Ratios and Proportions

Transcription

1 . Ratios and Rates Ratios and Proportions. Proportions. Writing Proportions. Solving Proportions. Slope. Direct Variation I am doing an eperiment with slope. I want ou to run up and down the board 0 times. Now with more dog biscuits, do it again and we ll compare our rates. Dear Sir: I counted the number of bacon, cheese, and chicken dog biscuits in the bo I bought. There were bacon, cheese, and onl chicken. That s a ratio of ::. Please go back to the original ratio of ::.

2 What You Learned Before (MACC..NF..) I wonder if our rate is proportional to the slope of the hill. Eample Simplif 0. Eample Simplif. = 0 = Eample Is (MACC..NF..) equivalent to 0? Eample Is equivalent to? = 0 = 9 is equivalent to. 0 is not equivalent to. (MACC..EE..7) Eample Solve =. = = = Write the equation. Division Propert of Equalit Simplif. Check = () =? = Simplif Are the fractions equivalent? Eplain.. 0 =?. =? 7. 0 =?. =? Solve the equation. Check our solution. 9. = = 0.a. w = 9. 7 n =

3 . Ratios and Rates real-life problems? How do rates help ou describe Rate When ou rent snorkel gear at the beach, ou should pa attention to the rental rate. The rental rate is in dollars per hour. ACTIVITY: Finding Reasonable Rates Work with a partner. a. Match each description with a verbal rate. b. Match each verbal rate with a numerical rate. c. Give a reasonable numerical rate for each description. Then give an unreasonable rate. Description Verbal Rate Numerical Rate Your running rate in a 00-meter dash Dollars per ear in. r The fertilization rate for an apple orchard Inches per ear lb acre The average pa rate for a professional athlete Meters per second $ r COMMON CORE Ratios and Rates In this lesson, ou will find ratios, rates, and unit rates. find ratios and rates involving ratios of fractions. Learning Standards MACC.7.RP.. MACC.7.RP.. The average rainfall rate in a rain forest Work with a partner. Describe a situation where the given epression ma appl. Show how ou can rewrite each epression as a division problem. Then simplif and interpret our result. a. ACTIVITY: Simplifing Epressions That Contain Fractions c fl oz b. Pounds per acre m sec in. sec c. c sugar c flour d. gal sec 9 Chapter Ratios and Proportions

4 ACTIVITY: Using Ratio Tables to Find Equivalent Rates Work with a partner. A communications satellite in orbit travels about miles ever seconds. a. Identif the rate in this problem. b. Recall that ou can use ratio tables to find and organize equivalent ratios and rates. Complete the ratio table below. Time (seconds) 0 Distance (miles) c. How can ou use a ratio table to find the speed of the satellite in miles per minute? miles per hour? d. How far does the satellite travel in second? Solve this problem () b using a ratio table and () b evaluating a quotient. e. How far does the satellite travel in second? Eplain our steps. Math Practice View as Components What is the product of the numbers? What is the product of the units? Eplain. ACTIVITY: Unit Analsis Work with a partner. Describe a situation where the product ma appl. Then find each product and list the units. mi a. 0 gal gal b. 7 lb $ lb c. 0 ft sec sec. IN YOUR OWN WORDS How do rates help ou describe real-life problems? Give two eamples.. To estimate the annual salar for a given hourl pa rate, multipl b and insert 000 at the end. Sample: $0 per hour is about $0,000 per ear. a. Eplain wh this works. Assume the person is working 0 hours a week. b. Estimate the annual salar for an hourl pa rate of $ per hour. c. You earn $ million per month. What is our annual salar? d. Wh is the cartoon funn? We had someone appl for the job. He sas he would like $ million a month, but will settle for $ an hour. Use what ou discovered about ratios and rates to complete Eercises 7 0 on page 0. Section. Ratios and Rates 99

5 . Lesson Lesson Tutorials Ke Vocabular ratio, p. 00 rate, p. 00 unit rate, p. 00 comple fraction, p. 0 A ratio is a comparison of two quantities using division., to, : A rate is a ratio of two quantities with different units. 0 miles hours A rate with a denominator of is called a unit rate. 0 miles hour EXAMPLE Finding Ratios and Rates There are males and 0 females in a subwa car. The subwa car travels. miles in minutes. a. Find the ratio of males to females. males females = 0 = The ratio of males to females is. b. Find the speed of the subwa car.. mi. miles in minutes = min =. mi min The speed is 0. mile per minute. = 0. mi min EXAMPLE Finding a Rate from a Ratio Table The ratio table shows the costs for different amounts of artificial turf. Find the unit rate in dollars per square foot. Amount (square feet) Cost (dollars) Remember The abbreviation ft means square feet. Use a ratio from the table to find the unit rate. cost amount = $00 Use the first ratio in the table. ft = $ ft Simplif. So, the unit rate is $ per square foot. 00 Chapter Ratios and Proportions

6 Eercises. In Eample, find the ratio of females to males.. In Eample, find the ratio of females to total passengers.. The ratio table shows the distance that the International Space Station travels while orbiting Earth. Find the speed in miles per second. Time (seconds) 9 Distance (miles) A comple fraction has at least one fraction in the numerator, denominator, or both. You ma need to simplif comple fractions when finding ratios and rates. EXAMPLE Finding a Rate from a Graph Distance (miles) 0 0 Subwa Car Speed ), ) ), ) 7 Time (minutes) The graph shows the speed of a subwa car. Find the speed in miles per minute. Compare the speed to the speed of the subwa car in Eample. Step : Choose and interpret a point on the line. ) The point (, indicates that the subwa car travels mile in minute. Step : Find the speed. distance traveled = elapsed time miles minutes = = = Rewrite the quotient. Simplif. The speed of the subwa car is mile per minute. Because mile per minute = 0. mile per minute, the speeds of the two subwa cars are the same. Eercise. You use the point (, ) our answer change? Eplain our reasoning. to find the speed of the subwa car. Does Section. Ratios and Rates 0

7 Math Practice EXAMPLE Analze Givens What information is given in the problem? How does this help ou know that the ratio table needs a total column? Eplain. Solving a Ratio Problem You mi cup of ellow paint for ever cup of blue paint to make cups of green paint. How much ellow paint and blue paint do ou use? Method : The ratio of ellow paint to blue paint is to. Use a ratio table to find an equivalent ratio in which the total amount of ellow paint and blue paint is cups. Yellow (cups) Blue (cups) Total (cups) + = 9 So, ou use cups of ellow paint and 9 cups of blue paint. Method : Use the fraction of the green paint that is made from ellow paint and the fraction of the green paint that is made from blue paint. You use cup of ellow paint for ever cup of blue paint, so the fraction of the green paint that is made from ellow paint is ellow green + = = =. Similarl, the fraction of the green paint that is made from blue paint is blue green + = = =. So, ou use = cups of ellow paint and blue paint. = 9 cups of Eercises and. How much ellow paint and blue paint do ou use to make 0 cups of green paint? 0 Chapter Ratios and Proportions

