Q1: A car travels at a speed of 60 miles per hour. What is this speed in miles per minute? (a) 1 mile per minute (b) 3600 miles per minute (c) 0.5 miles per minute (d) 120 miles per minute
Solution:
Ans: (a) Explanation: To convert from miles per hour to miles per minute, divide by 60 since there are 60 minutes in 1 hour. \(\frac{60 \text{ miles}}{1 \text{ hour}} \times \frac{1 \text{ hour}}{60 \text{ minutes}} = 1 \text{ mile per minute}\).
Q2: If a rectangle has a length of 5 feet and a width of 24 inches, what is the area in square feet? (a) 120 square feet (b) 10 square feet (c) 29 square feet (d) 60 square feet
Solution:
Ans: (b) Explanation: First, convert 24 inches to feet: \(24 \text{ inches} \times \frac{1 \text{ foot}}{12 \text{ inches}} = 2 \text{ feet}\). Then find the area: \(5 \text{ feet} \times 2 \text{ feet} = 10 \text{ square feet}\). Option (a) incorrectly multiplies 5 by 24 without converting units.
Q3: A bottle contains 2 liters of juice. How many milliliters is this? (a) 20 milliliters (b) 200 milliliters (c) 2000 milliliters (d) 0.002 milliliters
Q4: Water flows through a pipe at a rate of 12 gallons per minute. What is this rate in gallons per hour? (a) 720 gallons per hour (b) 0.2 gallons per hour (c) 12 gallons per hour (d) 72 gallons per hour
Solution:
Ans: (a) Explanation: Multiply by 60 to convert from gallons per minute to gallons per hour: \(12 \text{ gallons per minute} \times 60 \text{ minutes per hour} = 720 \text{ gallons per hour}\).
Q5: A recipe calls for 3 cups of flour. If 1 cup equals 8 fluid ounces, how many fluid ounces of flour are needed? (a) 11 fluid ounces (b) 24 fluid ounces (c) 3 fluid ounces (d) 32 fluid ounces
Q6: A person's weight is 150 pounds. If 1 kilogram equals approximately 2.2 pounds, what is the person's weight in kilograms (rounded to the nearest whole number)? (a) 330 kilograms (b) 68 kilograms (c) 152 kilograms (d) 75 kilograms
Solution:
Ans: (b) Explanation: Divide by the conversion factor: \(\frac{150 \text{ pounds}}{2.2 \text{ pounds per kilogram}} \approx 68.18 \text{ kilograms}\), which rounds to 68 kilograms. Option (a) incorrectly multiplies instead of dividing.
Q7: A garden has an area of 500 square feet. What is this area in square yards? (Note: 1 yard = 3 feet) (a) 1500 square yards (b) 167 square yards (c) 56 square yards (d) 4500 square yards
Q8: A cyclist travels 15 kilometers in 30 minutes. What is the cyclist's speed in kilometers per hour? (a) 0.5 kilometers per hour (b) 30 kilometers per hour (c) 7.5 kilometers per hour (d) 45 kilometers per hour
Solution:
Ans: (b) Explanation: First convert 30 minutes to hours: \(30 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} = 0.5 \text{ hours}\). Then calculate speed: \(\frac{15 \text{ kilometers}}{0.5 \text{ hours}} = 30 \text{ kilometers per hour}\).
Section B: Fill in the Blanks
Q9: To convert from feet to inches, you must multiply by __________.
Solution:
Ans: 12 Explanation: There are 12 inches in 1 foot, so the conversion factor is 12.
Q10: The unit rate of a quantity is found by dividing the total amount by the __________ of units.
Solution:
Ans: number Explanation: A unit rate expresses a quantity per one unit, which is found by dividing the total by the number of units.
Q11: If a rate is given as 45 miles per 3 hours, the simplified unit rate is __________ miles per hour.
Solution:
Ans: 15 Explanation: Divide the distance by the time: \(\frac{45 \text{ miles}}{3 \text{ hours}} = 15 \text{ miles per hour}\).
