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STUDY LINK 8 1 More Rates and Proportions Copyright © Wright Group/McGraw-Hill 246 Name Date Time 1. Bring nutrition labels from a variety of food packages and cans to class. A sample label is shown at the right. 2. Express each rate as a per-unit rate. a. 143 players per 11 teams players/team b. $260 for 40 hours /hour 3. Kendis types 150 words in 2 minutes. a. Fill in the rate table. b. At this rate, how many words can Kendis type in 5 minutes? Complete the proportion to show your solution.words minute words minutes c. How many minutes would it take Kendis to type 1,050 words? Complete the proportion to show your solution. 2% Amount Per Serving Serving Size 1 slice (23 g) Calories 65 Calories from Fat 9 % Daily Value 4% Total Carbohydrate 12 g Total Fat 1 g Protein 2 g Servings Per Container 20 Try This Practice Use any method you wish to solve the following problems. 4. How long would it take to lay 8 rows of 18 bricks each at a rate of 4 bricksper minute? Express your answer in hours. 5. Apples are on sale for $0.90/pound. One pound is about 4 apples. Trisha purchased a crate of apples for $10. About how many apples should the crate contain? 6. 7 2 5m; m 7. x0.054 1.802; x minutes 12 4 5 words 150 words words minute minutes

LESSON 8 1 Name Date Time Patterns and Equations 247 Copyright © Wright Group/McGraw-Hill While walking with her father, Stephanie noticed that for every 2 steps her father took, she needed to take 3 steps to cover the same distance. 1. Complete the rate table below. 2. Describe any pattern(s) you used to complete the table. 3. Suppose Stephanie’s father takes 100 steps. Explain how you can calculate the number of steps Stephanie will take. 4. a. Write an equation to calculate the number of steps Stephanie takes (s) for any given number of her father’s steps (f). Equation: b. Check your equation by substituting values from the completed rate table for for s. c. Use your equation to find the number of steps Stephanie will take if her father takes 1,500 steps. Father’s steps Stephanie?s steps Number of Father’s Steps (f) 2 4 5 8 10 15 20 36 Number of Stephanie’s Steps (s) 327

STUDY LINK 8 2 More Rate Problems and Proportions Copyright © Wright Group/McGraw-Hill 248 Name Date Time For each of the following problems, first complete the rate table. Use the table to write an open proportion. Solve the proportion. Then write the answer to the problem. 1. A science museum requires 3 adult chaperones for every 15 students on a field trip. How many chaperones would be needed for a group of 125 students? Answer: A group of 125 students would need adult chaperones. 2. Crust and Crunch Deli sells 30 salads for every 48 sandwiches. At this rate, how many salads will they sell for every 64 sandwiches? Answer: For every 64 sandwiches, they will sell salads. 3. Tonya’s car averages 240 miles for each 10 gallons of gasoline. How many gallons of gasoline will the car need to travel 216 miles? Answer: Tonya’s car needs gallons of gasoline to travel 216 miles. 4. There are 60.96 centimeters in 2 feet. How many centimeters are in 1 yard? Answer: There are centimeters in 1 yard. adults 3a students 15 salads 30w sandwiches 48 miles 240 gallons 10 cm 60.96 ft 2     Practice Estimate each quotient and then divide. Round your answer to the nearest whole number. Show your work on the back of this sheet. 5. 38,419 57 is about . 38,419 57  6. 7,648 84 is about . 7,648 84  7. 86.5 2.5 is about . 86.5 2.5 

STUDY LINK 8 3 Calculating Rates 249 Name Date Time Copyright © Wright Group/McGraw-Hill If necessary, draw a picture, find a per-unit rate, make a rate table, or use a proportion to help you solve these problems. 1. A can of worms for fishing costs $2.60. There are 20 worms in a can. a. What is the cost per worm? b. At this rate, how much would 26 worms cost? 2. An 11-ounce bag of chips costs $1.99. a. What is the cost per ounce, rounded to the nearest cent? b. What is the cost per pound, rounded to the nearest cent? 3. Just 1 gram of venom from a king cobra snake can kill 150 people. At this rate, about how many people would 1 kilogram kill? 4. A milking cow can produce nearly 6,000 quarts of milk each year. At this rate, about how many gallons of milk could a cow produce in 5 months? 5. A dog-walking service costs $2,520 for 6 months. What is the cost for 2 months? For 3 years? Explain what you did to find the answer. Sources: 2201 Fascinating Facts; Everything Has Its Price Try This 6. A 1-pound bag of candy containing 502 pieces costs 16.8 cents per ounce. What is the cost of 1 piece of candy? Circle the best answer. 1.86 cents 2.99 cents 0.33 cent 1 2cent 7. Mr. Rainier’s car uses about 1.6 fluid ounces of gas per minute when the engine is idling. One night, he parked his car but forgot to turn off the motor. He had just filled his tank. His tank holds 12 gallons. About how many hours will it take before his car runs out of gas? 111–116

