Grade 7 Ratios & Proportional Relationships Practice

Question 1 of 34Score 0/0Medium

Question 1 of 34: A car travels 3/4 of a mile in 1/3 of an hour. What is the unit rate in miles per hour?

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Answer key for parents & teachers (34 questions)
  1. A car travels 3/4 of a mile in 1/3 of an hour. What is the unit rate in miles per hour? — 9/4 mph. (3/4) Ãˇ (1/3) = (3/4) × (3/1) = 9/4 = 2.25 mph.
  2. A painter covers 2/5 of a wall in 1/2 an hour. How many walls per hour can she paint? — 4/5 wall per hour. (2/5) Ãˇ (1/2) = (2/5) × (2/1) = 4/5 of a wall per hour.
  3. A runner completes 5/6 of a mile in 5/12 of an hour. What is the unit rate? — 2 mph. (5/6) Ãˇ (5/12) = (5/6) × (12/5) = 60/30 = 2 mph.
  4. A faucet drips 3/10 of a liter of water in 1/5 of a minute. What is the rate in liters per minute? — 3/2 L/min. (3/10) Ãˇ (1/5) = (3/10) × (5/1) = 15/10 = 3/2 = 1.5 L/min.
  5. Sam earns $3/4 every 1/8 of an hour. What is his hourly wage? — $6 per hour. (3/4) Ãˇ (1/8) = (3/4) × (8/1) = 24/4 = $6 per hour.
  6. The unit rate for (2/3) Ãˇ (4/9) is: — 3/2. (2/3) × (9/4) = 18/12 = 3/2 = 1.5.
  7. A snail travels 5/8 cm in 5/16 of a minute. How fast is it in cm per minute? — 2 cm/min. (5/8) Ãˇ (5/16) = (5/8) × (16/5) = 80/40 = 2 cm/min.
  8. If a hose fills 2/9 of a pool in 1/3 of an hour, what fraction of the pool does it fill per hour? — 2/3. (2/9) Ãˇ (1/3) = (2/9) × (3/1) = 6/9 = 2/3 of the pool per hour.
  9. A recipe needs 3/5 cup of flour for 3/10 of a recipe. How many cups are needed for the full recipe? — 2 cups. (3/5) Ãˇ (3/10) = (3/5) × (10/3) = 30/15 = 2 cups.
  10. A printer prints 4/5 of a page in 2/5 of a second. How many pages per second? — 2 pages/sec. (4/5) Ãˇ (2/5) = (4/5) × (5/2) = 20/10 = 2 pages per second.
  11. Aria reads 2/7 of a book in 1/2 of a day. At this rate, how many books does she read per day? — 4/7 book/day. (2/7) Ãˇ (1/2) = (2/7) × 2 = 4/7 of a book per day.
  12. If you travel 5/8 of a kilometer in 1/4 of an hour, what is your speed? — 5/2 km/h. (5/8) Ãˇ (1/4) = (5/8) × 4 = 20/8 = 5/2 = 2.5 km/h.
  13. Which table does NOT show a proportional relationship? — x: 1, 2, 3 and y: 3, 6, 10. In the third table, 3/1 = 3, 6/2 = 3, but 10/3 ≠ 3. The ratio is not constant, so it is not proportional.
  14. The equation y = 4x + 1 represents: — A non-proportional linear relationship. Because of the "+1", the graph does not pass through the origin. It is linear but NOT proportional.
  15. A proportional relationship has k = 12. Which point is on the graph? — (3, 36). y = 12x. When x = 3, y = 12 × 3 = 36. So (3, 36) is on the graph.
  16. Two points on a proportional graph are (2, 9) and (6, 27). What is the constant of proportionality? — 4.5. k = 9/2 = 4.5 (or 27/6 = 4.5). Both ratios are equal, confirming k = 4.5.
  17. Which statement is true about all proportional relationships? — The ratio y/x is constant for all points. By definition, a proportional relationship has a constant ratio y/x = k for every point (excluding origin).
  18. A taxi charges $3 per mile. The relationship between miles m and cost C is: — Proportional: C = 3m. If the ONLY charge is $3/mile with no base fee, C = 3m is proportional. A base fee would make it non-proportional.
  19. A proportional relationship has k = 0.5. What does this mean? — For every 1 unit of x, y increases by 0.5. k = 0.5 means y = 0.5x. For every increase of 1 in x, y increases by 0.5.
  20. The ratio y/x for a proportional relationship is always equal to: — The constant of proportionality k. In y = kx, dividing both sides by x gives y/x = k. This ratio equals the constant of proportionality.
  21. A recipe calls for 3 cups of flour for every 2 cups of sugar. What is k (flour per sugar)? — 3/2. k = flour/sugar = 3/2 = 1.5 cups of flour per cup of sugar.
  22. If y = 45 when x = 9 and the relationship is proportional, what is y when x = 5? — 25. k = 45/9 = 5. So y = 5x. When x = 5, y = 5 × 5 = 25.
  23. Water drains from a tank at a constant rate. After 4 minutes, 24 gallons have drained. How many gallons drain in 7 minutes? — 42 gallons. Rate k = 24/4 = 6 gallons/min. In 7 minutes: 6 × 7 = 42 gallons.
  24. A worker earns $180 for 9 hours. Using proportionality, how much does she earn in 15 hours? — $300. k = 180/9 = $20/hr. In 15 hours: 20 × 15 = $300.
  25. A store marks up a product by 40%. If the cost price is $35, what is the selling price? — $49. Markup = $35 × 0.40 = $14. Selling price = $35 + $14 = $49.
  26. If a price increases from $40 to $50, what is the percent increase? — 25%. Percent increase = (change/original) × 100 = (10/40) × 100 = 25%.
  27. A $500 loan has a 6% annual interest rate. How much is owed after 2 years (principal + interest)? — $560. I = 500 × 0.06 × 2 = $60. Total owed = $500 + $60 = $560.
  28. You buy a $75 shirt and pay 9% sales tax. What is the total cost? — $81.75. Tax = $75 × 0.09 = $6.75. Total = $75 + $6.75 = $81.75.
  29. If a price decreases from $80 to $60, what is the percent decrease? — 25%. Percent decrease = (20/80) × 100 = 25%.
  30. You deposit $1,000 at 3% annual simple interest. After 5 years, what is your total balance? — $1,150. I = 1000 × 0.03 × 5 = $150. Balance = $1,000 + $150 = $1,150.
  31. A coat costs $90, but is on sale for $72. What percent off is the coat? — 20%. Discount = $90 − $72 = $18. Percent off = 18/90 = 0.20 = 20%.
  32. A school population grew from 400 to 460 students. What is the percent increase? — 15%. Percent increase = (60/400) × 100 = 15%.
  33. A store adds a 60% markup to items that cost $25 to make. What is the retail price? — $40. Markup = $25 × 0.60 = $15. Retail = $25 + $15 = $40.
  34. What is 12.5% of 200? — 25. 200 × 0.125 = 25. Or: 10% = 20, 2.5% = 5, total = 25.