Unit Rates, and Proportions

Transcription

1 Unit Rates, and Proportions Multiple hoice Identify the choice that best completes the statement or answers the question. 1. The scale used to create a blueprint of a new house is 0.25 inches = 1 foot. If the dimensions of the master bedroom are 4 inches by 3.25 inches on the drawing, what is the actual area of the room? a. 52 square feet c. 256 square feet b. 208 square feet d. 13 square feet 2. The Great Pyramid of Giza originally had a height of about 150 meters. If a scale model of the pyramid is built as shown below, what will be the height of the model? Round your answer to the nearest tenth if necessary. Scale: 1 cm = 4.25 m a centimeters c centimeters b centimeters d. 48 centimeters 3. The amount of fencing running around the perimeter of Lin s vegetable garden is 24 yards. If he doubles the dimensions of the garden, how much fencing will be required? 5 yd 7 yd a. 48 feet c. 96 feet b. 45 feet d. 72 feet 4. If the model car below was built using the scale 1 inch = 1.5 feet, what is the length of the actual car? 10 in. a. 12 feet c. 6.7 feet

2 b feet d. 15 feet 5. The distance between two state parks on a map is about 4.5 centimeters. Use the scale shown in the table to find the actual distance between the two parks. Round your answer to the nearest tenth of a kilometer if necessary. Map Scale Map istance ctual istance 1 centimeter 3 kilometers a kilometers c kilometers b. 1.5 kilometers d kilometers 6. Sumio plans to have a screened-in patio built on the back of his home. The patio floor plan will have the dimensions shown in the scale drawing below. If the scale of the drawing is 0.5 inches = 1 foot, what are the actual dimensions of the patio? 8 in. 11 in. a. 22 feet by 22 feet c. 22 feet by 16 feet b. 16 feet by 12 feet d. 25 feet by 19 feet 7. Lisa is drawing a map of her backyard. She plans to use the scale inch : 4 feet. If the actual distance between the tree house and the swing set is 32 feet, what should the distance on the scale drawing be? Round your answer to the nearest tenth of an inch if necessary. a. 4.8 inches c. 4 inches b. 2 inches d. 256 inches 8. The Eiffel Tower in France was built for the Paris Exposition of The structure stands at a height of about 986 feet. If a scale model of the tower is created using the scale 1 inch : 75 feet, how tall will the model be? Round your answer to the nearest tenth of an inch if necessary. a inches c inches b. 6.6 inches d. 8.8 inches 9. Mi-Yung is driving across the United States. If Mi-Yung s map is 12 inches across, and the United States is 3,000 miles across, what is the scale of the map? a. 1 inch = 12 miles c. 1 inch = 0 miles b. 1 inch = 3,000 miles d. 1 inch = 250 miles 10. circular above ground swimming pool has a circumference of approximately 73 feet. If the dimensions of the pool are doubled, what will the new circumference be?

3 = 73 ft a. 584 feet c. 110 feet b. 292 feet d. 146 feet 11. arl took a 4-inch by 6-inch picture for his photography class. He wants to enlarge the picture and frame it for his wall. The larger picture will be similar to the smaller picture. What scale factor should he use if the dimensions of the frame are 6 inches by 9 inches? a. 1.5 c. 2 3 b. 3.5 d Rectangle is similar to Rectangle WXYZ. What is the length, in units, of? 8 units Z 12 units W 4 units a. 9 units c. 8 units b. 6 units d. 7 units Y X 13. The two quadrilaterals shown below are similar figures. What is the value of x? 6 mm 9 mm 9 mm x a millimeters c millimeters b millimeters d. 6 millimeters Solve the proportion. 14.

4 a b c d. 8 Numeric Response 15. The floor plan for a detached garage is shown in the scale drawing below. If the scale of the drawing is 0.5 inches = 1 foot, what is the actual area of the garage in square feet? 17 in. 14 in. 16. The actual distance between two cities is 42 miles. bout how far apart would these cities appear on a map that has the scale shown in the table? Round your answer to the nearest tenth of an inch. Map Scale Map ctual istance istance 3.5 inches 15 miles? inches 42 miles 17. arlton used a ruler to measure the distance between two towns on a map and found them to be about 5.5 centimeters apart from each other. If the map has the scale shown below, about how many kilometers apart are the two towns? Scale cm = 4 km 18. The developer of a golf course is hiring a graphic design company to create a scale drawing of the course s layout to print on the score cards. How many inches long will the seventh hole appear to be on the score card if the actual length of the hole is 380 yards? Round your answer to the nearest tenth of an inch, if necessary. Twin Meadows Golf ourse Scorecard Scale 1 inch 200 yards 19. dress originally designed for girls is being duplicated in a smaller version to be worn by a new line of children s dolls. The scale for the doll dresses will be 1 inch = 10 inches. The length of the original dress is shown in the figure below.