LESSON 8 3 Name Date Time Ingredients for Peanut Butter Fudge 250 Copyright © Wright Group/McGraw-Hill 1. The list at the right shows the ingredients used to make peanut butter fudge but not how much of each ingredient is needed. Use the following clues to calculate the amount of each ingredient needed to make 1 pound of peanut butter fudge. Record each amount in the ingredient list. Clues Use 20 cups of sugar to make 10 pounds of fudge. You need 3 3 4cups of milk to make 5 pounds of fudge. You need 15 cups of peanut butter to make 48 pounds of fudge. (Hint:1 cup 16 tablespoons) An 8-pound batch of fudge uses 1 cup of corn syrup. Use 6 teaspoons of vanilla for each 4 pounds of fudge. Use 1 2teaspoon of salt for each 4 pounds of fudge. 2. Suppose you wanted to make an 80-pound batch of fudge. Record how much of each ingredient you would need. Peanut Butter Fudge (makes 1 pound) cups of sugar cup of milk tablespoons of peanut butter tablespoons of corn syrup teaspoons of vanilla teaspoon of salt Ingredient List for 80 Pounds of Peanut Butter Fudge cups of sugar tablespoons of corn syrup cups of milk teaspoons of vanilla tablespoons of peanut butter teaspoons of salt Use the following equivalencies and your ingredient lists to complete each problem. 3 teaspoons 1 tablespoon 16 tablespoons 1 cup 3. cups of peanut butter are needed for 80 pounds of fudge. 4. cups of corn syrup are needed for 80 pounds of fudge. 5. tablespoons of vanilla are needed for 80 pounds of fudge.

STUDY LINK 8 4 Food Costs as Unit Rates 251 Name Date Time Copyright © Wright Group/McGraw-Hill Visit a grocery store with a parent or guardian. Select 10 different items and record the cost and weight of each item in Part A of the table below. Select items that include a wide range of weights. Select only items whose containers list weights in pounds and ounces or a combination of pounds and ounces, such as 2 lb 6 oz. Do not choose produce items (fruits and vegetables). Do not choose liquids that are sold by volume (gallons, quarts, pints, liters, milliliters, or fluid ounces). 1. Complete Part A of the table at the store. 2. Complete Parts B and C of the table by converting each weight to ounces and pounds. calculating the unit cost in cents per ounce and in dollars per pound. Example:A jar of pickles weighs 1 lb 5 oz and costs $2.39. Convert Weight Calculate Unit Cost to ounces: 1 lb 5 oz 21 oz in cents per ounce: $ 22 1.3 o9 z   11. 14 oce znts  to pounds: 1 lb 5 oz 1 15 6lb 1.31 lb in dollars per pound: 1$ .2 3. 139 lb   $ 11. l8 b2  Part A Part B Part C Weight Weight in Cents per Weight in Dollars per Item Cost Shown Ounces Ounce Pounds Pound 111 112

LESSON 8 4 Name Date Time Calorie Use for a Triathlon 252 Copyright © Wright Group/McGraw-Hill In a triathlon, athletes compete in swimming, cycling, and running races. In a short-course triathlon, athletes go the distances shown in the table below. Tevin is a fit sixth grader who plans to compete in the short-course triathlon. He estimates his rate of speed for each event to be as shown. Refer to the information above and the table on journal page 292 to answer these questions. 1. a. About how long will it take Tevin to swim the mile? (Hint:Find the number of yards in a mile.) b. About how many calories will he use? 2. a. About how long will it take Tevin to cycle 25 miles? b. About how many calories will he use? 3. a. About how long will it take Tevin to run 6.2 miles? b. About how many calories will he use? 4. About how many calories will Tevin use to complete the triathlon? 5. Use the following equivalencies to express the distance of each event and Tevin’s estimated times in kilometers. 1 mi is about 1.6 km. 1 m is about 39 in. 1 yd is about 0.9 m. Event Miles Tevin’s Estimated Times Swimming 1 40 yards per minute Cycling 25 20 miles per hour Running 6.2 7.5 miles per hour Kilometers Event (approximate)Tevin’s Estimated Times Swimming 1.6 meters per minute Cycling kilometers per hour Running kilometers per hour

STUDY LINK 8 5 Calculating Calories from Fat 253 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Choose 5 breakfast items from the menu at the right. Pay no attention to total calories, but try to limit the percent of calories from fat to 30% or less. Put a check mark next to each of your 5 items. 2. Record the 5 items you chose in the table. Then find the total number of calories for each column. 3. What percent of the total number of calories comes from fat? Food Total Calories Calories from Fat Toast (1 slice) 70 10 Corn flakes (8 oz) 95 trace Oatmeal (8 oz) 130 20 Butter (1 pat) 25 25 Doughnut 205 105 Jam (1 tbs) 55 trace Pancakes (butter, syrup) 180 60 Bacon (2 slices) 85 65 Yogurt 240 25 Sugar (1 tsp) 15 0 Scrambled eggs (2) 140 90 Fried eggs (2) 175 125 Hash browns 130 65 Skim milk (8 fl oz) 85 0 2% milk (8 fl oz) 145 45 Blueberry muffin 110 30 Orange juice (8 fl oz) 110 0 Bagel 165 20 Bagel with cream cheese 265 105 Food Total Calories Calories from Fat Total 49

LESSON 8 5 Name Date Time Planning a Meal 254 Copyright © Wright Group/McGraw-Hill Plan a menu of foods that you would enjoy for one meal of the day—breakfast, lunch, or dinner. In the table below, record nutrition label information for the foods you chose. Fill in the rest of the table and find the total number of calories for each column. Then find the total percent for each column. (Note:The percents from fat, carbohydrate, and protein should total about 100%.) Meal In the space at the right, make a circle graph to show the percentages of calories from fat, carbohydrate, and protein in the meal you planned. Be sure to label each section of the circle graph and write the percent of the total number of calories. Title your graph. FoodNumber Calories Calories from Calories of Calories from Fat Carbohydrate from Protein Total Number of Calories Percent of Calories 100% (title)

1. Find the average speed (in meters per second) for each running event. 2. Why do you think the average speed is different for each event? The picture at the right shows a stack of 50 pennies, drawn to actual size. 3. Carefully measure the height of the stack. Use your measurement to calculate about how many pennies would be in a stack 1 centimeter high. About (unit) 4. About how many pennies would be in a 50-foot stack of pennies? (1 inch is about 2.5 centimeters.) About (unit) 5. Some people believe that to determine the temperature in degrees Fahrenheit, you can count the number of times a cricket chirps in 14 seconds and then add 40. a. What is the temperature if a cricket chirps 3 times per second? b. At a temperature of 61°F, how many times does a cricket chirp per second? Source: The Handy Science Answer Book LESSON 8 5 Name Date Time Rate Problems 255 Copyright © Wright Group/McGraw-Hill EventTime Time Average Speed (minutes and seconds) (seconds) (meters per second) 100 meters 0 min 10.94 sec 10.94 sec m/sec 200 meters 0 min 22.12 sec 22.12 sec m/sec 400 meters 0 min 48.25 sec 48.25 sec m/sec 800 meters 1 min 57.73 sec sec m/sec 1,500 meters 4 min 0.83 sec sec m/sec Stack of 50 pennies (actual size) (unit)

STUDY LINK 8 6 Solving Ratio Problems Copyright © Wright Group/McGraw-Hill 256 Name Date Time Solve the following problems. Use coins or 2-color counters to help you. If you need to draw pictures, use the back of this page. 1. You have 45 coins. Five out of every 9 are HEADS and the rest are TAILS . How many coins are HEADS ? coins 2. You have 36 coins. The ratio of HEADS to TAILS is 3 to 1. How many coins are HEADS ? coins 3. You have 16 coins that are HEADS up and 18 coins that are TAILS up. After you add some coins that are TAILS up, the ratio of HEADS up to TAILS up is 1 to 1.5. How many coins are TAILS up? coins How many coins in all? coins 4. At Richards Middle School, there are 448 students and 32 teachers. The San Miguel Middle School has 234 students and 18 teachers. Which school has a better ratio of students to teachers; that is, fewer students per teacher? Explain how you found your answer. 5. You have 6 shelves for books. Numbers of books are listed in the table at the right. The ratio of mystery books to adventure books to humor books is the same on each shelf. Complete the table. Write each quotient as a 2-place decimal. 6. 121 78 7. 847 ,4 28 8. 364 34 117–119 PracticeMystery Adventure Humor Shelf Books Books Books 1 4 10 18 26 3 425 512 663

STUDY LINK 8 7 Body Composition by Weight 257 51 52 Name Date Time Copyright © Wright Group/McGraw-Hill Solve using any method of your choice. 1. About 1 out of every 5 pounds of an average adult’s body weight is fat. What percent of body weight is fat? % 2. About 60% of the human body is water. At this rate, how many pounds of water are in the body of a 95-pound person? lb For Problems 3–6, use a variable to represent each part, whole, or percent that is known. Set up and solve each proportion. 3. The width of a singles tennis court is 75% the width of a doubles court. A doubles court is 36 ft wide. How wide is a singles court? A singles court is ft wide. 4. Nadia put $500 into a savings account. At the end of 1 year, she had earned $30 in interest. What interest rate was the bank paying? 5. 15 is 6% of what number? (w(p ha or lt e) )  15 is 6% of . 6. 25% of what number is 10 1 2? (w(p ha or lt e) )  25% of is 10 1 2. (interest) (savings account) (width of singles court)(width of doubles court)  100  100 100 100 Practice 7. 52 36 3 8 8. 32 3 7 9 9. 23 51 3 4 10. 51 41 3 7  The bank was paying % interest.

LESSON 8 7 Name Date Time Fractions, Decimals, and Percents 258 Copyright © Wright Group/McGraw-Hill Shade the grid and fill in the numbers to represent the fractions your teacher assigns. 1. Ways of showing :  0.% 2. Ways of showing :  0.% 3. Ways of showing :  0.% 4. Ways of showing :  0.% 5. Ways of showing :  0.% 6. Ways of showing :  0.% 7. Ways of showing :  0.% 8. Ways of showing :  0.% 4 100 5 100 5 100 10 100 10 100 10 100 5 100 100% large square 5 100

