Ratios Comparing Fractions

Transcription

1 Ratios Comparing Fractions Labels are very important with ratios. If the ratio of red candies to green is 3:2, your setup must show the labels red and green; and the numbers 3 and 2 must go with the proper colors. After setting the labels equal to the numbers, Do the Fish to solve the equations. Remember Keep, Change, Flip to divide fractions. #1 A cookie recipe requires 3 4 cup of flour to make flour is needed to make 1 dozen cookies? dozen cookies. How much Set up a ratio in fraction form for flour to cookies. It doesn t matter which goes in the numerator, as long as you properly match the labels with their numbers. Turn mixed numbers into improper fractions. flour cups = = x = x = x = x 6 12 = 1 2 cup of flour = x

2 #2 Andrew proofread 1 4 of a page of a technical report in 2 of an hour. What is the 5 unit rate at which he proofread the pages? Remember, unit rate means that you have a denominator of 1. Therefore we are trying to find the number of pags read per one hour. pages 1 4 hours = = x = x = x = x 5 8 of a page per hour = x

3 #3 Susan used kilowatts of electricity to power her house for average, how many kilowatts did Susan use per hour? hours. On kilowatts hours 77 8 = = x = x = x = x = 7 4 = kilowatts per hour = x

4 3. Kevin purchased ft 2 of hardwood floor to install in his living room. This amount covered of the room. How many square feet of flooring will cover Kevin s living room floor? ft 2 ft 2 ft 2 ft 2 5. A cookie recipe requires cup of sugar for batch of cookies. How much sugar is needed for 1 batch of cookies? cup cup cups cups

5 6. Ally s hair grew from inches to inches over 5 months. At what rate did Ally s hair grow per month? inch inch inches 8. Mary used of a can of paint to cover of the outside of her house. How many cans of paint will Mary need to cover the entire outside of her house?

6 9. A bag of chips holds ounces. One serving is of an ounce. About how many servings are in the bag? Brenda completed of a crossword puzzle in of an hour. If she continues at this same rate, which problem shows the number of crossword puzzles she could complete in one hour?

7 11. The table shows distances run by Jeremy and Mateo in particular amounts of time. Part A What is Jeremy s running rate, in miles per hour? Part B What is Mateo s running rate, in miles per hour? Part C Jeremy and Mateo both plan to run 7 miles. They will run at their rates given in the table. How many hours apart should they start so that they finish at the same time? 12. A -pound bag of grass seed covers of an acre. How much grass seed is needed for 1 acre? 12 pounds 14 pounds 16 pounds 20 pounds

8 13. If a plant grows inch in of a week, at what rate is the plant growing? inches per week inches per week inches per week inches per week 14. Which problem can be solved by calculating? A bag of apples is full. Some friends eat of the apples in the bag. How much of the bag of apples is left? A person takes day to type of an essay. How many essays can the person type in one day? A girl ran mile on Monday and mile on Tuesday. How far did the girl run on those two days?

9 A snail crawls foot in of an hour. How far will the snail crawl in one hour? 15. One-sixth of a bag of bird seed fills a bird feeder of its capacity. How many times will a bag of bird seed completely fill the feeder? Mateo is draining a pool at a rate of of a gallon of water every hour. If he continues to drain the pool at this rate, how much water will be drained in 1 hour? 4 gallons 1 gallon gallon gallon

10 17. Jerry ran of a mile in of an hour. What was Jerry s rate of speed? miles per hour miles per hour miles per hour miles per hour 18. Karen drove miles in of an hour. At this rate, how far did she drive in one hour? 25 miles 30 miles 48 miles 50 miles

11 19. Jessie has a container that contains cups of ice cream. How many - cup servings of ice cream are in the container? Doug drove miles in hours. How many miles did Doug average per hour? miles per hour miles per hour miles per hour

12 21. A pizza shop uses ounce of pepperoni for every of a large pizza. How much pepperoni does one large pizza have? ounce ounce 1 ounce 2 ounce 22. A cookie recipe needs cups of flour to make batch of cookies. How much flour is needed to make 1 batch of cookies? cups cups cups

13 23. Susan walked miles in hours. How many miles can Susan walk in 1 hour? 24. Amy jogs of a mile in of an hour, while John takes of an hour to jog of a mile. If they continued at this rate, who would jog farther in one hour and by how much? Amy would jog 1 mile farther than John. John would jog 1 mile farther than Amy. Amy would jog 2 miles farther than John. John would jog 2 miles farther than Amy.