5 50 in. What will be the length of the doll dress, in inches? Round the answer to the nearest tenth, if necessary. 20. Members of the Performing rts lub are selling tickets for the spring play at Middleton High School. fter 55 minutes, they have sold 33 tickets to students and faculty members. t this rate, how many tickets will be sold by the end of the 7-hour school day? Short nswer L1ii Identify if the following are unit rates(u), ratios(r), or neither(n): You run 1400 steps in 2 miles 23. L4ii map has a scale of 1inch is 11 km. The distance between two towns is 60km. How far is it on the map?.

6 12 cm RP.1 L5 One lakefront property with 100 feet of shoreline is worth $120,000. ssuming that this rate is the same per foot of shoreline how much would a property of 80 feet of shoreline be worth?. 25. L3 Measuring out 3 cm on a map of Mississippi gives you 200 miles in real life. Using proportional reasoning predict how many miles 5.1 inches on the map will actually represent. Show all work!. 26. n artist is creating a new metal sculpture. The sculptor needs a piece shaped like the one shown in the scale drawing below. 2.5 cm 4.5 cm 2.5 cm 1 cm = 4 meters If the piece is cut out of a rectangular piece of metal, what area (in square meters) must the metal have prior to cutting? Round your answer to the nearest tenth of a meter if necessary. 27. This is a map of Louisiana. ESTIMTE the land area of this state. Explain the method you used.

7 = 1,000 square miles 28. Sue s car has a highway fuel efficiency rating of 28 miles per gallon. t this rate, how many highway miles should she expect to be able to drive on 8 gallons of gasoline? Show your work. Find the value of the variable that makes the ratios equivalent. 29. Solve the proportion. 30.

8 nswer Section Unit Rates, and Proportions MULTIPLE HOIE 1. NS: Set up and solve a proportion to find the actual length of the room and another proportion to find the actual width of the room. Then calculate the area of the bedroom. The actual area of the master bedroom is square feet. What are the actual dimensions of the master bedroom? orrect! Set up two proportions to find the actual dimensions of the room. Then find its area. Is this the area of the drawing or the actual area of the room? NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: scale drawing proportion MS: M NS: Set up and solve a proportion. orrect! id you switch the numerator and denominator in one of your ratios? What two ratios are equal in the problem statement? Use these to set up a proportion. Set up a proportion to solve the problem. REF: Science NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale drawing MS: M

9 3. NS: The new perimeter becomes feet. orrect! What is the perimeter of the larger garden? What will the new dimensions of the vegetable garden be? Find the perimeter of the garden with twice the width and twice the length. NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: area rectangle scale dimensions MS: M NS: Set up a proportion and solve. How can you use the information given to set up a proportion? Set up a proportion using the information in the problem statement. e careful when setting up your proportion. orrect! NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale model scale MS: M NS: Set up a proportion and solve. Set up a proportion using the information in the problem statement. Make sure you set up your proportion correctly. orrect! How can you use the information given to set up a proportion?

10 REF: Social Studies NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale distance maps MS: M NS: Set up and solve a proportion for the length and a proportion for the width. The actual dimensions of the patio are 22 feet by 16 feet. Will the length and width of the patio be the same? How can you set up two different proportions to find the length and width of the patio? orrect! Set up a proportion to find each dimension of the patio. NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: scale drawing proportion dimensions scale MS: M NS: Set up and solve a proportion. How can you use the information given to set up a proportion? What is the scale of the drawing? orrect! e careful when setting up your proportion. Make sure the ratios are proportional. NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale drawing scale MS: M NS: Set up and solve a proportion.

