Unit Conversion

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Answer Key & Explanations

Unit Conversion · Grade 6 · Worksheet 1

1. Convert 7.5 gallons to liters using the ratio 1 gallon : 3.785 liters = ? Answer: 28.3875 Solution: Identify the conversion ratio: 1 gallon = 3.785 liters. Write a proportion: 1 gallon / 3.785 liters = 7.5 gallons / x liters. Cross-multiply: 1 * x = 7.5 * 3.785.
   Full step-by-step solution

   Step 1: Identify the conversion ratio: 1 gallon = 3.785 liters. Step 2: Write a proportion: 1 gallon / 3.785 liters = 7.5 gallons / x liters. Step 3: Cross-multiply: 1 * x = 7.5 * 3.785. Step 4: Calculate: 7.5 * 3.785 = 28.3875. Step 5: So x = 28.3875 liters. The answer is 28.3875 liters.

2. A rectangular swimming pool is drawn on a coordinate plane with corners at (2,3), (14,3), (14,9), and (2,9). The scale ratio for the drawing is 1 unit = 4 meters. What is the actual area of the swimming pool in square meters? Answer: 1152 Solution: Find the length of the rectangle on the coordinate plane. The x-coordinates are 2 and 14, so the length is 14 - 2 = 12 units. Find the width of the rectangle on the coordinate plane.
   Full step-by-step solution

   Step 1: Find the length of the rectangle on the coordinate plane. The x-coordinates are 2 and 14, so the length is 14 - 2 = 12 units. Step 2: Find the width of the rectangle on the coordinate plane. The y-coordinates are 3 and 9, so the width is 9 - 3 = 6 units. Step 3: Convert the drawing dimensions to actual dimensions using the scale ratio. The scale is 1 unit = 4 meters, so: Actual length = 12 units × 4 meters/unit = 48 meters Actual width = 6 units × 4 meters/unit = 24 meters Step 4: Calculate the actual area of the swimming pool. Area = length × width = 48 meters × 24 meters = 1152 square meters The answer is 1152.

3. 1 mile = 1.6 km. Convert 16 miles to km using the ratio 1 : 1.6 = ? Answer: 25.6 Solution: Write the conversion ratio: 1 mile = 1.6 km. Set up a proportion: 1 mile / 1.6 km = 16 miles / x km. Cross-multiply: 1 * x = 16 * 1.6.
   Full step-by-step solution

   Step 1: Write the conversion ratio: 1 mile = 1.6 km. Step 2: Set up a proportion: 1 mile / 1.6 km = 16 miles / x km. Step 3: Cross-multiply: 1 * x = 16 * 1.6. Step 4: Calculate: 16 * 1.6 = 25.6. Step 5: So x = 25.6 km. The answer is 25.6 km.

4. 1 mile = 1.6 km. Convert 15 miles to kilometers using the ratio 1:1.6 = ? Answer: 24 Solution: Write the conversion ratio: 1 mile = 1.6 km. Set up the proportion: 1 mile / 1.6 km = 15 miles / x km. Cross-multiply: 1 × x = 15 × 1.6.
   Full step-by-step solution

   Step 1: Write the conversion ratio: 1 mile = 1.6 km. Step 2: Set up the proportion: 1 mile / 1.6 km = 15 miles / x km. Step 3: Cross-multiply: 1 × x = 15 × 1.6. Step 4: Calculate: 15 × 1.6 = 24. Step 5: So x = 24 km. The answer is 24.

5. Convert 12.5 gallons to liters using the ratio 1 gallon = 3.785 liters = ? Answer: 47.3125 Solution: Write the conversion ratio: 1 gallon = 3.785 liters Set up the proportion: 1/3.785 = 12.5/x Cross-multiply: 1 × x = 12.5 × 3.785 Calculate: 12.5 × 3.785 = 47.3125 So x = 47.3125 The answer is 47.3125 liters.
   Full step-by-step solution

   Step 1: Write the conversion ratio: 1 gallon = 3.785 liters Step 2: Set up the proportion: 1/3.785 = 12.5/x Step 3: Cross-multiply: 1 × x = 12.5 × 3.785 Step 4: Calculate: 12.5 × 3.785 = 47.3125 Step 5: So x = 47.3125 The answer is 47.3125 liters.

