Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 MAP 2 D Ratios and Proportions

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Writing Ratios 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 girls boys Step 3 Simplify 20 girls 16 boys 4 ∙ 5 girls 4 ∙ 4 boys 5 girls 4 boys == 5.1 Ratios 5 girls : 4 boys 5 girls to 4 boys

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

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

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

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Step 1: Write a ratio using words 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? Step 2: Set-up a proportion Pages Minutes x How many pages does Jared have left to print? 240 ― 60 = 180

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Solving Real-Life Problems Using Proportions (cont.) Step 3: Cross multiply and solve for x 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? 60x = x = 4 3 x = 12 It will take 12 minutes to print the rest of the paper! x

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 75 sq. ft. 3 cans 1075 sq. ft. p cans 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 Step 2: Set-up a proportion 5.3 Proportions Square feet Cans of paint Square feet Cans of paint Wall 1 + Wall =1075 = =

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Step 3: Cross multiply and solve Austin needs 43 cans of paint. 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? p = Solving Real-life Problems Using Proportions (Continued)

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

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

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

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent is defined as how many parts out of100. Percent is defined as how many parts out of Fraction, Decimals, Percents % 25 

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade X X X X X X 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. 6-2 Estimating with Percents 10%20% number

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

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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? 18 x x = 18  x = x = 20 The survey had 20 questions. 6-4 finding a number when % is known Part Whole 100 Percent

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

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Equations for Percent Problems Whole Percent = Part Change to a Decimal! Change to a Decimal! The variable can be placed in the Part, Whole, or Percent.

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Equations for Percent Problems Currently there are 1,100 seniors (12 th grade students) enrolled at Wilson High School. The number of seniors completing all college admission requirements is 495. What percent of the seniors completed college requirements? Whole Percent = Part 1100 p = 495  Substitute  Solve 1100 p = 0.45  Change to % p = 45% 45% 45% of the seniors at Wilson completed college admission requirements

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Equations for Percent Problems Giselle answered 15 problems correct on her test. If her percent correct was 75%. How many questions were on her test? Whole Percent = Part w  Substitute  Solve 0.75 w = 20 Change % to decimal  Change % to decimal w 0.75 = questions were on Giselle’s test. 1575%=

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Equations for Percent Problems Six hundred students applied to Millikan's Quest Program. How many will get accepted if Quest only accepts 70% ? Whole Percent = Part = q 420 = q 420 students were accepted into Millikan’s Quest Program.  Substitute  Solve Change % to decimal  Change % to decimal %= q

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent of Increase At Julio’s Computers they buy computers for $500 and sell them for $650. What is the percent of increase? 1.Find the amount of change between the old price and new price 650 — 500 = 2.Use The percent of increase is 30%. 6-5 Applying % increase and decrease Original Amount of Change Change to percent Change to decimal 0 150

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent of Increase (equation) At Kat’s Computers they buy computers for $250 and sell them for $400. What is the percent of increase? 1.Find the amount of change between the old price and new price 400 – 250 = Use an equation and solve Original Percent = Amount of price change 250 p = p = 0.6 Change to percent p = 60% The percent of increase is 60%.

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Percent of Decrease Kat’s Computers is having a sale. They are advertising a $1000 computer for $600. What is the percent of decrease? 1.Find the amount of change between old price and new price 1000―600 = Use an equation and solve Original Percent = Amount of price change 1000 p = p = 0.4 Change to percent Change to percent p = 40% The percent of decrease is 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 Step 2: Subtract the discount from the original price The discount is $45 $150 original price - 45 discount $105 sale price 6-5 Applying % increase and decrease Part Whole 100 Percent

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 $360 original price ― 144 discount $216 sale price Discounts (equation) 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 Step 2: Subtract the discount from the original price The discount is $ Applying % increase and decrease Whole Percent = Part % = ? = 144

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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 Step 2: Add the sales tax to the price The sales tax is $4.80 $80.00 price sales tax $84.80 price after tax 6-6 Sales Tax, Commission, and Profit Part Whole 100 Percent

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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 Step 2: Add the Sales tax to the original price The sales tax is $7.20 $80.00original price sales tax $87.20 Total price 6-5 Applying % increase and decrease Whole Percent = Part 80 9% = ? = 7.2

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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? Step 1: Find the discount Price Percent off = discount % = ? = $33 Step 2: Find the sales price $220-$33 = $187 Original – discount = sales price

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 Total Price (cont.) 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? Step 3 Find the sales tax 187 9% = ? = Step 4 Find the total price = Sale price tax rate = Sales tax Sales price = $187 The total price of the Wii is $ Sales price + tax = Total price

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? Phillip made $1200 in commission! 6-6 Sales Tax, Commission, and Profit Part Whole 100 Percent

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 7 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? Marilee’s total sales were $300,000. Whole Percent = Part s 20% = 60,000 s 0.20 = 60, s = 300,000