# Worksheet: Working With Units ## Section A: Multiple Choice Questions
Q1: A car travels 180 miles in 3 hours. What is the car's average speed in miles per hour? (a) 60 miles per hour (b) 183 miles per hour (c) 54 miles per hour (d) 540 miles per hour
Solution:
Ans: (a) Explanation: To find average speed, divide the total distance by the total time. \(\text{Speed} = \frac{180 \text{ miles}}{3 \text{ hours}} = 60 \text{ miles per hour}\). Option (b) incorrectly adds the values, option (c) uses incorrect division, and option (d) incorrectly multiplies.
Q2: Which of the following correctly converts 5 feet to inches? (a) 5 inches (b) 60 inches (c) 50 inches (d) 15 inches
Solution:
Ans: (b) Explanation: Since 1 foot = 12 inches, we use the conversion factor: \(5 \text{ feet} × 12 = 60 \text{ inches}\). Option (a) forgets to convert, option (c) incorrectly multiplies by 10, and option (d) incorrectly multiplies by 3.
Q3: A rectangle has a length of 8 meters and a width of 5 meters. What is the area in square meters? (a) 13 square meters (b) 26 square meters (c) 40 square meters (d) 40 meters
Solution:
Ans: (c) Explanation:Area of a rectangle is calculated using \(A = \text{length} × \text{width} = 8 × 5 = 40 \text{ square meters}\). Option (a) incorrectly adds the dimensions, option (b) calculates the perimeter, and option (d) has incorrect units (should be square meters, not meters).
Q4: A recipe requires 2.5 cups of flour. How many cups are needed for 4 batches of the recipe? (a) 6.5 cups (b) 8 cups (c) 10 cups (d) 2.9 cups
Solution:
Ans: (c) Explanation: To find the total amount needed, multiply the amount per batch by the number of batches: \(2.5 × 4 = 10 \text{ cups}\). Option (a) incorrectly adds 4 to 2.5, option (b) uses incorrect multiplication, and option (d) incorrectly adds 0.4 to 2.5.
Q5: A student measures the mass of an object as 3.2 kilograms. What is the mass in grams? (a) 32 grams (b) 320 grams (c) 3200 grams (d) 0.32 grams
Solution:
Ans: (c) Explanation: Since 1 kilogram = 1000 grams, the conversion is \(3.2 × 1000 = 3200 \text{ grams}\). Option (a) multiplies by 10 instead of 1000, option (b) multiplies by 100, and option (d) incorrectly divides instead of multiplying.
Q6: Water flows from a faucet at a rate of 4 liters per minute. How many liters flow in 15 minutes? (a) 19 liters (b) 11 liters (c) 60 liters (d) 3.75 liters
Solution:
Ans: (c) Explanation: To find the total volume, multiply the rate by the time: \(4 \text{ liters/minute} × 15 \text{ minutes} = 60 \text{ liters}\). Option (a) incorrectly adds the values, option (b) calculates the difference, and option (d) incorrectly divides instead of multiplying.
Q7: A rectangular prism has dimensions 3 cm × 4 cm × 5 cm. What is the volume in cubic centimeters? (a) 12 cubic centimeters (b) 60 cubic centimeters (c) 15 cubic centimeters (d) 20 cubic centimeters
Solution:
Ans: (b) Explanation: The volume of a rectangular prism is \(V = \text{length} × \text{width} × \text{height} = 3 × 4 × 5 = 60 \text{ cubic centimeters}\). Option (a) only multiplies two dimensions, option (c) only multiplies 3 and 5, and option (d) only multiplies 4 and 5.
Q8: A bottle contains 2 liters of juice. If 1 liter equals approximately 33.8 fluid ounces, approximately how many fluid ounces are in the bottle? (a) 35.8 fluid ounces (b) 67.6 fluid ounces (c) 16.9 fluid ounces (d) 33.8 fluid ounces
Solution:
Ans: (b) Explanation: Using the conversion factor, multiply: \(2 × 33.8 = 67.6 \text{ fluid ounces}\). Option (a) incorrectly adds 2 to 33.8, option (c) incorrectly divides 33.8 by 2, and option (d) forgets to account for 2 liters.
## Section B: Fill in the Blanks Q9: The formula for calculating speed is speed = __________ divided by time.
Solution:
Ans: distance Explanation: The speed formula is \(\text{speed} = \frac{\text{distance}}{\text{time}}\), which shows the relationship between distance traveled and time taken.
Q10: To convert from a larger unit to a smaller unit, you should __________ by the conversion factor.
Solution:
Ans: multiply Explanation: When converting from a larger unit to a smaller unit (e.g., meters to centimeters), you multiply by the conversion factor because there are more of the smaller units.
Q11: The unit for measuring area is always a __________ unit.
Solution:
Ans: square Explanation:Area measures two-dimensional space, so it uses square units such as square meters (m²), square feet (ft²), or square centimeters (cm²).
Q12: In the metric system, 1 meter equals __________ centimeters.
Solution:
Ans: 100 Explanation: The metric system uses powers of 10. Since centi- means one-hundredth, 1 meter = 100 centimeters.
Q13: The volume of a three-dimensional object is measured in __________ units.
Solution:
Ans: cubic Explanation:Volume measures three-dimensional space, so it uses cubic units such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³).
Q14: When multiplying two measurements with units, the resulting unit is found by __________ the original units.
Solution:
Ans: multiplying Explanation: In dimensional analysis, when you multiply measurements, you also multiply their units. For example, \(5 \text{ m} × 3 \text{ m} = 15 \text{ m}^2\).
## Section C: Word Problems Q15: A swimming pool is being filled with water at a rate of 25 gallons per minute. How many gallons of water will be in the pool after 18 minutes?
Q16: A garden measures 12 feet by 8 feet. Landscaping fabric costs $2.50 per square foot. How much will it cost to cover the entire garden with the fabric?
Q19: A scientist measures a sample with a mass of 4.5 kilograms. If she needs to convert this measurement to grams for her lab report, what value should she record?
Solution:
Ans: \[\text{Mass in grams} = 4.5 \text{ kg} × 1000 \text{ g/kg} = 4500 \text{ g}\] Final Answer: 4500 grams
Q20: A rectangular parking lot is 150 meters long and 80 meters wide. The lot needs to be resurfaced at a cost of $15 per square meter. What is the total cost to resurface the parking lot?
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