14 25. Armin used of a glue stick to decorate of his poster. At this rate, how many glue sticks will he use to decorate one entire poster? 26. A painter used gallons of paint to paint of a room. At this same rate, how many gallons will it take to paint the whole room? 2 6

15 27. The blueprint of a garden uses of an inch to represent of a meter. Part 1. How many meters are represented by 1 inch in the blueprint? Part 2. How many inches in the blueprint represent 1 meter? 28. Stanley is having wood flooring installed in his living room. The installer has used boxes of flooring on of the room. How many total boxes of flooring will be needed for Stanley s living room? Tony walked miles in of an hour. At this rate, how many miles can Tony walk in one hour?

16 30. A -ft 2 piece of tile covers of the area of a kitchen floor. What is the area of the kitchen floor? 96 ft ft ft ft Over a year period, inches of snow fell in Jackson City. What was the average yearly snowfall in Jackson City? inches per year inches per year inches per year inches per year

17 32. Mr. Roman drove from his hometown to another city. He used gallons of gas for the mile trip. On average, how many miles did Mr. Roman travel per gallon of gas? miles miles miles miles 33. Marie can make quart of orange juice in of a minute by squeezing oranges. At this rate, how much juice can she make in 1 minute? quart quart quart quarts

18 34. Jane put a 12-in. tall bucket under a leak in her sink. The bucket fills at a constant rate of in. every of an hour. How many hours will it take to fill the bucket? 35. Edward can run mile in 300 seconds. What is Edward s unit rate? mile per minute mile per minute mile per minute 10 mile per minute

19 36. If a dog can eat of a bag of food in week, how many bags of food can the dog eat in 1 week? 37. A painter used of a gallon of paint to cover of a wall. How many gallons of paint will the painter use for the entire wall?

20 38. Each section of a fence measures feet. Each section is of the length of a side of the fence. How long is the side of the fence? feet feet feet feet 39. At a gas station, Lora took minute to fill gallon of gas. At this rate, how many gallons of gas could Lora fill in 1 minute? Use a mixed number to express your answer. 40. Tom started with a full tank of gasoline and drove his car refilled the gas tank, he had to add 6.6 gallons of gasoline. miles. When Tom Part A What is the fuel efficiency, in miles per gallon, of Tom s car? Show or explain your work. Part B Tom wanted to compare his car s fuel efficiency with that of a car belonging to a friend in Australia. The friend said his car uses 6.5 liters of gasoline to drive 100 kilometers. Is Tom s car more or less fuel efficient than his friend s car? Find the number of liters of gasoline Tom s car would use to drive 100 kilometers to make the comparison and answer the question. Show or explain your work.

21 Note: 1 mile = 1.6 kilometers (km) and 1 U.S. gallon = 3.8 liters (L) 41. Jamal runs for a track team. He ran miles in of an hour. What was Jamal s rate of speed? miles per hour miles per hour miles per hour miles per hour 42. A certain laundry detergent recommends cup of detergent for a load of clothes. How much detergent is recommended for 4 loads of clothes? 1 cup 2 cups 4 cups 8 cups

22 43. It took Melanie of an hour to ride her bike of a mile. How many miles per hour can Melanie ride her bike? 44. Mrs. Richard uses cups of flour to make dozen cakes. How many cups of flour does Mrs. Richard need to make a dozen cakes? cups cups cups cups

23 45. Paul used gallons of paint to cover of the walls in his living room. How many gallons of paint will Paul need to paint all the walls in his living room? gallons gallons gallons gallons 46. Jennifer walks mile in hour, and Gavin walks mile in hour. Part What is Jennifer's walking rate, in miles per hour? Part What is Gavin's walking rate, in miles per hour? Part Jennifer and Gavin both plan on walking 4.5 miles, and they want to finish at the same time. If Gavin starts walking at 1:00 pm, at what time should Jennifer start walking? Use words, numbers, and/or pictures to show your work. Write your answer(s) on the paper provided.