LESSON 8 7 Name Date Time The World of Percents 259 Copyright © Wright Group/McGraw-Hill Solve. 1. If reduced-fat hot dogs have 8 fewer grams of fat than regular hot dogs, how much fat do regular hot dogs have? 2. If the public transportation system is currently collecting about $28,000 per day, what will it collect per day if it reaches its goal? 3. If 420 fewer people attended the concert series, what was the total attendance for the previous year? 4. Reginald read 168 pages of his book. He has 42 pages left. What percent of the book has he read? 5. Last year, Maria’s insect collection had 250 insects. She added 60 more to her collection this summer. By what percent did she increase her collection? 6. Jackie had a batting average of .250 for the season. If she went to bat 52 times during the season, how many hits did she get? (Hint:0.250 0.25 ___%) 7. Make up and solve a problem. Write it on the back of this page. Public Transportation Authority Aims to Increase Ridership by 25% Attendance at Music Hall Down 12% Over Previous Year for 10-Concert Series

STUDY LINK 8 8 Home Data Copyright © Wright Group/McGraw-Hill 260 Name Date Time 1. Record the following data about all the members of your household. a. Total number of people b. Number of males c. Number of females d. Number of left-handed people e. Number of right-handed people (For people who are ambidextrous, record the hand most often used for writing.) For the rectangles in this Study Link, use length as the measure of the longer sides and width as the measure of the shorter sides. 2. Find an American flag or a picture of one. Measure its length and width. a. length b. width (unit) (unit) 3. Measure the length and width of a television screen to the nearest 1 2inch. a. length b. width (unit) (unit) 4. Find 3 books of different sizes, such as a small paperback, your math journal, and a large reference book. Measure the length and width of each book to the nearest 1 2inch. a. Small book: length width (unit) (unit) b. Medium book: length width (unit) (unit) c. Large book: length width (unit) (unit) length width length diagonal width width length width length length width

STUDY LINK 8 8 Home Data continued 261 Name Date Time Copyright © Wright Group/McGraw-Hill 5. Find samples of the following items. Measure the length and width of each to the nearest 1 4inch. a. Postcard length width (unit) (unit) b. Index card length width (unit) (unit) c. Envelope (regular) length width (unit) (unit) d. Envelope (business) length width (unit) (unit) e. Notebook paper length width (unit) (unit) 6. Show the 4 rectangles below to each member of your household. Ask each person to select the rectangle that he or she likes best or thinks is the nicest looking. Tally the answers. Remember to include your own choice. 7. Measure the rise and run of stairs in your home. The diagram shows what these dimensions are. (If there are no stairs in your home, measure stairs outdoors or in a friend’s or neighbor’s home.) a. rise in. b. run in. A B C D Voting ResultsABCD Tally of Votes Number of Votes run rise Practice Round each quotient to the nearest tenth. 8. 327 4.9  9. 158 64.9  10. 686 96.1 

LESSON 8 8 Name Date Time Converting and Rounding 262 Copyright © Wright Group/McGraw-Hill One way to convert fractions to decimals and percents is to use a calculator. Depending on your calculator, to convert 3 7to a percent, press: 3 7 Display: 42.85714286% OR 3 7 100 Display: 42.857143 You can round decimals and percents when you want to estimate an answer or when you don’t need a precise measurement. For example, 42.85714286% rounded to the nearest whole percent is 43%. Use your calculator to convert each fraction in the table below to a decimal. Write all the digits shown in your calculator display. Then write the equivalent percent rounded to the nearest whole percent. The first row has been completed for you. d n Percent Fraction Decimal (rounded to nearest whole percent) 1 38 5 51. 42857143 51% 1 62 7 2 94 3 1 23 4 15 ,37 36 9 

LESSON 8 8 Name Date Time From Fractions to Percents 263 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Write ,  , or . 1. 13 1 30% 2. 1 4 8 9 35% 3. 2 38 5 80% 4. 1 25 4 60% 5. 30% 39 4 6. 45% 4 7 7. On the back of this page, explain how you got your answer to Problem 4. \ Circle the percent that is the best estimate for each fraction. 8. 13 7 25% 50% 75% 100% 9. 29 9 25% 50% 75% 100% 10. 6 7 25% 50% 75% 100% 11. 5 9 25% 50% 75% 100% LESSON 88 Name Date Time From Fractions to Percents Write ,  , or . 1. 13 1 30% 2. 1 4 8 9 35% 3. 2 38 5 80% 4. 1 25 4 60% 5. 30% 39 4 6. 45% 4 7 7. On the back of this page, explain how you got your answer to Problem 4. \ Circle the percent that is the best estimate for each fraction. 8. 1 3 7 25% 50% 75% 100% 9. 29 9 25% 50% 75% 100% 10. 6 7 25% 50% 75% 100% 11. 5 9 25% 50% 75% 100%      

LESSON 8 9 Name Date Time A Pizza Problem 264 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Math Message Zach and Regina both wanted cheese pizza. An 8-inch pizza costs $2 and a 12-inch pizza costs $4. Zach said that they should buy two 8-inch pizzas because the 12-inch pizza costs twice as much as the 8-inch pizza, and 2 times 8 is more than 12. Regina disagreed. She said that the 12-inch pizza was a better deal. Who was right? Explain your answer. LESSON 8 9 Name Date Time A Pizza Problem Math Message Zach and Regina both wanted cheese pizza. An 8-inch pizza costs $2 and a 12-inch pizza costs $4. Zach said that they should buy two 8-inch pizzas because the 12-inch pizza costs twice as much as the 8-inch pizza, and 2 times 8 is more than 12. Regina disagreed. She said that the 12-inch pizza was a better deal. Who was right? Explain your answer.