8 . Eercises Help with Homework. VOCABULARY How can ou tell when a rate is a unit rate?. WRITING Wh do ou think rates are usuall written as unit rates?. OPEN-ENDED Write a real-life rate that applies to ou. Estimate the unit rate.. $7.7. $.9. $. Grade AA Eggs 9+(-)= +(-)= +(-9)= 9+(-)= Find the product. List the units. 7. h $9 h. lb $.0 lb 9. 9 sec 0 MB sec 0. h 9 mi h Write the ratio as a fraction in simplest form.. to. :. girls : bos. correct : 9 incorrect. dogs to cats. feet : feet Find the unit rate miles in hours. miles per gallons 9. $9.0 for pounds 0. $.0 for cans. 97 words in. minutes. meters in hours Use the ratio table to find the unit rate with the specified units.. servings per package. feet per ear Packages 9 Servings Years 0 Feet DOWNLOAD At :00 p.m., ou have megabtes of a movie. At : p.m., ou have 9 megabtes. What is the download rate in megabtes per minute? Section. Ratios and Rates 0

9 . POPULATION In 007, the U.S. population was 0 million people. In 0, it was million. What was the rate of population change per ear? 7. PAINTING A painter can paint 0 square feet in. hours. What is the painting rate in square feet per hour?. TICKETS The graph shows the cost of buing tickets to a concert. a. What does the point (, ) represent? b. What is the unit rate? c. What is the cost of buing 0 tickets? 9. CRITICAL THINKING Are the two statements equivalent? Eplain our reasoning. The ratio of bos to girls is to. Cost (dollars) Concert (, ) (, ) (, ) 7 Tickets The ratio of girls to bos is to. 0. TENNIS A sports store sells three different packs of tennis balls. Which pack is the best bu? Eplain.. FLOORING It costs $ for square feet of flooring. How much does it cost for square feet of flooring?. OIL SPILL An oil spill spreads square meters ever hour. How much area does the oil spill cover after hours?. JUICE You mi cup of juice concentrate for ever cups of water to make cups of juice. How much juice concentrate and water do ou use?. LANDSCAPING A supplier sells pounds of mulch for ever pounds of gravel. The supplier sells 7 pounds of mulch and gravel combined. How man pounds of each item does the supplier sell?. HEART RATE Your friend s heart beats times in seconds when at rest. While running, our friend s heart beats times in 0 seconds. a. Find the heart rate in beats per minute at rest and while running. b. How man more times does our friend s heart beat in minutes while running than while at rest? 0 Chapter Ratios and Proportions

10 . PRECISION The table shows nutritional information for three beverages. a. Which has the most calories per fluid ounce? b. Which has the least sodium per fluid ounce? Beverage Serving Size Calories Sodium Whole milk c 9 mg Orange juice pt 0 0 mg Apple juice fl oz mg 7. RESEARCH Fire hdrants are painted one of four different colors to indicate the rate at which water comes from the hdrant. a. Use the Internet to find the ranges of the rates for each color. b. Research wh a firefighter needs to know the rate at which water comes out of a hdrant.. PAINT You mi cup of red paint for ever cup of blue paint to make gallons of purple paint. a. How much red paint and blue paint do ou use? b. You decide that ou want to make a lighter purple paint. You make the new miture b adding 0 cup of white paint for ever cup of red paint and cup of blue paint. How much red paint, blue paint, and white paint do ou use to make gallon of lighter purple paint? 9. You and a friend start hiking toward each other from opposite ends of a 7.-mile hiking trail. You hike mile ever hour. Your friend hikes miles per hour. a. Who hikes faster? How much faster? b. After how man hours do ou meet? c. When ou meet, who hiked farther? How much farther? Cop and complete the statement using <, >, or =. (Section.) MULTIPLE CHOICE Which fraction is greater than and less than? (Section.) A B 7 C D Section. Ratios and Rates 0

11 . Proportions How can proportions help ou decide when things are fair? Proportional When ou work toward a goal, our success is usuall proportional to the amount of work ou put in. An equation stating that two ratios are equal is a proportion. ACTIVITY: Determining Proportions Work with a partner. Tell whether the two ratios are equivalent. If the are not equivalent, change the net da to make the ratios equivalent. Eplain our reasoning. a. On the first da, ou pa $ for boes of popcorn. The net da, ou pa $7.0 for boes. b. On the first da, it takes ou hours to drive 7 miles. The net da, it takes ou hours to drive 00 miles. COMMON CORE Proportions In this lesson, ou will use equivalent ratios to determine whether two ratios form a proportion. use the Cross Products Propert to determine whether two ratios form a proportion. Learning Standard MACC.7.RP..a 0 Chapter c. On the first da, ou walk miles and burn 00 calories. The net da, ou walk miles and burn 0 calories. First Da $.00? $7.0 boes boes = First Da paint 00 square feet in hours. Ratios and Proportions Net Da? h = h 7 mi First Da 00 mi Net Da mi mi? = 00 cal 0 cal d. On the first da, ou paint 0 square First Da feet in hours. The net da, ou Net Da Net Da 0 ft? 00 ft = h h

12 ACTIVITY: Checking a Proportion Work with a partner. a. It is said that one ear in a dog s life is equivalent to seven ears in a human s life. Eplain wh Newton thinks he has a score of 0 points. Did he solve the proportion correctl? ear points =? 7 ears 0 points b. If Newton thinks his score is 9 points, how man points does he actuall have? Eplain our reasoning. I got on m online test. That s 0 in dog points! Isn t that an A+? ACTIVITY: Determining Fairness Math Practice Justif Conclusions What information can ou use to justif our conclusion? Work with a partner. Write a ratio for each sentence. Compare the ratios. If the are equal, then the answer is It is fair. If the are not equal, then the answer is It is not fair. Eplain our reasoning. a. b. You pa $ for tickets to a concert. You get 7 points for answering questions correctl. & & I pa $ for tickets to the same concert. I get 70 points for answering questions correctl. Is this fair? Is this fair? c. You trade football cards for baseball cards. & I trade 0 football cards for baseball cards. Is this fair?. Find a recipe for something ou like to eat. Then show how two of the ingredient amounts are proportional when ou double or triple the recipe.. IN YOUR OWN WORDS How can proportions help ou decide when things are fair? Give an eample. Use what ou discovered about proportions to complete Eercises 0 on page 0. Section. Proportions 07