11 orrect! e careful when solving your proportion. re there two equivalent ratios that you can compare in a proportion? What two ratios are equal in the problem statement? Use these to set up a proportion. REF: Social Studies NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale model scale MS: M NS: If the map width is 12 inches and the United States is 3,000 miles wide, then the scale is 1 inch = miles. The width of the United States should be divided by some number. ivide the distance across the United States by the width of the map. heck your division. orrect! REF: Social Studies NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: maps scale distance MS: M NS: The circumference of a circle is given by the formula. If the diameter is doubled, the new circumference becomes, or twice the original circumference. So the new circumference of the pool will be about 146 feet. How is the expression for the circumference of a circle changed when the diameter is doubled? How many dimensions are being scaled? What is the formula for the circumference of a circle? orrect!

12 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: circle dimensions scale circumference MS: M NS: ivide the dimensions of the frame by the corresponding dimensions of the picture to find the scale factor. orrect! ivide the dimensions of the frame by the corresponding dimensions of the picture. Is the print a reduction or an enlargement? How do the dimensions of the frame compare to the dimensions of the picture? REF: The rts NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: similar figures scale MS: M NS: ivide the length of by to find how many times larger Rectangle WXYZ is than. Multiply the length of by 1.5 to find the length of. What number can you multiply by the sides of the smaller rectangle to find the sides of the larger rectangle? orrect! How many times larger is Rectangle WXYZ? What scale factor was used to create the larger rectangle? REF: Mathematics NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: similar figures rectangle MS: M NS: Set up a proportion using the corresponding sides of the similar figures.

13 Set up a proportion using two equal ratios from the similar figures. What are two equal ratios in the similar figures? orrect! e careful when setting up your proportion. REF: Mathematics OJ: Represent proportional relationships by equations. NT: 7: 7.RP.2.c ST: 7: 7.RP.2.c TOP: Ratios and Proportional Relationships KEY: similarity similar figures proportion ratio MS: M NS: PTS: 1 IF: Level REF: ML30385 LO: NTM 6-8.NOP.3.d TOP: Lesson 7.2 Writing and Solving Proportions KEY: solve proportion MS: Knowledge NOT: NUMERI RESPONSE 15. NS: 952 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale drawing MS: M NS: 9.8 PTS: 1 IF: loom s Level: pplication Webb s Level: Level 2 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: scale drawing proportion MS: M NS: 44 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: scale drawing proportion scale maps MS: M NS: 1.9 REF: Health/Physical Education

14 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: proportion scale drawing scale MS: M NS: 5 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: scale MS: M NS: 252 REF: The rts OJ: Represent proportional relationships by equations. NT: 7: 7.RP.2.c ST: 7: 7.RP.2.c TOP: Ratios and Proportional Relationships KEY: conversion rate problem solving MS: M SHORT NSWER 21. NS: no PTS: NS: U PTS: NS: kjh PTS: NS: $80 PTS: NS: 25.2 miles PTS: NS: Note: The following is only a sample answer. ll reasonable answers should be accepted. 1,824 square meters REF: Science

15 NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: scale drawing area model MS: M NS: Note: The following is only a sample answer. ll reasonable answers should be accepted. approximately 38.5,000 to 48.5,000 square miles The area of Louisiana is approximately 43.5,000 square miles. First, count 27 squares that were completely covered by land. Then count 33 squares that were partly or mostly covered by land. ivide 33 by 2 (16.5) because on average these squares were only half covered. dd 27 and 16.5 together for a total of 43.5 squares, which is equal to 43,500 square miles. PTS: 1 IF: loom s Level: pplication Webb s Level: Level 3 REF: Social Studies NT: 7: 7.G.1 ST: 7: 7.G.1 TOP: Geometry KEY: estimation area MS: M NS: Note: The following is only a sample answer. ll reasonable answers should be accepted. 224 miles Multiply the fuel efficiency (in miles per gallon) by the number of gallons. OJ: ompute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. NT: 7: 7.RP.1 ST: 7: 7.RP.1 TOP: Ratios and Proportional Relationships KEY: rate problem solving MS: M NS: PTS: 1 IF: Level REF: ML30383 LO: NTM 6-8.NOP.3.d TOP: Lesson 7.1 Ratios and Rates KEY: solve proportion cross product MS: Knowledge NOT: NS: 25 PTS: 1 IF: Level REF: ML10434 NT: NT.SS.MTH EE.5 LO: NTM 6-8.NOP.3.d TOP: Lesson 7.2 Writing and Solving Proportions KEY: solve proportion MS: Knowledge NOT: