60 1 x = 4 • 3 x = 12 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Solving Real-life Problems Using Proportions Austin needs to paint two walls. One wall is 450 square feet and the other is 625 square feet. If 3 cans of paint covers 75 square feet, how many cans will Austin need? Step 1: Write as proportion using words Square feet Square feet = Cans of paint Cans of paint Wall 1 + Wall 2 450 + 625 =1075 Step 2: Set-up a proportion 75 sq. ft. 3 cans 1075 sq. ft. p cans = Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.3 Proportions

Austin needs 43 cans of paint. Solving Real-life Problems Using Proportions (Continued) Austin needs to paint two walls. One wall is 450 square feet and the other is 625 square feet. If 3 cans of paint covers 75 square feet, how many cans will Austin need? Step 3: Cross multiply and solve 1 1 25 1 75 3 = 1075 p Austin needs 43 cans of paint. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Dimensional Analysis Convert 5.5 ft to inches Step 1 Write 5.5 ft as a fraction Step 2 Find the conversion factor How many inches in 1 ft? 1 ft = 12 in Step 3 Multiply 5.5 ft and the conversion factor Step 4 Simplify 66 in Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.4 Dimensional Analysis

How many minutes in 1 hour? Dimensional Analysis Convert 480 minutes into hours Step 1 Write 480 minutes as a fraction Step 2 Find the conversion factor How many minutes in 1 hour? 1 hour = 60 minutes Step 3 Multiply 480 min. and the conversion factor 8 hours Step 4 Simplify Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 5.4 Dimensional Analysis

Percents Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

6-1 Fraction, Decimals, Percents Let’s Find Percents Per  Out of or Divide Cent  100 Percent means out of a hundred 70% of 90 “of” means multiply 70% • 90 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-1 Fraction, Decimals, Percents

= = % 25 25 100 Fractions to Decimals to Percents! Fraction DECIMAL 2 5 Fraction 4 1 8 1 DECIMAL 2 2 25 = = % 25 100 DECIMAL Percent Percent is defined as how many parts out of100. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-1 Fraction, Decimals, Percents

Let's Find 10% and 20% of a Number ! 75 X .10 7.50 75 X .20 15.00 7.5 X 2 15.0 75 OR 50 X .10 5.00 50 X .20 10.00 5 X 2 10 50 OR Notice that to find 10% of a number move the decimal one spot to the left Notice that 20% of a number is 2 times 10% of a number. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-2 Estimating with Percents

Proportions for Percent Problems Part (is) 100 Whole (of) The variable can be placed in the Part, Whole, or Percent. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Proportions for Percent Problems Louis got 40 out of 50 correct on his test. What is his percent correct? Part Whole 100 Percent 50x = 40  100 50x = 4000 x 40 50 100 50 x = 80 Louis got 80% right. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-3 Finding Percents

Proportions for Percent Problems Susan answered 90% of the questions from an online survey. If she has answered 18 questions, how many questions were on the survey? Part Whole 100 Percent 90x = 18  100 90x = 1800 90 18 90 100 x x = 20 The survey had 20 questions. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-4 finding a number when % is known

Proportions for Percent Problems Five hundred students applied to Jordan’s IB magnet. How many will get accepted if Jordan IB only accepts 40% ? Part Whole 100 Percent 100x = 40  500 100x = 20000 1 40 x 100 100 100 500 x = 200 200 students will be accepted into Jordan’s IB magnet. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-4 finding a number when % is known

The percent of increase is 30%. At Julio’s Computers they buy computers for $500 and sell them for $650. What is the percent of increase? Find the amount of change between the old price and new price 650 — 500 = Use 150 Original Amount of Change Change to decimal The percent of increase is 30%. Change to percent Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-5 Applying % increase and decrease

Percent of Increase (equation) Find the amount of change between the old price and new price 400 – 250 = 150 Use an equation and solve At Kat’s Computers they buy computers for $250 and sell them for $400. What is the percent of increase? Original • Percent = Amount of price change 250 • p = 150 250 250 The percent of increase is 60%. p = 0.6 Change to percent p = 60% Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