13 . Lesson Lesson Tutorials Ke Vocabular proportion, p. 0 proportional, p. 0 cross products, p. 09 Proportions Words Numbers A proportion is an equation stating that two ratios are equivalent. Two quantities that form a proportion are proportional. = The proportion is read is to as is to. EXAMPLE Determining Whether Ratios Form a Proportion Tell whether and form a proportion. Compare the ratios in simplest form. = = = = The ratios are not equivalent. EXAMPLE So, and do not form a proportion. Determining Whether Two Quantities Are Proportional Reading Two quantities that are proportional are in a proportional relationship. Tell whether and are proportional. Compare each ratio to in simplest form. = 9 = The ratios are equivalent. So, and are proportional. = 9 Tell whether the ratios form a proportion. Eercises., 0.,. 0,. 0,. Tell whether and are proportional. Birdhouses Built, Nails Used, 7 0 Chapter Ratios and Proportions

14 Stud Tip You can use the Multiplication Propert of Equalit to show that the cross products are equal. a b = c d bd a b = bd c d ad = bc Cross Products In the proportion a b = c cross products. d, the products a d and b Cross Products Propert Words The cross products of a proportion are equal. Numbers = Algebra a b = c d c are called = ad = bc, where b 0 and d 0 EXAMPLE Identifing Proportional Relationships You swim our first laps in. minutes. You complete laps in minutes. Is the number of laps proportional to our time? Method : Compare unit rates.. min laps = 0. min lap min laps = 0.7 min lap The unit rates are not equivalent. length lap So, the number of laps is not proportional to the time. Method : Use the Cross Products Propert.. min laps =? min laps Test to see if the rates are equivalent.. =? Find the cross products.. The cross products are not equal. So, the number of laps is not proportional to the time. Eercises 0. You read the first 0 pages of a book in minutes. You read pages in minutes. Is the number of pages read proportional to our time? Section. Proportions 09

15 . Eercises Help with Homework. VOCABULARY What does it mean for two ratios to form a proportion?. VOCABULARY What are two was ou can tell that two ratios form a proportion?. OPEN-ENDED Write two ratios that are equivalent to.. WHICH ONE DOESN T BELONG? Which ratio does not belong with the other three? Eplain our reasoning. 0 9+(-)= +(-)= +(-9)= 9+(-)= Tell whether the ratios form a proportion.., 7., 0 7.,., , 0. 7,. 7,. 0, Tell whether and are proportional Tell whether the two rates form a proportion.. 7 inches in 9 hours; inches in hours. plaers from teams; plaers from teams 7. 0 calories in servings; 00 calories in servings. 0 units made in das; units made in das 9. wins in games; 99 wins in games 0. hits in 7 at bats; hits in at bats. FITNESS You can do 90 sit-ups in minutes. Your friend can do sit-ups in minutes. Do these rates form a proportion? Eplain.. HEART RATES Find the heart rates of Heartbeats Seconds ou and our friend. Do these rates You 0 form a proportion? Eplain. Friend 0 Chapter Ratios and Proportions

16 Tell whether the ratios form a proportion..., 7.. to, to. :, : 0. PAY RATE You earn $ walking our neighbor s dog for hours. Your friend earns $ painting our neighbor s fence for hours. a. What is our pa rate? b. What is our friend s pa rate? c. Are the pa rates equivalent? Eplain. 7. GEOMETRY Are the heights and bases of the two triangles proportional? Eplain. b cm h cm h cm b 0 cm. BASEBALL A pitcher coming back from an injur limits the number of pitches thrown in bull pen sessions as shown. a. Which quantities are proportional? b. How man pitches that are not curveballs do ou think the pitcher will throw in Session? Session Number, Pitches, Curveballs, z NAIL POLISH A specific shade of red nail polish requires 7 parts red to parts ellow. A miture contains quarts of red and quarts of ellow. How can ou fi the miture to make the correct shade of red? 0. COIN COLLECTION The ratio of quarters to dimes in a coin collection is :. You add the same number of new quarters as dimes to the collection. a. Is the ratio of quarters to dimes still :? b. If so, illustrate our answer with an eample. If not, show wh with a countereample.. AGE You are ears old, and our cousin is 9 ears old. As ou grow older, is our age proportional to our cousin s age? Eplain our reasoning.. Ratio A is equivalent to Ratio B. Ratio B is equivalent to Ratio C. Is Ratio A equivalent to Ratio C? Eplain. Add or subtract. (Section. and Section.) ( ) ( ) 7. MULTIPLE CHOICE Which fraction is not equivalent to? (Skills Review Handbook) A B C D 9 Section. Proportions

17 Etension. Graphing Proportional Relationships Lesson Tutorials Recall that ou can graph the values from a ratio table Time, (seconds) Height, (meters) Height (meters) (, ) (, ) (9, ) (, ) Time (seconds) The structure in the ratio table shows wh the graph has a constant rate of change. You can use the constant rate of change to show that the graph passes through the origin. The graph of ever proportional relationship is a line through the origin. EXAMPLE Determining Whether Two Quantities Are Proportional Use a graph to tell whether and are in a proportional relationship. a. 0 b. Plot (, ), (, ), and (, 0). Plot (, ), (, ), and (, ). Draw a line through the points. Draw a line through the points. COMMON CORE Proportions In this etension, ou will use graphs to determine whether two ratios form a proportion. interpret graphs of proportional relationships. Learning Standards MACC.7.RP..a MACC.7.RP..b MACC.7.RP..d (, ) 0 0 (, 0) (, ) The graph is a line that does not pass through the origin. So, and are not in a proportional relationship. (, ) (, ) (, ) 0 0 The graph is a line that passes through the origin. So, and are in a proportional relationship. Use a graph to tell whether and are in a proportional relationship Chapter Ratios and Proportions

18 EXAMPLE Interpreting the Graph of a Proportional Relationship Stud Tip In the graph of a proportional relationship, ou can find the unit rate from the point (, ). The graph shows that the distance traveled b the Mars rover Curiosit is proportional to the time traveled. Interpret each plotted point in the graph. (0, 0): The rover travels 0 inches in 0 seconds. (,.): The rover travels. inches in second. So, the unit rate is. inches per second. (,.): The rover travels. inches in seconds. Because the relationship is proportional, ou can also use this point to find the unit rate.. in. sec =. in., or. inches per second sec Curiosit Rover at Top Speed Distance (inches) 0 0 (,.) (0, 0) (,.) 7 Time (seconds) Interpret each plotted point in the graph of the proportional relationship.. Mone. Hot-Air Balloon Earnings (dollars) (, 0) (, ) (0, 0) 7 Hours worked Height (feet) (0, 0) (, 0) (, ) 7 Seconds Tell whether and are in a proportional relationship. If so, find the unit rate.. (hours) 7 0 (feet) 0 0. Let be the temperature hours after midnight. The temperature is 0 F at midnight and decreases F ever hour. 7. REASONING The graph of a proportional relationship passes through (, ) and (, ). Find.. MOVIE RENTAL You pa $ to rent a movie plus an additional $0.0 per da until ou return the movie. Your friend pas $. per da to rent a movie. a. Make tables showing the costs to rent a movie up to das. b. Which person pas an amount proportional to the number of das rented? Etension. Graphing Proportional Relationships