STUDY LINK 8 9 Scale Drawings 265 Name Date Time Copyright © Wright Group/McGraw-Hill Measure the object in each drawing to the nearest millimeter. Then use the size-change factor to determine the actual size of the object. 1. a. Diameter in drawing: b. Actual diameter: 2. a. Height in drawing: b. Actual height: 4. a. Height in drawing: b. Actual height: Size ChangeSize-change Factor Scale 2:1 Size ChangeSize-change Factor 1 4X Size ChangeSize-change Factor Scale 1:3 CRAFT GLUE 3. a. Length in drawing: b. Actual length: Size ChangeSize-change Factor Scale 3:1 Size-change Factor: glue bottlebutton insect watering can changed length actual length 121 122

LESSON 8 9 Name Date Time Considering Size Changes 266 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill A size change of “10 times as many” or “ 11 0as many” can mean a big difference when considering events or items. Complete the table below. Use the last row to write your own event or item. Original Measure 10 Times 11 0as Much Event or Item or Count as Much or Many or Many Length of your math journal (in millimeters) Length of your stride (in millimeters) Number of students in your math class Length of school day (in minutes) LESSON 8 9 Name Date Time Considering Size Changes A size change of “10 times as many” or “ 11 0as many” can mean a big difference when considering events or items. Complete the table below. Use the last row to write your own event or item. Original Measure 10 Times 11 0as Much Event or Item or Count as Much or Many or Many Length of your math journal (in millimeters) Length of your stride (in millimeters) Number of students in your math class Length of school day (in minutes)

LESSON 8 9 Name Date Time Reductions: Scale Models 267 Copyright © Wright Group/McGraw-Hill The dimensions in the drawing below are for a scale model of an actual car. Every length measured on the scale model is 31 0of the same length on the actual car. 31 0actual size Scale: 1:30 1 inch represents 30 inches. 1. Use the information in the drawing to find the dimensions of the actual car. a. length inches feet b. wheel base inches feet c. height inches feet d. door width inches feet 2. Aletta’s dad built her a dollhouse that is a scale model of the house pictured at the right. The model was built to a scale of 1 to 12. a. Find the dimensions of the scale model. length feet width feet height feet b. Find the area of the first floor. Scale model ft 2 Actual house ft 2 c. Find the following ratios. d. Compare the ratio of the lengths to the ratio of the areas. Are they the same? e. How many times greater is the ratio of the areas than the ratio of the lengths? 2 inches 5.3 inches 3.4 inches 1.3 inches height 27 ft width 18 ftlength 36 ft 1 ft 2 model length actual length 12 ft  1 ft  ft2 ft2 ft2 (first-floor area of actual house) (first-floor area of scale model) 1 ftft (length of actual house) (length of scale model)

LESSON 8 9 Name Date Time Perimeter of Figures 268 Copyright © Wright Group/McGraw-Hill Measure the sides of each polygon below to the nearest half-centimeter. Record your measurements next to the sides. Circle Enlargement or Reduction. Record the size-change factor. (Reminder: This is the ratio of the measures of the enlarged or reduced polygon to the measures of the original polygon.) Calculate the perimeter. 1. Perimeter 2. Perimeter 3. Perimeter 4. Explain how the perimeter and the size-change factor are related. Enlargement Reduction Size-change factor Perimeter Enlargement Reduction Size-change factor Perimeter Enlargement Reduction Size-change factor Perimeter

STUDY LINK 8 10 Similar Polygons 269 179 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Triangles JKLand RSTare similar. a. Find the ratio KL:ST. b. mR c. The length of R S  d.  2. Quadrangles ABCDand MLONare similar. a. The length of M N  b. The size-change factor: sla mrg ae llt tr ra ap pe ez zo oi id d  X 3. Find the distance (d) across the pond if the small triangle is similar to the large triangle. dm 30 m d 40 m 80 m 120 m FG H C B D A 108 N M LO? 12 perimeter of JKLperimeter of RST 1830 24 K JL Round each number to the nearest thousandth. 4. 0.00673 5. 63.4982 6. 4.8919 7. 5.9198 Practice 15 12 S RT

LESSON 8 10 Name Date Time Identifying Proportions 270 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Tell whether each pair of ratios forms a proportion. 1. 1 5, 12 0 2. 5 7, 7 9 3. 2 20 5, 1 26 0 4. 4 98, 1 36 5. 2 3, 1 28 1 6. 1 14 0, 7 50 0 7. 8 3, 2 94 8. 5 4, 2 10 2 9. 13 1, 1 31 Use each set of 4 numbers to form 2 proportions. 10. 3, 4, 24, 32 11. 5, 2, 20, 50 12. 7, 6, 30, 35 13. 220, 4, 1.5, 82.5 Tell whether each pair of ratios forms a proportion. 1. 1 5, 12 0 2. 5 7, 7 9 3. 2 20 5, 1 26 0 4. 4 98, 1 36 5. 2 3, 1 28 1 6. 1 14 0, 7 50 0 7. 8 3, 2 94 8. 5 4, 2 10 2 9. 13 1, 1 31 Use each set of 4 numbers to form 2 proportions. 10. 3, 4, 24, 32 11. 5, 2, 20, 50 12. 7, 6, 30, 35 13. 220, 4, 1.5, 82.5 LESSON 8 10 Name Date Time Identifying Proportions

