5-1 Ratios. Express each ratio as a fraction in simplest form boys to 16 girls ANSWER: out of 60 light bulbs ANSWER:
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1 1. 12 boys to 16 girls out of 60 light bulbs DVDs out of 84 DVDs 8. 9 inches to 1 yard 9. 6 gallons to 3 quarts out of 15 pets tiles to 25 tiles wins out of 36 games 5. In Mr. Blackwell s class, 15 out of 24 students play sports. Express this ratio as a fraction in simplest Explain its meaning. ; For every 8 students, 5 participate in sports 6. 3 pints to 4 quarts players to 52 cards out of 60 days pens to 10 pencils 7. 2 pounds to 6 ounces people to 3 buses esolutions Manual - Powered by Cognero Page 1
2 16. On a full size piano, there are 36 black keys and 52 white keys. Express the ratio of black keys to white keys as a fraction in simplest Explain its meaning. 22. A department store conducted a study to determine what age group shops in their store. ; For every 9 black keys, there are 13 white keys. 17. In a restaurant, 72 out of 108 tables are booths. Express the ratio of tables that are booths to the total number of tables as a fraction in simplest Explain its meaning. ; For every 3 tables, 2 of them are booths yards to 10 feet a. Express the ratio of people ages 0 17 to people ages as a fraction in simplest b. Express the ratio of people 30 or under to people over the age of 30 as a fraction in simplest c. Express the ratio of people age to the total number of people as a fraction in simplest a. b. c ounces to 2 pounds quarts to 4 gallons feet to 14 inches 23. A water park has 14 body slides, 8 tube slides, 2 types of swimming pools, and 6 water play areas. Use this information to write each ratio as a fraction in simplest a. body slides : tube slides b. play areas : tube slides c. slides : all attractions d. slides : not slides a. b. c. d. esolutions Manual - Powered by Cognero Page 2
3 24. A cell phone store displayed the phone below on a poster. The length of the phone on the poster is 3 feet 4 inches. Write a ratio comparing the length of the actual cell phone to length of the cell phone on the poster as a fraction in simplest 27. When cooking a turkey, you should bake it for about 1 hour for every four pounds of meat. If an 18 pound turkey is cooked for 4 hours, was it cooked long enough? If not, how long should the turkey have been cooked? No; Sample answer: An 18 pound turkey should be cooked for hours. 28. The table shows the number of touchdowns and interceptions each NFL quarterback had in a recent season. Which quarterback had the best touchdown to interception ratio? Explain its meaning. 25. Justify Conclusions The table shows the heart rates of different animals. Philip Rivers; for every interception he throws, he throws 2.44 touchdowns. a. What is the ratio of a cat's mass to its heart rate? Express the ratio as a fraction in simplest b. Order the animals from greatest mass to heart rate ratio to least mass to heart rate ratio. c. Which animal had the greatest ratio? Explain your reasoning. Compare each pair of ratios using <, >, or =. 29. $27 for 9 key chains, $45 for 15 key chains girls out of 18 students, 12 girls out of 22 students a. b. horse, cow, cat, hamster c. horse; Sample answer: The ratio is approximately 27,273 to Bonnie s Boutique had a T-shirt sale to make room for new inventory. At the end of the sale, 16 T-shirts were left. Of these, 6 were blue. Write the ratio of blue T-shirts to total T-shirts as a fraction in simplest cases for $48, 14 cases for $ thriller movies out of 36 DVDs, 10 thriller movies out of 15 DVDs esolutions Manual - Powered by Cognero Page 3
4 33. Model with Mathematics Give three different examples of ratios that might occur in a real-world situation. Sample answers: number of girls to boys in a class, number of apples to bananas in a fruit basket, a sale price of 3 for $8 34. Use Math Tools Which of the technique(s) listed below might you use to determine which of the following ratios is the greatest: 440:1200, 1200:3750, or 350:450? Justify your selection(s). Then use the technique(s) to solve the problem. estimation; Sample answer: Each of the ratios can be easily rounded to common fraction. 35. Persevere with Problems The ratio of Mieko s age to his brother Sado s age is 2:3. In ten years, the ratio will be 4:5. How old is Mieko? Building on the Essential Question In a recent year, the Jacksonville Jaguars took the ball away from their opponents 21 times. They gave the ball up to their opponents 22 times. A sports writer claims the takeaway/giveaway ratio is or 1. Is this statement correct? Explain. Sample answer: No; the takeaway/giveaway ratio is 21 to 22 or.the sports writer subtracted instead of dividing. 39. Of 48 orchestra members, 30 are girls. What ratio compares the number of boys to girls in the orchestra? A 3:8 B 8:3 C 3:5 D 5:3 C 40. Which of the following ratios does not describe a relationship between the squares shown? 36. Which One Doesn't Belong? Select the ratio that does not have the same value as the other three. Explain your reasoning to a classmate. 2 qt:3 gal; Sample answer: Since 2 qt:3 gal involves measurement units, the units need to be the same. 37. Persevere with Problems Students in Mrs. Miller s class are measuring the length and width of a table using nonstandard materials like pencils and pieces of paper. No matter which tools they use, will the ratio of the length to the width always, sometimes, or never be the same? Explain. Always; Sample answer: No matter what is used to measure the dimensions of the table, the actual dimensions will never change so the ratio will always be the same. F 2 black:3 white G 2 black:5 white H 2 black:5 total J 3 white:5 total G esolutions Manual - Powered by Cognero Page 4
5 41. Of newly manufactured volleyballs, 12 were defective and 56 passed inspection. What ratio compares the number of defective volleyballs to the total number of volleyballs manufactured? A 3:14 B 3:17 C 4:14 D 4:17 B 42. Short Response Marisol counted the number of coins she had in her piggy bank. The table shows her results There are approximately centimeters in 1 foot. Express as a mixed number. Write a ratio that compares the number of dimes to the number of total coins. 9:50 Name the ordered pair for each point graphed below. Write each rational number as a decimal A 51. B 52. C 53. D ( 4, 3) (2, 1) ( 3, 2) (3, 4) esolutions Manual - Powered by Cognero Page 5
6 54. E 55. F (1, 3) (4, 4) 56. To simulate space travel, NASA s Lewis Research Center in Cleveland uses a 430-foot shaft. The free fall of an object in the shaft takes 5 seconds to travel the 430 feet. a. Write an integer to represent the change in the height of the object. b. On average, how far does the object travel each second? a. 430 b. 86 ft ( 4) Divide. 57. $ $ $ $ $ $ $ $2.30 Find each difference ( 5) esolutions Manual - Powered by Cognero Page 6
4-5 Convert Measurement Units. Complete ft = yd SOLUTION: Since 1 yard = 3 feet, multiply by lb = oz SOLUTION:
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