Q12: When converting from a larger unit to a smaller unit, you __________ by the conversion factor.
Solution:
Ans: multiply Explanation: Converting from a larger unit to a smaller unit requires multiplying because you need more of the smaller units to equal the larger unit.
Q13: A speed of 88 feet per second is equal to __________ miles per hour. (Note: 1 mile = 5280 feet)
Solution:
Ans: 60 Explanation: Convert feet per second to miles per hour: \(88 \frac{\text{feet}}{\text{second}} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{5280 \text{ feet}} = \frac{88 \times 3600}{5280} = 60 \text{ miles per hour}\).
Q14: When multiplying quantities with units, the units must be treated like __________ in algebra.
Solution:
Ans: variables Explanation: Units follow the same rules as algebraic variables, where identical units in the numerator and denominator cancel out.
Section C: Word Problems
Q15: A printer prints 8 pages per minute. How many pages can it print in 2.5 hours?
Solution:
Ans: First, convert 2.5 hours to minutes: \(2.5 \text{ hours} \times 60 \text{ minutes per hour} = 150 \text{ minutes}\) Then multiply by the printing rate: \(8 \text{ pages per minute} \times 150 \text{ minutes} = 1200 \text{ pages}\) Final Answer: 1200 pages
Q16: A rectangular swimming pool is 25 yards long and 36 feet wide. What is the area of the pool in square feet? (Note: 1 yard = 3 feet)
Solution:
Ans: Convert 25 yards to feet: \(25 \text{ yards} \times 3 \text{ feet per yard} = 75 \text{ feet}\) Calculate the area: \(75 \text{ feet} \times 36 \text{ feet} = 2700 \text{ square feet}\) Final Answer: 2700 square feet
Q17: A train travels 180 miles in 3 hours at a constant speed. At this same speed, how far will the train travel in 7 hours?
Solution:
Ans: Find the unit rate (speed): \(\frac{180 \text{ miles}}{3 \text{ hours}} = 60 \text{ miles per hour}\) Multiply by 7 hours: \(60 \text{ miles per hour} \times 7 \text{ hours} = 420 \text{ miles}\) Final Answer: 420 miles
Q18: A water tank can hold 500 gallons. If water flows into the tank at a rate of 4 gallons per minute, how many hours will it take to fill an empty tank completely?
Solution:
Ans: Find the time in minutes: \(\frac{500 \text{ gallons}}{4 \text{ gallons per minute}} = 125 \text{ minutes}\) Convert to hours: \(125 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{125}{60} = 2.083\overline{3} \text{ hours}\) This equals approximately 2.08 hours or 2 hours and 5 minutes. Final Answer: 2.08 hours (or 2 hours and 5 minutes)
Q19: A sports drink costs $3.60 for a 24-ounce bottle and $5.00 for a 40-ounce bottle. Which bottle has the lower unit price per ounce, and what is that unit price?
Solution:
Ans: Calculate the unit price for the 24-ounce bottle: \(\frac{\$3.60}{24 \text{ ounces}} = \$0.15 \text{ per ounce}\) Calculate the unit price for the 40-ounce bottle: \(\frac{\$5.00}{40 \text{ ounces}} = \$0.125 \text{ per ounce}\) The 40-ounce bottle has the lower unit price. Final Answer: The 40-ounce bottle has the lower unit price at $0.125 per ounce (or 12.5 cents per ounce)
Q20: A farmer has a field that measures 300 feet by 450 feet. He wants to know the area in acres. If 1 acre equals 43,560 square feet, what is the area of the field in acres? Round to the nearest hundredth.
Solution:
Ans: Calculate the area in square feet: \(300 \text{ feet} \times 450 \text{ feet} = 135,000 \text{ square feet}\) Convert to acres: \(\frac{135,000 \text{ square feet}}{43,560 \text{ square feet per acre}} \approx 3.0992 \text{ acres}\) Rounded to the nearest hundredth: 3.10 acres Final Answer: 3.10 acres
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