24 47. Britney ran miles in hour. At this rate, how many hours will it take Britney to run 1 mile? hours hours hour 48. Eric drove his car miles and used gallons of gasoline. How many miles did Eric drive per gallon of gasoline? 49. Debbie made gallons of tea. She is putting gallon of tea into each cup. How many cups can Debbie fill? 12

25 A box contains ounces of spaghetti. A serving size is ounces. How many servings are in one box of spaghetti? Terry bought dozen chocolate chip cookies. She paid $15 for her purchase. If there were 12 cookies in each dozen, what was the cost per cookie? $0.17 $0.50 $0.83 $1.25

26 52. Kira finished of a puzzle in of an hour. At this rate, how many puzzles could she finish in 1 hour? 53. In a fireplace, about of an 18-inch log will burn in of an hour. How many hours will it take to burn logs? of an hour of an hour hours hours

27 54. Sam bought cups of trail mix. He eats a -cup serving each day. How many days will the trail mix last? A group of students and teachers are going on a field trip. One-ninth of the group will fit on of a school bus. How many buses are needed to transport the entire group? The side length of a larger square is ft. The side length of a smaller square is ft. Without overlapping, how many smaller squares are needed to cover the entire area of the larger square? 6

28 Jason drove his car miles and used gallons of gas. How many miles did Jason drive per gallon of gas? miles per gallon miles per gallon miles per gallon miles per gallon

29 58. Marcus is training for an adventure race. In the race he will swim mile, hike miles, and then kayak miles. The table below shows distances and times taken from his most recent training session. Use the information in the table to answer the questions below. Part What is the difference, in miles per hour, between Marcus swimming speed and his hiking speed? Part In which sport is Marcus s speed the fastest? Part If Marcus kayaks an additional mile per each of an hour, how fast (in miles per hour) will he be kayaking? Part How long will it take Marcus to complete the adventure race, if Marcus swims, hikes, and kayaks at the rates given in the table? Give your answer in the number of hours and minutes. Round your answer to the nearest minute. Use words, numbers, and/or pictures to show your work. 59. One-half of a roll of wallpaper covers of a wall. How many rolls of wallpaper are needed to cover half the wall?

30 60. Franco read of a chapter of his history book in of an hour. At this rate, how many chapters of his history book can he read in 1 hour? 61. Kendall used of a bag of seed to plant of her garden. How many bags will Kendall use to plant her garden?

31 If a snail can move of a meter every hour, what is the speed of the snail, in meters per hour? 63. Aliya hikes up a mountain for 2 hours. During this time, she hikes a distance of miles. Which expression shows Aliya s rate in miles per hour?

32 64. Mr. Rogers needs fertilizer for his 1-acre garden. The package suggests pound of fertilizer for of an acre. How many pounds of fertilizer does Mr. Rogers need for his entire garden? 65. An artist made a design using tiles. The design had an area of square meters, and each tile used in the design had an area of square meters. A different design by the artist used 19 of the same tiles. What is the difference between the number of tiles used for the two designs? 1 tile 2 tiles

33 3 tiles 4 tiles 66. A plant grew inches over a -month period. What was the average monthly growth rate for the plant? inch per month inches per month inches per month 67. Alicia ran miles in of an hour. At this rate, how far could Alicia run in one hour? miles miles miles

34 68. A recipe for 48 biscuits uses from each cup of biscuit mix? cups of biscuit mix. How many biscuits are made 6 biscuits 18 biscuits 30 biscuits 128 biscuits 69. John is painting a box that is shaped like a cube. One-eighth of a bottle of paint covers of one face of the box. How many bottles of paint will John need to paint the entire box? 70. Mr. Adams used lb of nails to secure yards of fence. How many yards of fence can Mr. Adams secure with 1 lb of nails?

35 71. Janelle types at the rate of is true? of a page per minute. Which statement about Janelle Janelle can type 8 pages in of a minute. Janelle can type 2 pages in of a minute. Janelle can type of a page in of a minute. Janelle can type of a page in of a minute. 72. A local car wash is open 8 hours each day. It uses of a container of wax for each car. The car wash waxes an average of cars per hour. How many containers of wax does the car wash use in one day?

36 73. Sara used packs of pencils in the first of the year. At what rate is Sara using pencils? packs per year packs per year packs per year packs per year 74. Sally paid $1.50 for pounds of apples at the Grocery Mart. Fred paid $1.95 for 3 pounds of apples at the Corner Fruit Stand. Part A Who paid less money per pound for their apples, Sally or Fred? Show the computations to find each unit rate.

37 Part B John went to the Grocery Mart and purchased pounds of apples. How much, in dollars, did John pay for the apples? Show or explain your work. Part C Write an equation that can be used to compute the total cost, in dollars (y), to purchase any total weight, in pounds (x), of apples at the Corner Fruit Stand. 75. On a drawing of a house, inches is equal to feet of the actual house. How many feet are equal to 1 inch on the drawing? feet feet feet