LESSON 8 10 Name Date Time Cutting It Down to Size 271 Copyright © Wright Group/McGraw-Hill Use the grids to make 2 similar copies of the original design below. Make the copies so that they fit exactly on the grids provided. Figure out the scale you used to make each drawing. Scale Scale

LESSON 8 11 Name Date Time Survey Slips 272 Copyright © Wright Group/McGraw-Hill People in Your Household Number of males Number of females People in Your Household Number of males Number of females People in Your Household Number of males Number of females People in Your Household Number of males Number of females People in Your Household Number of males Number of females People in Your Household Number of males Number of females People in Your Household Number of males Number of females People in Your Household Number of males Number of females

STUDY LINK 8 11 Comparing Ratios 273 117–119 Name Date Time Copyright © Wright Group/McGraw-Hill 1. A dictionary measures 24 centimeters by 20 centimeters. The ratio of its length to its width is about to 1. Explain. 2. A sheet of legal-size paper measures 14 inches by 8 1 2inches. The ratio of its length to its width is about to 1. Is this the same ratio as for a sheet of paper that measures 11 inches by 8 1 2inches? Explain. 3. Jeffrey answered 28 out of 30 problems correctly on his math test. Lucille answered 47 out of 50 problems correctly on her math test. Who did better on the test? Explain. 4. A ruler is 30 centimeters long and 2.5 centimeters wide. The ratio of its length to its width is about to 1. 5. If a ruler is 33.6 centimeters long, how wide would it have to be to have the same length-to-width ratio as the ruler in Problem 4? centimeters Explain. Try This 6. 74 7. 366 8. 483 9. 806 º 12 º 58 º 32 º 157 Practice

274 Copyright © Wright Group/McGraw-Hill LESSON 8 11 Name-Collection Boxes Name Date Name Date Name Date Name Date

LESSON 8 11 Name Date Time Finding the Slope of a Line 275 Copyright © Wright Group/McGraw-Hill –1 –2 –3 –4 –5 12345 1 2 4 5 3 –1 –2 –3 –4 –50 x y –1 –2 –3 –4 –5 12345 1 2 4 5 3 –1 –2 –3 –4 –50 x y Just like stairs, a line has steepness, or slope. As you move from one point to another on a line, the vertical movement is called the riseand the horizontal movement is called the run. The slope of a line is the ratio of the rise to the run. Slope  r ri us ne The slope of the line above is 2 3. The slope of the line above is 2 1. Find the slope of each line. Slope  Slope  1. 2. –1 –2 –3 –4 –5 12345 1 2 4 5 3 –1 –2 –3 –4 –50 y x run rise –1 –2 –3 –4 –5 12345 1 2 4 5 3 –1 –2 –3 –4 –50 x run rise y

LESSON 8 11 Name Date Time Finding the Slope of a Line continued 276 Copyright © Wright Group/McGraw-Hill A line that moves upward A line that moves downward from left to right has from left to right has positive slope. negative slope. Slope  3 2 Slope  3 2 The slope of a line tells how the value of ychanges as the value of xchanges. You can find the slope of a line by choosing 2 points on the line and using the following formula: Slope , or Example:Find the slope of the line that passes through points (2,3) and (2,3). Slope   3 2 3 2    6 4  6 4 3 2 3. Find the slope of the line that passes through each pair of points. a. (2,1) and (5,3) b. (5,2) and (3,3) Slope Slope  c. (1,1) and (2,6) d. (2,5) and (6,1) Slope Slope  second yfirst ysecond xfirst x –1 –2 –3 –4 –5 12345 1 2 4 5 3 –1 –2 –3 –4 –50 x y –1 –2 –3 –4 –5 12345 1 2 4 5 3 –1 –2 –3 –4 –50 x y y x2 2 y x 1 1 

STUDY LINK 8 12 Rate and Ratio Review 277 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Match each ratio on the left with one of the ratios on the right. a. Circumference to diameter of a circle 1.6 to 1 b. Length to width of a Golden Rectangle 3 to 5 c. Diameter to radius of a circle 2 to 1 d. Length of one side of a square to another 3.14 to 1 e. 12 correct answers out of 20 problems 1 to 1 2. Refer to the following numbers to answer the questions below. 12345678910 a. What percent of the numbers are prime numbers? b. What is the ratio of numbers divisible by 3 to numbers divisible by 2? 3. A 12-pack of Chummy Cola costs $3 at Stellar Supermart. a. Complete the rate table at the right to find the per-unit rates. b. At this price, how much would 30 cans of Chummy Cola cost? c. How many cans could you buy for $2.00? 4. Complete or write a proportion for each problem. Then solve the problem. a. Only 4 9of the club members voted in the last election. There are 54 members in the club. How many members voted? Proportion 4 9 5x 4 Answer b. During basketball practice, Christina made 3 out of every 5 free throws she attempted. If she made 12 free throws, how many free throws did she attempt in all? Proportion Answer dollars 3.00 1.00 cans 112 109–119

