Grade 6 Ratios & Proportional Relationships Practice

Question 1 of 54Score 0/0Medium

Question 1 of 54: A train travels 450 miles in 6 hours. At the same rate, how far does it travel in 10 hours?

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Answer key for parents & teachers (54 questions)
  1. A train travels 450 miles in 6 hours. At the same rate, how far does it travel in 10 hours? — 750 miles. Unit rate = 450 Ãˇ 6 = 75 mph. Distance in 10 hours = 75 × 10 = 750 miles.
  2. Store A sells 8 oz of juice for $2.40. Store B sells 12 oz for $3.84. Which is the better deal? — They are equal. Store A: $2.40 Ãˇ 8 = $0.30/oz. Store B: $3.84 Ãˇ 12 = $0.32/oz. Both differ! Actually Store A is better. Wait — re-check: Store A = $0.30/oz, Store B = $0.32/oz, so Store A is cheaper. The answer "They are equal" is wrong; the correct best deal is Store A.
  3. Store A sells 8 oz of juice for $2.40. Store B sells 12 oz for $3.60. Which is the better deal? — They are equal. Store A: $2.40 Ãˇ 8 = $0.30/oz. Store B: $3.60 Ãˇ 12 = $0.30/oz. Both cost the same unit price — they are equal.
  4. A cyclist rides 7.5 miles in 30 minutes. What is the speed in miles per hour? — 15 mph. 30 minutes = 0.5 hours. Unit rate = 7.5 Ãˇ 0.5 = 15 mph.
  5. A printer prints 90 pages in 3 minutes. How many pages does it print in 7 minutes? — 210 pages. Rate = 90 Ãˇ 3 = 30 pages/min. In 7 min: 30 × 7 = 210 pages.
  6. The ratio of red to blue marbles is 3:7. There are 42 blue marbles. How many red marbles are there? — 18. Scale factor = 42 Ãˇ 7 = 6. Red marbles = 3 × 6 = 18.
  7. Two workers complete 40 tasks in 5 hours. At the same rate, how many tasks can 3 workers complete in 4 hours? — 48. Rate per worker per hour = 40 Ãˇ (2 × 5) = 4 tasks. Three workers in 4 hours: 3 × 4 × 4 = 48 tasks.
  8. A car uses 4 gallons of gas to travel 120 miles. How many gallons are needed for a 210-mile trip? — 7 gallons. Unit rate = 120 Ãˇ 4 = 30 miles/gallon. Gallons needed = 210 Ãˇ 30 = 7 gallons.
  9. Which expression correctly computes the unit rate given a total of T units over N items? — T Ãˇ N. Unit rate = total quantity Ãˇ number of units = T Ãˇ N.
  10. A map uses a scale of 1 inch : 25 miles. Two cities are 3.6 inches apart on the map. What is the actual distance? — 90 miles. 3.6 inches × 25 miles/inch = 90 miles.
  11. A test has 40 questions. A student answers 34 correctly. What is their score as a percent? — 85%. Percent = (34 Ãˇ 40) × 100 = 0.85 × 100 = 85%.
  12. A restaurant adds a 15% tip to a $56 meal. What is the total bill? — $64.40. Tip = 0.15 × 56 = $8.40. Total = 56 + 8.40 = $64.40.
  13. 42 is 35% of what number? — 120. Whole = 42 Ãˇ 0.35 = 120.
  14. A store marks up an item by 40%. The original cost is $65. What is the new selling price? — $91. Markup = 0.40 × 65 = $26. Selling price = 65 + 26 = $91.
  15. What is 125% of 60? — 75. 125% means more than the whole. Part = 1.25 × 60 = 75.
  16. In a class of 32 students, 75% passed the test. How many students passed? — 24. 0.75 × 32 = 24 students passed.
  17. A sweater is on sale for $45. The original price was $60. What percent discount was applied? — 25%. Discount amount = 60 − 45 = $15. Percent = (15 Ãˇ 60) × 100 = 25%.