19 . Writing Proportions problem in real life? How can ou write a proportion that solves a ACTIVITY: Writing Proportions Work with a partner. A rough rule for finding the correct bat length is the bat length should be half of the batter s height. So, a -inch-tall batter uses a bat that is inches long. Write a proportion to find the bat length for each given batter height. a. inches b. 0 inches c. inches ACTIVITY: Bat Lengths Work with a partner. Here is a more accurate table for determining the bat length for a batter. Find all the batter heights and corresponding weights for which the rough rule in Activit is eact. Height of Batter (inches) Over 7 COMMON CORE Proportions In this lesson, ou will write proportions. solve proportions using mental math. Learning Standards MACC.7.RP..c MACC.7.RP.. Weight of Batter (pounds) Under Over 0 Chapter Ratios and Proportions

20 ACTIVITY: Writing Proportions Math Practice Evaluate Results How do ou know if our results are reasonable? Eplain. Work with a partner. The batting average of a baseball plaer is the number of hits divided b the number of at bats. hits (H) batting average = at bats (A) A plaer whose batting average is 0.0 is said to be batting 0. Actual hits Actual at bats 0 hits 0 at bats = 0.0 = 0 hits 000 at bats Batting 0 out of 000 Batting average Write a proportion to find how man hits H a plaer needs to achieve the given batting average. Then solve the proportion. a. 0 times at bat; batting average is b. times at bat; batting average is 0.0. c. 0 times at bat; batting average is 0.0. d. time at bat; batting average is IN YOUR OWN WORDS How can ou write a proportion that solves a problem in real life?. Two plaers have the same batting average. At Bats Hits Batting Average Plaer Plaer Plaer gets four hits in the net five at bats. Plaer gets three hits in the net three at bats. a. Who has the higher batting average? b. Does this seem fair? Eplain our reasoning. Use what ou discovered about proportions to complete Eercises 7 on page. Section. Writing Proportions

21 . Lesson Lesson Tutorials One wa to write a proportion is to use a table. Last Month This Month Purchase ringtones ringtones Total Cost dollars dollars Use the columns or the rows to write a proportion. Use columns: ringtones dollars = ringtones dollars Numerators have the same units. Denominators have the same units. Use rows: ringtones ringtones = dollars dollars The units are the same on each side of the proportion. EXAMPLE Writing a Proportion Black Bean Soup. cups black beans 0. cup salsa cups water tomato teaspoons seasoning A chef increases the amounts of ingredients in a recipe to make a proportional recipe. The new recipe has cups of black beans. Write a proportion that gives the number of tomatoes in the new recipe. Organize the information in a table. Original Recipe New Recipe Black Beans. cups cups Tomatoes tomato tomatoes. cups beans cups beans One proportion is = tomato tomatoes. Eercises. Write a different proportion that gives the number of tomatoes in the new recipe.. Write a proportion that gives the amount of water in the new recipe. Chapter Ratios and Proportions

22 EXAMPLE Solving Proportions Using Mental Math Solve =. Step : Think: The product of and what number is? =? = Step : Because the product of and is, multipl the numerator b to find. = = = The solution is =. EXAMPLE Solving Proportions Using Mental Math In Eample, how man tomatoes are in the new recipe? Solve the proportion. =. cups black beans tomatoes Step : Think: The product of Step : Because the product of. and what number is?. and is, multipl the denominator b to find..? =. =. =. = = So, there are tomatoes in the new recipe. Solve the proportion. Eercises. = 0 d. 7 z = 0. =. A school has 90 students. The ratio of female students to all students is. Write and solve a proportion to find the 9 number f of students who are female. Section. Writing Proportions 7

23 . Eercises Help with Homework. WRITING Describe two was ou can use a table to write a proportion.. WRITING What is our first step when solving =? Eplain.. OPEN-ENDED Write a proportion using an unknown value and the ratio :. Then solve it. 9+(-)= +(-)= +(-9)= 9+(-)= Write a proportion to find how man points a student needs to score on the test to get the given score.. test worth 0 points; test score of 0%. test worth 0 points; test score of 7%. test worth 0 points; test score of 0% 7. test worth 0 points; test score of 9% Use the table to write a proportion.. Game Game Points Shots w 9. Ma June Winners n Entries Toda Yesterda Miles m Hours.. Race Race Meters Seconds.. ERROR ANALYSIS Describe and correct the error in writing the proportion. Monda Tuesda Dollars.0 d Ounces.0 = d. T-SHIRTS You can bu T-shirts for $. Write a proportion that gives the cost c of buing 7 T-shirts.. COMPUTERS A school requires computers for ever students. Write a proportion that gives the number c of computers needed for students.. SWIM TEAM The school team has 0 swimmers. The ratio of seventh-grade swimmers to all swimmers is :. Write a proportion that gives the number s of seventh-grade swimmers. Chapter Ratios and Proportions

24 Solve the proportion.. = z 0 7. =. k = 7 9. = c 0. b = 9... = g. ORCHESTRA In an orchestra, the ratio of trombones to violas is to. a. There are 9 violas. Write a proportion that gives the number t of trombones in the orchestra. b. How man trombones are in the orchestra?. ATLANTIS Your science teacher has a : 00 scale model of the space shuttle Atlantis. Which of the proportions can ou use to find the actual length of Atlantis? Eplain. = 9. = 00 = = cm. YOU BE THE TEACHER Your friend sas =. Is our friend right? Eplain. Solve =.. There are 0 white lockers in the school. There are white lockers for ever blue lockers. How man lockers are in the school? Solve the equation. (Section.). = 7. = 7. 0 = 9. = 0. MULTIPLE CHOICE What is the value of 9 + A 7 0 B 7 0 C 0? (Section.) D 0 Section. Writing Proportions 9