The percent of decrease is 40%. Kat’s Computers is having a sale. They are advertising a $1000 computer for $600. What is the percent of decrease? Find the amount of change between old price and new price 1000―600 = 400 Use an equation and solve Original • Percent = Amount of price change 1000 • p = 400 1000 1000 p = 0.4 The percent of decrease is 40%. Change to percent p = 40% Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Discounts (proportions) Sheila bought a dress that is 30% off. The original price of the dress is $150. What is the discount? What is the sale price? Step 1: Calculate the discount Part Whole 100 Percent The discount is $45 $150 original price - 45 discount $105 sale price Step 2: Subtract the discount from the original price Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-5 Applying % increase and decrease

Discounts (equation) 360 • 40% = ? 360 • 0.40 = 144 Caleb bought a suit that is 40% off. The original price of the suit is $360. What is the discount? What is the sale price? Step 1: Calculate the discount 360 • 40% = ? Whole • Percent = Part 360 • 0.40 = 144 The discount is $144 $360 original price ― 144 discount $216 sale price Step 2: Subtract the discount from the original price Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-5 Applying % increase and decrease

Sales Tax (proportion) Steve bought a jacket that was priced at $80. Find the sales tax and price including tax if the sales tax is 6%. Step 1: Calculate the sales tax Part Whole 100 Percent The sales tax is $4.80 Step 2: Add the sales tax to the price $80.00 price + 4.80 sales tax $84.80 price after tax Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-6 Sales Tax, Commission, and Profit

6-5 Applying % increase and decrease Sales Tax (equation) Felicia is buying a pair of steel toe work boots for $80. Find the sales tax and price including tax if the sales tax is 9%. Step 1: Calculate sales tax 80 • 9% = ? Whole • Percent = Part 80 • 0.09 = 7.2 The sales tax is $7.20 $80.00 original price + 7.20 sales tax $87.20 Total price Step 2: Add the Sales tax to the original price Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-5 Applying % increase and decrease

Total Price (multi- step problem) Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii? Price • Percent off = discount Step 1: Find the discount 220 • 15% = ? 220 • 0.15 = $33 Step 2: Find the sales price Original – discount = sales price $220-$33 = $187 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Total Price (cont.) The total price of the Wii is $203.83 Lupe is buying a Wii console that regularly sells for $220. It is on sale for 15% off and the tax rate is 9%. How much will she pay for the Wii? Sales price = $187 Step 3 Find the sales tax Sale price • tax rate = Sales tax 187 • 9% = ? 187 • 0.09 = 16.83 Step 4 Find the total price Sales price + tax = Total price 187 + 16.83 = 203.83 The total price of the Wii is $203.83 Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Commission Phillip makes 8% commission at AA Appliance store. His sales last month were $15,000. What was his commission last month? Part Whole 100 Percent Phillip made $1200 in commission! Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-6 Sales Tax, Commission, and Profit

Profit Marilee's Travel Agency makes 20% profit on all tickets sold. Last month Marilee’s Travel Agency made $60,000 in profit, what were the total sales last month? Whole • Percent = Part s • 20% = 60,000 s • 0.20 = 60,000 0.20 0.20 s = 300,000 Marilee’s total sales were $300,000. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7

Simple Interest Interest = Principal  rate  time I = P  r  t Interest: the amount of money paid to you on savings, or paid by you on money borrowed Principal: the initial amount of money rate: the percent charged or paid (must be changed to a decimal or fraction) time: measured in years Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 6-7 Applying Simple and Compound Interest

Simple Interest I = Prt I = 5000  0.03  2 I = 300 $300 interest You have $5000 in a savings account earning 3% interest. How much interest will you earn in 2 years? Write the formula Step 1 I = Prt Step 2 Substitute the values I = 5000  0.03  2 Step 3 Simplify I = 300 Step 4 Answer the question $300 interest Your savings account will have earned $300 in interest in 2 years. Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7