STUDY LINK 8 12 Rate and Ratio Review continued Copyright © Wright Group/McGraw-Hill 278 Name Date Time 1 2 Scale: inch represents 1 00 feet. 5. a. Draw circles and squares so the ratio of circles to squares is 3 to 2 and the total number of shapes is 10. b. Draw circles and squares so the ratio of circles to total shapes is 2 to 3 and the total number of squares is 2. c. Draw circles and squares so the ratio of circles to squares is 1 to 3 and the total number of shapes is 12. 6. The city is planning to build a new park. The park will be rectangular in shape, approximately 800 feet long and 625 feet wide. Make a scale drawing of the park on the 1 2-inch grid paper below. 117–122

LESSON 8 12 Name Date Time Leonardo’s Rabbits 279 Copyright © Wright Group/McGraw-Hill In January, Leonardo began with 1 pair of baby rabbits. He kept track of his rabbits in a table. The row for January shows 1 pair of baby rabbits. In February, the baby rabbits grew to be adolescents. Leonardo still had 1 pair of rabbits. He recorded this information for February. In March, Leonardo’s pair of rabbits became parents—they had a pair of baby rabbits. He now had a total of 2 pairs of rabbits. In April, the baby rabbits born in March became adolescents. The parent pair also had another pair of baby rabbits. Leonardo now had 3 pairs of rabbits. The rabbits kept multiplying in this way. 1. Use these rules to fill in the table. Every month, the babies from the month before become adolescents. Every month, the adolescents from the month before become parents. The rabbits that were already parents become parents again. Every month, each pair of parents has a pair of baby rabbits. 2. Continue this number sequence. Each number is the sum of the two numbers before it. 112358 34 3. The numbers in Problem 2 are called the Fibonacci numbers. Where are the Fibonacci numbers in the table above? Month Parent Pairs Adolescent Pairs Baby PairsTotal Number of Pairs January 0011 February 0 1 0 1 March 1 0 1 2 April 1 1 1 3 May 2 1 2 5 June 3 2 3 8 July 535 August 8 5 8 21 September 8 October 13 55 November December 55

STUDY LINK 8 13 Unit 9: Family Letter Copyright © Wright Group/McGraw-Hill 280 Name Date Time More about Variables, Formulas, and Graphs You may be surprised at some of the topics that are covered in Unit 9. Several of them would be traditionally introduced in a first-year algebra course. If you are assisting your child, you might find it useful to refer to the Student Reference Bookto refresh your memory. Your child has been applying many mathematical properties, starting as early as first grade. In Unit 9, the class will explore and apply one of these properties, the distributive property, which can be stated as follows: For any numbers a, b,andc, a (bc)(ab)(ac). Students will use this property to simplify algebraic expressions. They will use these procedures, together with the equation-solving methods that were presented in Unit 6, to solve more difficult equations that contain parentheses or like terms on at least one side of the equal sign. Here is an example: To solve the equation 5(b3)3b54(b1), 1.Use the distributive property to remove the parentheses. 5b153b54b4 2.Combine like terms. 2b 204b4 3.Solve the equation. 20 2b4 242b b12 Much of Unit 9 also focuses on applying formulas—in computer spreadsheets and in calculating the areas of circles, rectangles, triangles, and parallelograms, the perimeters of polygons, and the circumferences of circles. Students will also use formulas for calculating the volumes of rectangular prisms, cylinders, and spheres to solve a variety of interesting problems. Finally, your child will be introduced to the Pythagorean theorem, which states that if aandbare the lengths of the legs of a right triangle and cis the length of the hypotenuse, thena 2b 2c 2. By applying this theorem, students will learn how to calculate long distances indirectly—that is, without actually measuring them. Please keep this Family Letter for reference as your child works through Unit 9.

281 Copyright © Wright Group/McGraw-Hill Vocabulary Important terms in Unit 9: Unit 9: Family Letter cont. STUDY LINK 813 combine like terms To rewrite the sum or difference of like termsas a single term. For example, 5a6acan be rewritten as 11a, because 5a6a(56)a11a. Similarly, 16t3t13t. Distributive Property of Multiplication over Addition A property relating multiplication to a sum of numbers by distributing a factor over the terms in the sum. For example, 2º(53)(2º5)(2º3) 10616. In symbols: For any numbers a, b,andc: aº(bc)(aºb)(aºc), ora(bc) ab ac Distributive Property of Multiplication over Subtraction A property relating multiplication to a difference of numbers by distributing a factor over the terms in the difference. For example, 2 º(53)(2º5)(2º3) 1064. In symbols: For any numbers a, b,andc: aº(bc)(aºb)(aºc), ora(bc) ab ac equivalent fractions Fractions with different denominators that name the same number. hypotenuse In a right triangle, the side opposite the right angle. indirect measurement The determination of heights, distances, and other quantities that cannot be directly measured. leg of a right triangle Either side of the right angle in a right triangle; a side that is not the hypotenuse. like terms In an algebraic expression, either the constant terms or any terms that contain the same variable(s) raised to the same power(s). For example, 4yand 7yare like terms in the expression 4y7yz. Pythagorean theorem If the legs of a right trianglehave lengths aandband the hypotenuse has length c, then a 2b 2c 2. simplify an expression To rewrite an expression by clearing grouping symbols and combining like termsand constants. hypotenuse leg leg 30 ft 5 ft 25 ft 6 ft c hypotenuseleg a b leg Indirect measurement lets you calculate the height of the tree from the other measure.