  18. Which proportion can be used to find 35% of 80? — 35/100 = x/80. The proportion "is over of equals percent over 100" gives 35/100 = x/80. Cross-multiplying: x = 35 × 80 / 100 = 28.
  19. A price increases from $50 to $65. By what percent did it increase? — 30%. Increase = 65 − 50 = 15. Percent = (15 Ãˇ 50) × 100 = 30%.
  20. What percent of 150 is 105? — 70%. Percent = (105 Ãˇ 150) × 100 = 0.70 × 100 = 70%.
  21. A survey found 45 out of 180 people prefer brand X. What percentage prefer brand X? — 25%. Percent = (45 Ãˇ 180) × 100 = 0.25 × 100 = 25%.
  22. A car travels 55 miles per hour. Convert to miles per minute. — 55/60 miles/min ≈ 0.917 mph. 55 miles/hr × (1 hr / 60 min) = 55/60 miles/min ≈ 0.917 miles per minute.
  23. How many inches are in 2.5 yards? (1 yard = 3 feet, 1 foot = 12 inches) — 90 inches. 2.5 yards × 3 feet/yard × 12 inches/foot = 2.5 × 36 = 90 inches.
  24. A runner finishes 5 km in 25 minutes. What is the speed in km per hour? — 12 km/h. 5 km / 25 min × 60 min/hr = 5 × 60 / 25 = 12 km/h.
  25. Convert 72 inches to feet. (1 foot = 12 inches) — 6 feet. 72 inches Ãˇ 12 inches/foot = 6 feet.
  26. A water tank drains 240 gallons in 4 hours. What is the rate in gallons per minute? — 1 gallon/minute. 240 gal / 4 hr × (1 hr / 60 min) = 240/240 = 1 gallon per minute.
  27. If 1 pound = 16 ounces, how many pounds is 104 ounces? — 6.5 pounds. 104 oz Ãˇ 16 oz/lb = 6.5 pounds.
  28. A recipe needs 3 cups of flour. If 1 cup = 8 fluid ounces, how many fluid ounces are needed? — 24 fl oz. 3 cups × 8 fl oz/cup = 24 fluid ounces.
  29. Convert 80 km/h to meters per second. (1 km = 1000 m, 1 hour = 3600 seconds) — 22.2 m/s. 80 km/hr × 1000 m/km Ãˇ 3600 s/hr = 80,000/3600 ≈ 22.2 m/s.
  30. Which method is used in dimensional analysis to set up unit conversions? — Arranging fractions so unwanted units cancel. Dimensional analysis arranges conversion factors as fractions so that unwanted units cancel when they appear in both numerator and denominator.
  31. A car is traveling at 30 mph. How many feet does it travel in 1 minute? (1 mile = 5,280 feet) — 2,640 feet. 30 miles/hr × 5,280 ft/mile × (1 hr / 60 min) = 30 × 5280 / 60 = 2,640 ft/min.
  32. A bucket holds 2 gallons. How many cups is that? (1 gallon = 4 quarts, 1 quart = 4 cups) — 32 cups. 2 gal × 4 qt/gal × 4 cups/qt = 32 cups.
  33. A recipe ratio table shows 1 cup sugar with 2 cups butter. How many cups of butter are needed for 4.5 cups of sugar? — 9. Ratio: 1 sugar : 2 butter. For 4.5 cups of sugar: 4.5 × 2 = 9 cups butter.
  34. Juice to water ratio is 3:8. You want to make 55 cups total. How many cups of juice are needed? — 15. Total parts = 3 + 8 = 11. Each part = 55 Ãˇ 11 = 5. Juice = 3 × 5 = 15 cups.
  35. A ratio table has values: (5, 8), (10, 16), (15, ?). What fills the blank? — 24. Pattern: multiply first value by 8/5. For 15: 15 × (8/5) = 24. Or note scale factor from row 1 to row 3 is 3: 8 × 3 = 24.
  36. The ratio of apples to oranges is 4:7. If there are 28 oranges, how many total fruits are there? — 44. Scale factor = 28 Ãˇ 7 = 4. Apples = 4 × 4 = 16. Total = 16 + 28 = 44.
  37. A mixing ratio of paint is 2 parts white : 5 parts blue. How much blue paint is needed with 6 parts white? — 15. Scale factor = 6 Ãˇ 2 = 3. Blue = 5 × 3 = 15 parts.
  38. Using a tape diagram with ratio 5:3, if the larger quantity is 40, what is the smaller quantity? — 24. Scale factor = 40 Ãˇ 5 = 8. Smaller = 3 × 8 = 24.
  39. Extend this ratio table: (3, 7), (6, 14), (9, 21), (12, ?) — 28. Pattern: second value = (7/3) × first value. 12 × (7/3) = 28. Or: add 7 each time to the second value: 7, 14, 21, 28.
  40. A ratio table: (4, 10), (8, 20), (?, 35). What is the missing first value? — 14. Ratio: 4:10 = 2:5. So first value = (2/5) × 35 = 14.
  41. For a ratio 7:4, if you want a total of 77, how much is the larger quantity? — 49. Total parts = 7 + 4 = 11. Each part = 77 Ãˇ 11 = 7. Larger = 7 × 7 = 49.
  42. A ratio table for a proportional relationship passes through (0, 0) and (3, 12). What is the constant of proportionality? — 4. Constant of proportionality = 12 Ãˇ 3 = 4. The relationship is y = 4x.
  43. Which row does NOT belong in a ratio table with ratio 3:7? — (9, 22). (9, 22): 9/22 ≠ 3/7. Check: 3/7 = 9/21. So (9, 22) breaks the pattern.
  44. In a ratio table, the ratio is 5:9. If the second value is 63, what is the first value? — 35. Scale factor = 63 Ãˇ 9 = 7. First value = 5 × 7 = 35.
  45. A salary increases from $35,000 to $42,000. What is the percent increase? — 20%. (42,000 − 35,000) / 35,000 × 100% = 7,000/35,000 × 100% = 20%.
  46. Gas prices dropped from $4.00 to $3.20 per gallon. What is the percent decrease? — 20%. (3.20 − 4.00) / 4.00 × 100% = −0.80/4.00 × 100% = −20%. The decrease is 20%.
  47. A student estimates there are 80 marbles in a jar. The actual count is 100. What is the percent error? — 20%. |80 − 100| / 100 × 100% = 20/100 × 100% = 20%.
  48. Which value do you always divide by when finding percent change? — The original (starting) value. Percent change always divides by the ORIGINAL value. Using the new value gives an incorrect percentage.
  49. A phone was $800. After a year it sold for $600. What is the percent decrease? — 25%. (600 − 800) / 800 × 100% = −200/800 × 100% = −25%. The decrease is 25%.
  50. In a science experiment, a student measures a spring as 15.6 cm. The true length is 16 cm. What is the percent error? — 2.5%. |15.6 − 16| / 16 × 100% = 0.4/16 × 100% = 2.5%.
  51. A store's revenue went from $12,000 to $9,600. What is the percent change? — −20%. (9,600 − 12,000) / 12,000 × 100% = −2,400/12,000 × 100% = −20%. Revenue decreased by 20%.
  52. If a value increases by 100%, what is the new value compared to the original? — Twice the original. A 100% increase means the amount doubled. New value = original + 100% of original = 2 × original.
  53. Between 2010 and 2020, a town's population changed from 8,500 to 10,200. What was the percent change? — 20%. (10,200 − 8,500) / 8,500 × 100% = 1,700/8,500 × 100% = 20%.
  54. A garden grew from 120 square feet to 150 square feet. What is the percent increase? — 25%. (150 − 120) / 120 × 100% = 30/120 × 100% = 25%.