25 Stud Help Graphic Organizer You can use an information wheel to organize information about a concept. Here is an eample of an information wheel for ratio. a comparison of two quantities using division to : Ratio You can write ratios in different was. If the two quantities have different units, then the ratio is called a rate. Make information wheels to help ou stud these topics.. rate. unit rate. proportion. cross products. graphing proportional relationships After ou complete this chapter, make information wheels for the following topics.. solving proportions 7. slope. direct variation M information wheel summarizes how cats act when the get baths. 0 Chapter Ratios and Proportions

26 .. Quiz Progress Check Write the ratio as a fraction in simplest form. (Section.). red buttons : blue buttons. inches to inch Use the ratio table to find the unit rate with the specified units. (Section.). cost per song. gallons per hour Songs 0 Cost $0 $.9 $.9 $.9 Hours 9 Gallons 0.. Tell whether the ratios form a proportion. (Section.).,., , Tell whether the two rates form a proportion. (Section.). 7 miles in hours; 0 miles in hours 9. gallons in minutes; gallons in 7 minutes 0. 0 steps in 0 feet; 7 steps in feet. rotations in 7 das; rotations in 70 das Use the table to write a proportion. (Section.). Monda Tuesda. Series Series Dollars Games g Hours h Wins. MUSIC DOWNLOAD The amount of time needed to download music is shown in the table. Find the unit rate in megabtes per second. (Section.) Seconds Megabtes. SOUND The graph shows the distance that sound travels through steel. Interpret each plotted point in the graph of the proportional relationship. (Section.). GAMING You advance levels in minutes. Your friend advances levels in 0 minutes. Do these rates form a proportion? Eplain. (Section.) 7. CLASS TIME You spend 0 minutes in classes. Write and solve a proportion to find how man minutes ou spend in classes. (Section.) Distance (km) Sound through Steel (, ) 9 (, ) 0 0 Time (seconds) Sections.. Quiz

27 . Solving Proportions products to solve proportions? How can ou use ratio tables and cross ACTIVITY: Solving a Proportion in Science Work with a partner. You can use ratio tables to determine the amount of a compound (like salt) that is dissolved in a solution. Determine the unknown quantit. Eplain our procedure. a. Salt Water Salt Water L L Salt 0 g g L = Write proportion. = = Simplif. Set cross products equal. liter liters There are grams of salt in the -liter solution. b. White Glue Solution Water cup cup White Glue cup cups Recipe for c. Bora Solution COMMON CORE Proportions In this lesson, ou will solve proportions using multiplication or the Cross Products Propert. use a point on a graph to write and solve proportions. Learning Standards MACC.7.RP..b MACC.7.RP..c Bora tsp tsp Water cup cups d. Slime (See recipe.) Bora Solution White Glue Solution cup cup cups cups Chapter Ratios and Proportions

28 Math Practice Use Operations How can ou use the name of the game to determine which operation to use? ACTIVITY: The Game of Criss Cross Preparation: Cut inde cards to make plaing cards. Write each number on a card.,,,,,,,,,,,,,,,,,, 7, 7, 7,,,, 9, 9, 9, 0, 0, 0,,,,,,,,,,,,,,,,, 0, Make a cop of the game board. To Pla: Pla with a partner. Deal eight cards to each plaer. Begin b drawing a card from the remaining cards. Use four of our cards to tr to form a proportion. La the four cards on the game board. If ou form a proportion, then sa Criss Cross. You earn points. Place the four cards in a discard pile. Now it is our partner s turn. If ou cannot form a proportion, then it is our partner s turn. When the original pile of cards is empt, shuffle the cards in the discard pile. Start again. The first plaer to reach 0 points wins. CRISS CROSS. IN YOUR OWN WORDS How can ou use ratio tables and cross products to solve proportions? Give an eample.. PUZZLE Use each number once to form three proportions. 0 0 Use what ou discovered about solving proportions to complete Eercises 0 on page. Section. Solving Proportions

29 . Lesson Lesson Tutorials Solving Proportions Method Use mental math. (Section.) Method Use the Multiplication Propert of Equalit. (Section.) Method Use the Cross Products Propert. (Section.) EXAMPLE Solving Proportions Using Multiplication Solve 7 =. 7 = 7 = Write the proportion. Multiplication Propert of Equalit = Simplif. The solution is. Use multiplication to solve the proportion. Eercises 9. w = 9. 0 = a. = EXAMPLE Solving Proportions Using the Cross Products Propert Solve each proportion. a. = 7 0 Cross Products Propert b. 9 = 7 0 = = 0 = Multipl. = =. Divide. = The solution is.. The solution is. Chapter Ratios and Proportions

30 Eercises 0 Use the Cross Products Propert to solve the proportion.. 7 =. =. 0 z + = EXAMPLE Real-Life Application The graph shows the toll due on a turnpike for driving miles. Your toll is $7.0. How man kilometers did ou drive? The point (00, 7.) on the graph shows that the toll is $7.0 for driving 00 miles. Convert 00 miles to kilometers. Toll (dollars) Turnpike (00, ) (00, 7.) Distance (miles) Method : Convert using a ratio.. km 00 mi = km mi mi. km So, ou drove about kilometers. Method : Convert using a proportion. Let be the number of kilometers equivalent to 00 miles. kilometers miles. = 00 kilometers miles Write a proportion. Use. km mi.. 00 = Cross Products Propert = Simplif. So, ou drove about kilometers. Eercises 0 Write and solve a proportion to complete the statement. Round to the nearest hundredth, if necessar in. cm. 00 g oz 9. L qt 0. m ft Section. Solving Proportions

31 . Eercises Help with Homework. WRITING What are three was ou can solve a proportion?. OPEN-ENDED Which wa would ou choose to solve =? Eplain our reasoning.. NUMBER SENSE Does = have the same solution as =? Use the Cross Products Propert to eplain our answer. )= 9+(- )= +(- 9)= +(- = ) 9+(- Use multiplication to solve the proportion. 9 z 0 h. = 7 9. =. =. =. = n 7. = w 9 Use the Cross Products Propert to solve the proportion. a 0. =. = 0 7 k. = v. = 7. =. = r. = 9 0 d.. = c 9. = 0 d 0. =. = 0 0. ERROR ANALYSIS Describe and correct the error m in solving the proportion =. n m.. w 7. k. = m = m = m =. PENS Fort-eight pens are packaged in boes. How man pens are packaged in 9 boes?. PIZZA PARTY How much does it cost to bu 0 medium pizzas? Medium Pizzas for $0.0 Solve the proportion. 9. = Chapter d. = Ratios and Proportions k+ 7. =

32 Write and solve a proportion to complete the statement. Round to the nearest hundredth if necessar.. km mi 9.. L gal lb kg. TRUE OR FALSE? Tell whether the statement is true or false. Eplain. If a b =, then = b a.. CLASS TRIP It costs $9 for 0 students to visit an aquarium. How much does it cost for students? Length (inches) Human Hair (, ) (,.) Time (months). GRAVITY A person who weighs 0 pounds on Earth weighs 0 pounds on the Moon. How much does a 9-pound person weigh on the Moon?. HAIR The length of human hair is proportional to the number of months it has grown. a. What is the hair length in centimeters after months? b. How long does it take hair to grow inches? c. Use a different method than the one in part (b) to find how long it takes hair to grow 0 inches.. SWING SET It takes hours for people to build a swing set. Can ou use the proportion = to determine the number of hours h it will take people to h build the swing set? Eplain.. REASONING There are people in an audience. The ratio of adults to children is to. How man are adults? 7. PROBLEM SOLVING Three pounds of lawn seed covers 00 square feet. How man bags are needed to cover 00 square feet?. Consider the proportions m n = and n k =. What is the ratio m? Eplain our reasoning. k Plot the ordered pair in a coordinate plane. (Section.) 9. A(, ) 0. B(, 0). C (, ). D(, ). MULTIPLE CHOICE What is the value of (w ) (w + )? (Section.) A w + B w C w + D w 0 Section. Solving Proportions 7

33 . Slope How can ou compare two rates graphicall? ACTIVITY: Comparing Unit Rates Work with a partner. The table shows the maimum speeds of several animals. a. Find the missing speeds. Round our answers to the nearest tenth. b. Which animal is fastest? Which animal is slowest? c. Eplain how ou convert between the two units of speed. COMMON CORE Slope In this lesson, ou will find the slopes of lines. interpret the slopes of lines as rates. Learning Standard MACC.7.RP..b Speed Animal (miles per hour) Antelope.0 a snake Speed (feet per second) Black mamba snake 9. Cheetah 0. Chicken. Coote.0 Domestic pig.0 Elephant. Elk.0 Giant tortoise 0. Giraffe.0 Gra fo. Grehound 9. Grizzl bear.0 Human.0 Hena 0.0 Jackal.0 Lion 7. Peregrine falcon 00.0 Quarter horse 7. Spider.7 Squirrel.0 Thomson s gazelle 0.0 Three-toed sloth 0. Tuna 7.0 Chapter Ratios and Proportions

34 ACTIVITY: Comparing Two Rates Graphicall Math Practice Appl Mathematics How can ou use the graph to determine which animal has the greater speed? Work with a partner. A cheetah and a Thomson s gazelle run at maimum speed. a. Use the table in Activit to calculate the missing distances. Cheetah Gazelle Time (seconds) Distance (feet) Distance (feet) 0 7 b. Use the table to write ordered pairs. Then plot the ordered pairs and connect the points for each animal. What do ou notice about the graphs? c. Which graph is steeper? The speed of which animal is greater? Distance (feet) Time (seconds). IN YOUR OWN WORDS How can ou compare two rates graphicall? Eplain our reasoning. Give some eamples with our answer.. REPEATED REASONING Choose 0 animals from Activit. a. Make a table for each animal similar to the table in Activit. b. Sketch a graph of the distances for each animal. c. Compare the steepness of the 0 graphs. What can ou conclude? Section. Slope 9

35 . Lesson Lesson Tutorials Ke Vocabular slope, p. 0 Stud Tip The slope of a line is the same between an two points on the line because lines have a constant rate of change. Slope Slope is the rate of change between an two points on a line. It is a measure of the steepness of a line. To find the slope of a line, find the ratio of the change in (vertical change) to the change in (horizontal change). change in slope = change in 7 Slope 7 EXAMPLE Finding Slopes Find the slope of each line. a. (, ) (0, 0) b. (, ) (, ) change in slope = change in = change in slope = change in = = The slope of the line is. The slope of the line is. Find the slope of the line. Eercises 9. (0, 0) (, ). 0 (, ) (, ) 0 Chapter Ratios and Proportions

36 EXAMPLE Interpreting a Slope The table shows our earnings for babsitting. a. Graph the data. b. Find and interpret the slope of the line through the points. Hours, 0 0 Earnings, (dollars) a. Graph the data. Draw a line through the points. Babsitting b. Choose an two points to find the slope of the line. Earnings (dollars) (, 0) (, 0) Hours change in slope = change in = 0 = dollars hours The slope of the line represents the unit rate. The slope is. So, ou earn $ per hour babsitting. Eercises 0 and. In Eample, use two other points to find the slope. Does the slope change?. The graph shows the amounts ou and our friend earn babsitting. Babsitting Earnings (dollars) You Friend (, ) (, 0) (, ) (, 0) Hours a. Compare the steepness of the lines. What does this mean in the contet of the problem? b. Find and interpret the slope of the blue line. Section. Slope

37 . Eercises Help with Homework. VOCABULARY Is there a connection between rate and slope? Eplain.. REASONING Which line has the greatest slope?. REASONING Is it more difficult to run up a ramp with a slope of or a ramp with a slope of? Eplain. A B C 9+(-)= +(-)= +(-9)= 9+(-)= Find the slope of the line.. (, ). (, ). (, ) (, ) (0, 0) (0, 0) 7. (, ) (, ). (, ) (,.) 9. (0, ) (,.) 0 Graph the data. Then find and interpret the slope of the line through the points. 0. Minutes, 7 9. Gallons, 0 0 Words, 0 Miles, ERROR ANALYSIS Describe and correct the error in finding the slope of the line passing through (0, 0) and (, ). slope = (0, 0) (, ) Chapter Ratios and Proportions

38 Graph the line that passes through the two points. Then find the slope of the line.. (0, 0), (, 7 ). (,. CAMPING The graph shows the amount of mone ou and a friend are saving for a camping trip. ), ( a. Compare the steepness of the lines. What does this mean in the contet of the problem? b. Find the slope of each line. c. How much more mone does our friend save each week than ou? d. The camping trip costs $. How long will it take ou to save enough mone?, ) (., ) (, Savings (dollars) Camping Trip (, 00) 0 (, 0) (, 0) ), Weeks 7. MAPS An atlas contains a map of Ohio. The table shows data from the ke on the map. (, 0) You Friend Toledo Cleveland Distance on Map (mm), Actual Distance (mi), Cincinnati Columbus a. Graph the data. b. Find the slope of the line. What does this mean in the contet of the problem? c. The map distance between Toledo and Columbus is millimeters. What is the actual distance? d. Cincinnati is about miles from Cleveland. What is the distance between these cities on the map?. CRITICAL THINKING What is the slope of a line that passes through the points (, 0) and (, 0)? Eplain. 9. A line has a slope of. It passes through the points (, ) and (, ). What is the value of? Multipl. (Section.) 0.. ( ). ( ). MULTIPLE CHOICE You have stamps from Meico in our stamp collection. These stamps represent of our collection. The rest of the stamps are from the United States. How man stamps are from the United States? (Section.) A B C 0 D Section. Slope

39 . Direct Variation How can ou use a graph to show the relationship between two quantities that var directl? How can ou use an equation? ACTIVITY: Math in Literature COMMON CORE Direct Variation In this lesson, ou will identif direct variation from graphs or equations. use direct variation models to solve problems. Learning Standards MACC.7.RP..a MACC.7.RP..b MACC.7.RP..c MACC.7.RP..d Gulliver s Travels was written b Jonathan Swift and published in 7. Gulliver was shipwrecked on the island Lilliput, where the people were onl inches tall. When the Lilliputians decided to make a shirt for Gulliver, a Lilliputian tailor stated that he could determine Gulliver s measurements b simpl measuring the distance around Gulliver s thumb. He said Twice around the thumb equals once around the wrist. Twice around the wrist is once around the neck. Twice around the neck is once around the waist. Work with a partner. Use the tailor s statement to complete the table. Thumb, t Wrist, w Neck, n Waist, 0 in. in. in. in. in. 0 in. Chapter Ratios and Proportions

40 ACTIVITY: Drawing a Graph Work with a partner. Use the information from Activit. a. In our own words, describe the relationship between t and w. b. Use the table to write the ordered pairs (t, w). Then plot the ordered pairs. c. What do ou notice about the graph of the ordered pairs? d. Choose two points and find the slope of the line between them w t e. The quantities t and w are said to var directl. An equation that describes the relationship is w = t. ACTIVITY: Drawing a Graph and Writing an Equation Math Practice Label Aes How do ou know which labels to use for the aes? Eplain. Work with a partner. Use the information from Activit to draw a graph of the relationship. Write an equation that describes the relationship between the two quantities. a. Thumb t and neck n (n = t) b. Wrist w and waist ( = w) c. Wrist w and thumb t (t = w) d. Waist and wrist w (w = ). IN YOUR OWN WORDS How can ou use a graph to show the relationship between two quantities that var directl? How can ou use an equation?. STRUCTURE How are all the graphs in Activit alike?. Give a real-life eample of two variables that var directl. 7. Work with a partner. Use string to find the distance around our thumb, wrist, and neck. Do our measurements agree with the tailor s statement in Gulliver s Travels? Eplain our reasoning. Use what ou learned about quantities that var directl to complete Eercises and on page. Section. Direct Variation

41 . Lesson Lesson Tutorials Ke Vocabular direct variation, p. constant of proportionalit, p. Direct Variation Words Two quantities and show direct variation when = k, where k is a number and k 0. The number k is called the constant of proportionalit. Graph The graph of = k is a line with a slope of k that passes through the origin. So, two quantities that show direct variation are in a proportional relationship. EXAMPLE Identifing Direct Variation Tell whether and show direct variation. Eplain our reasoning. a. 0 b. 0 0 Stud Tip Other was to sa that and show direct variation are varies directl with and and are directl proportional. Plot the points. Draw a line through the points. Plot the points. Draw a line through the points. The line does not pass through the origin. So, and do not show direct variation. The line passes through the origin. So, and show direct variation. EXAMPLE Identifing Direct Variation Tell whether and show direct variation. Eplain our reasoning. a. + = b. = = Solve for. = Solve for. The equation cannot be written as = k. So, and do not show direct variation. The equation can be written as = k. So, and show direct variation. Chapter Ratios and Proportions

42 Eercises 7 Tell whether and show direct variation. Eplain our reasoning =. =. + = EXAMPLE Real-Life Application The table shows the area (in square feet) that a robotic vacuum cleans in minutes. a. Graph the data. Tell whether and are directl proportional. Graph the data. Draw a line through the points. The graph is a line through the origin. So, and are directl proportional. Area (square feet) Robotic Vacuum (, ), ) ) ) (, ), ) Time (minutes) b. Write an equation that represents the line. Choose an two points to find the slope of the line. change in slope = change in = = The slope of the line is the constant of proportionalit, k. So, an equation of the line is =. c. Use the equation to find the area cleaned in 0 minutes. = Write the equation. = (0) Substitute 0 for. = 0 Multipl. So, the vacuum cleans 0 square feet in 0 minutes. Eercise 9 7. WHAT IF? The batter weakens and the robot begins cleaning less and less area each minute. Do and show direct variation? Eplain. Section. Direct Variation 7

43 . Eercises Help with Homework. VOCABULARY What does it mean for and to var directl?. WRITING What point is on the graph of ever direct variation equation?. DIFFERENT WORDS, SAME QUESTION Which is different? Find both answers. Do and show direct variation? Are and in a proportional relationship? Is the graph of the relationship a line? Does var directl with? 9+(-)= +(-)= +(-9)= 9+(-)= Graph the ordered pairs in a coordinate plane. Do ou think that graph shows that the quantities var directl? Eplain our reasoning.. (, ), (0, 0), (, ), (, ). (, ), (, 0), (0, ), (, ) Tell whether and show direct variation. Eplain our reasoning. If so, find k =. =. + = +. =. = 0. =. = 7. =. ERROR ANALYSIS Describe and correct the error in telling whether and show direct variation. 9. RECYCLING The table shows the profit for reccling pounds of aluminum. Graph the data. Tell whether and show direct variation. If so, write an equation that represents the line. The graph is a line, so it shows direct variation. Aluminum (lb), Profit, $.0 $9.00 $.0 $.00 Chapter Ratios and Proportions

44 The variables and var directl. Use the values to find the constant of proportionalit. Then write an equation that relates and. 0. = 7; =. = 0; =. = ; = 0. cm in.. MEASUREMENT Write a direct variation equation that relates inches to centimeters.. MODELING Design a waterskiing ramp. Show how ou can use direct variation to plan the heights of the vertical supports. Vertical supports Cost (dollars) Concert (9, 7) (, ) (, ) Tickets. REASONING Use = k to show wh the graph of a proportional relationship alwas passes through the origin.. TICKETS The graph shows the cost of buing concert tickets. Tell whether and show direct variation. If so, find and interpret the constant of proportionalit. Then write an equation and find the cost of tickets. 7. CELL PHONE PLANS Tell whether and show direct variation. If so, write an equation of direct variation. Minutes, Cost, $0 $0 $0 $7. CHLORINE The amount of chlorine in a swimming pool varies directl with the volume of water. The pool has. milligrams of chlorine per liter of water. How much chlorine is in the pool? 9. Is the graph of ever direct variation equation a line? Does the graph of ever line represent a direct variation equation? Eplain our reasoning. 000 gallons Write the fraction as a decimal. (Section.) MULTIPLE CHOICE Which rate is not equivalent to 0 feet per seconds? (Section.) A ft 0 sec B ft sec C ft sec D 0 ft sec Section. Direct Variation 9

45 .. Quiz Progress Check Solve the proportion. (Section.). 7 n =. = 0 Find the slope of the line. (Section.). (0, 0) (, ). (, ) (,.) O. = 7 z Graph the data. Then find and interpret the slope of the line through the points. (Section.). Hours, Miles, Packages, 0 Servings, 9 7 Tell whether and show direct variation. Eplain our reasoning. (Section.). 9 = + 9. = 0. CONCERT A benefit concert with three performers lasts hours. At this rate, how man hours is a concert with four performers? (Section.). LAWN MOWING The graph shows how much ou and our friend each earn mowing lawns. (Section.) Earnings (dollars) Lawn Mowing You Friend (, ) (7, 0) (, 0) (, 0) a. Compare the steepness of the lines. What does this mean in the contet of the problem? b. Find and interpret the slope of each line. c. How much more mone do ou earn per hour than our friend? Hours. PIE SALE The table shows the profits of a pie sale. Tell whether and show direct variation. If so, write the equation of direct variation. (Section.) Pies Sold, 0 Profit, $79.0 $9.0 $.0 $7.0 0 Chapter Ratios and Proportions

46 Chapter Review Review Ke Vocabular ratio, p. 00 rate, p. 00 unit rate, p. 00 comple fraction, p. 0 proportion, p. 0 proportional, p. 0 cross products, p. 09 slope, p. 0 Vocabular Help direct variation, p. constant of proportionalit, p. Review Eamples and Eercises. Ratios and Rates (pp. 9 0) There are orangutans and gorillas in a nature preserve. One of the orangutans swings 7 feet in seconds on a rope. a. Find the ratio of orangutans to gorillas. b. How fast is the orangutan swinging? a. orangutans gorillas = = The ratio of orangutans to gorillas is. 7 ft b. 7 feet in seconds = sec 7 ft = sec = ft sec The orangutan is swinging feet per second. Find the unit rate.. 9 miles on 0 gallons. revolutions in seconds. calories per serving Servings Calories Proportions (pp. 0 ) Tell whether the ratios 9 and form a proportion. 9 = 9 = = = The ratios are equivalent. So, 9 and form a proportion. Chapter Review

47 Tell whether the ratios form a proportion.. 9,.,. Use a graph to determine whether and are in a proportional relationship.. 0, ,. Writing Proportions (pp. 9) Write a proportion that gives the number r of returns on Saturda. Frida Saturda Sales 0 Returns r 0 sales sales One proportion is = returns r returns. Use the table to write a proportion. 9. Game Game Penalties Minutes m 0. Concert Concert Songs Hours. h. Solving Proportions (pp. 7) Solve = 0. = 0 Cross Products Propert = 0 Multipl. = Divide. The solution is. Solve the proportion.. =. =. 0 = w. s + = Chapter Ratios and Proportions

48 . Slope (pp. ) The graph shows the number of visits our website received over the past months. Find and interpret the slope. Choose an two points to find the slope of the line. change in slope = change in = 0 = 0 visits months Number of visits Website Visits (, 00) (, 0) 0 Months The slope of the line represents the unit rate. The slope is 0. So, the number of visits increased b 0 each month. Find the slope of the line.. (, ) (, ). (, ) (, ) 7. (, ) (, ). Direct Variation (pp. 9) Tell whether and show direct variation. Eplain our reasoning. a. + = b. = = Solve for. = Solve for. The equation cannot be written as = k. So, and do not show direct variation. The equation can be written as = k. So, and show direct variation. Tell whether and show direct variation. Eplain our reasoning.. + = 9. = 0 0. = 0. = + Chapter Review

49 Chapter Test Find the unit rate.. miles in das. kilometers in minutes Tell whether the ratios form a proportion. Test Practice. 9,. 9, 7 Use a graph to tell whether and are in a proportional relationship Use the table to write a proportion. 7. Monda Tuesda Gallons Miles 0 m. Thursda Frida Classes c Hours Solve the proportion. 9. = = Graph the line that passes through the two points. Then find the slope of the line.. (, 9), (, ). (, 9), (, ) Tell whether and show direct variation. Eplain our reasoning.. =. =. =. MOVIE TICKETS Five movie tickets cost $.. What is the cost of movie tickets? 7. CROSSWALK The graph shows the number of ccles of a crosswalk signal during the da and during the night. a. Compare the steepness of the lines. What does this mean in the contet of the problem? b. Find and interpret the slope of each line. Don t Walk Walk Ccles (, 0) 7 0 Crosswalk Signal (, 0) (, 90) (, 0) Da Night Hours. GLAZE A specific shade of green glaze requires parts blue to parts ellow. A glaze miture contains quarts of blue and 9 quarts of ellow. How can ou fi the miture to make the specific shade of green glaze? Chapter Ratios and Proportions

50 Standards Assessment. The school store sells pencils for $0.0. What is the unit cost of a pencil? (MACC.7.RP..) Test-Taking Strateg Read Question Before Answering A. $0.0 C. $.0 B. $0.0 D. $.00. Which epressions do not have a value of? (MACC.7.NS..) I. + ( ) II. ( ) III. ( ) IV. ( ) F. I onl H. II onl Be sure to read the question before choosing our answer. You ma find a word that changes the meaning. G. III and IV I. I, III, and IV. What is the value of the epression below? (MACC.7.NS..) ( ) ( ). What is the slope of the line shown? (MACC.7.RP..b) O (, 0) (0, ) A. B. C. D.. The graph below represents which inequalit? (MACC.7.EE..b) 0 F. < 7 H. > 7 G. + I. + Standards Assessment

51 . The quantities and are proportional. What is the missing value in the table? (MACC.7.RP..a) A. 0 C. B. D. 7. You are selling tomatoes. You have alread earned $ toda. How man additional pounds of tomatoes do ou need to sell to earn a total of $0? (MACC.7.EE..a) F. H. G. I. 9 $ per pound. The distance traveled b the a high-speed train is proportional to the number of hours traveled. Which of the following is not a valid interpretation of the graph below? (MACC.7.RP..d) High-Speed Train Distance (kilometers) (, 00) (, 00) (0, 0) 7 Hours A. The train travels 0 kilometers in 0 hours. B. The unit rate is 00 kilometers per hour. C. After hours, the train is traveling 00 kilometers per hour. D. The train travels 00 kilometers in hours. Chapter Ratios and Proportions