Copyright © Wright Group/McGraw-Hill 282 Unit 9: Family Letter cont. STUDY LINK 813 Do-Anytime Activities To work with your child on the concepts taught in this unit and previous units, try these interesting and rewarding activities: 1.To practice simplifying expressions and solving equations, ask your child to bring home the game materials for Algebra Election.Game directions are in the Student Reference Book. 2.If you have any mobiles in your home, ask your child to explain to you how to perfectly balance one. Have your child show you the equations he or she used to balance it. 3.Your child may need extra practice with the partial-quotients division algorithm. Have him or her show you this method. Provide a few problems to practice at home, and have your child explain the steps to you while working through them. Study Link 9 1 1. a.(8º4)(7º4)b.(8º6)(5º6) 4º(78) 6 º(58) c.(49)º3 (8 5)º6 (9º3)(4º3) 2. a.6 b.(93)º530 (9 º5)(3º5)30 3. a.Nb.Oc.O d.Ne.Pf.O 4.3.92 (8 º0.10)(8º0.39)3.92 Study Link 9 2 1. a.(7º3)(7º4) b.(7º3)(7º) c.(7º3)(7ºy) d.(7º3)(7º(2º4)) e.(7º3)(7º(2º)) f.(7º3)(7º(2ºy)) 2. b.(20 º42)(20º19)840380460 c.(32º40)(50º40)1,2802,0003,280 d.(90º11)(8º11)99088902 e. (9º15)(9º25)135225360 3. a.(80º5)(120º5)(80120)º5 c.12(dt)12d12t d.(ac)ºn(aºn)(cºn) f.(9º 1 2)( 1 3º 1 2)(9 1 3)º 1 2 4.35. 1 11 4 6. 58 7 As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through some of the Unit 9 Study Links.

283 Copyright © Wright Group/McGraw-Hill Unit 9: Family Letter cont. STUDY LINK 813 Study Link 9 3 1.15x 2. 13 0y 3.11 t 4.d 5. 6 6.3p 7.3 8.8.3 9. 7b  14 10.1 1 6a 1 4t 11. 53 12.23 13.132 14.19 Study Link 9 4 1. 45f 109 2.12m 3.32k 44 4. y 2b  24 5. 65,800 6.0.2348 7.0.5163 8.0.0796 Study Link 9 5 Column 1 Column 2 A. 4x  2 6C6 j 8 8 6j Solution: x 2A2 c 1 3 B6 w 12 C 2 2 h h 1 A 3 3 q 6 4 A3( r 4) 18 B. 3s  6 C 2(5 x 1) 10x 2 Solution: s 2 A5x  5(2 x)  2(x 7) D s 0 B5 b 3 2b  6b  3 C. 3y  2y  y B 4t 3 2 1 2 Solution: y A6z 12 any number D 2 a (4 7)a D. 5a  7a Solution: a 0 1. 2 5 2. 10 2 3.5 4 4. 4 1 Study Link 9 6 1.7 2.38 3.4 4.2 5. 23 14y 6.2b  32 7. 3f  55 10 k 8.225 35g 9. r 23 10.4b  72; 72 ( 4b) 11. W5b; D 4; w 30; d 12 Equation: 5 b* 4 30 * 12; Solution: b 18 Weight of the object on the left: 90 12. 5 1 21 4 13. 92 14.5 5 7 Study Link 9 7 3.2.7 feet Study Link 9 8 1.112 in. 2 2.2.5 ft 2 3.108 cm 2 4.45.5 mm 2 5.55 ft 2 6.696 m 2 7.aº b 8.(n  m)º y 9. 63.6 10.0.1 Study Link 9 9 1.120 in. 3 2.904.32 in. 3 3.11.97 in. 2 4.10.4 m 3 5.3,391 yd 2 6.3.22 ft 3 7.95 8.37.8 9.1,400 Study Link 9 10 1.Answers vary. 2.Answers vary. 3. 13.48 4.17.62

Copyright © Wright Group/McGraw-Hill 284 Study Link 9 11 1. a.C 5 9º (77 32); 25°C b. 50 5 9º(F  32); 122 F 2. a. A 1 2º 17 º5; 42.5 cm 2 b. 90 1 2º12 ºh; 15 in. 3. a. V 1 3º º 4º 9; 37.68 in. 3 b. 94.2  1 3ºº 9º h; 10 cm Study Link 9 12 1. 12 2.200 3.30 4.0.4 5. 1 5 1 6. 100 7.3.46 8.7.14 9. 7.94 10.25 m 11.9.8 ft 12.22 yd 13. 127.3 ft 14. 18 15.23 Study Link 9 13 1. a. 7x b.4x  7 c.6x  2 d.6 2. Sample answer: Liani did not multiply 10 by 8. The simplified expression should be 8 x 80. 3. a. x 10 b.g 5 c. y 4 d.x 14 4. Length of AB:5 in.; Length of BC:8 in.; Length of AC:5 in. 5. 6 cm 2 6.4 blocks 7. 1.5 8.1.75 9.0.6 Unit 9: Family Letter cont. STUDY LINK 813