6. Matiu is looking at a scale drawing of a rectangular park. The drawing shows the park's corners at (3, 4), (27, 4), (27, 19), and (3, 19). The scale ratio is 1 unit = 5 meters. What is the actual perimeter of the park in meters? Answer: 390 Solution: Find the length of the park in drawing units. The x-coordinates are 3 and 27, so length = 27 - 3 = 24 units. Find the width of the park in drawing units.
   Full step-by-step solution

   Step 1: Find the length of the park in drawing units. The x-coordinates are 3 and 27, so length = 27 - 3 = 24 units. Step 2: Find the width of the park in drawing units. The y-coordinates are 4 and 19, so width = 19 - 4 = 15 units. Step 3: Convert the drawing dimensions to actual meters using the scale ratio 1 unit = 5 meters. Actual length = 24 units x 5 meters/unit = 120 meters. Actual width = 15 units x 5 meters/unit = 75 meters. Step 4: Calculate the actual perimeter of the park. Perimeter = 2 x (length + width) = 2 x (120 + 75) = 2 x 195 = 390 meters. The answer is 390.

7. A factory produces 2,400 bottles of juice per hour. If each bottle contains 0.75 liters of juice, how many liters of juice does the factory produce in 3.5 hours? Answer: 6300 Solution: Find the total number of bottles produced in 3.5 hours. The factory produces 2,400 bottles per hour.
   Full step-by-step solution

   Step 1: Find the total number of bottles produced in 3.5 hours. The factory produces 2,400 bottles per hour. So in 3.5 hours, the number of bottles is: 2400 × 3.5 = 2400 × (3 + 0.5) = 2400 × 3 + 2400 × 0.5 = 7200 + 1200 = 8400 bottles. Step 2: Find the total liters of juice produced. Each bottle contains 0.75 liters. So total liters = number of bottles × liters per bottle = 8400 × 0.75. Step 3: Calculate 8400 × 0.75. 0.75 is the same as 3/4, so: 8400 × 3/4 = (8400 ÷ 4) × 3 = 2100 × 3 = 6300 liters. Final Answer: 6300 liters.

8. Liam is creating a scale model of the Golden Gate Bridge for his science project. The actual bridge is 2,737 meters long, and he's using a scale ratio of 1:500. If Liam needs to convert his model's length from meters to centimeters for display, how many centimeters long will his model be? Answer: 547.4 Solution: Calculate the model length in meters using the scale ratio 1:500 Model length (meters) = Actual length ÷ Scale factor Model length = 2,737 ÷ 500 = 5.474 meters Since 1 meter = 100 centimeters Model length (cm) = 5.474 × 100 = 547.4 centimeters The answer is 547.4 centimeters.
   Full step-by-step solution

   Step 1: Calculate the model length in meters using the scale ratio 1:500 Model length (meters) = Actual length ÷ Scale factor Model length = 2,737 ÷ 500 = 5.474 meters Step 2: Convert meters to centimeters Since 1 meter = 100 centimeters Model length (cm) = 5.474 × 100 = 547.4 centimeters The answer is 547.4 centimeters.

9. Convert 2.5 kilometers to meters using the ratio 1:1000 = ? Answer: 2500 Solution: We know that 1 kilometer equals 1000 meters. Write down the given quantity. We have 2.5 kilometers.
   Full step-by-step solution

   Step 1: Understand the relationship between kilometers and meters. We know that 1 kilometer equals 1000 meters. So the ratio 1 km : 1000 m is correct. Step 2: Write down the given quantity. We have 2.5 kilometers. Step 3: Set up the conversion. To convert kilometers to meters, multiply the number of kilometers by 1000. So: 2.5 km × 1000 = ? Step 4: Perform the multiplication. 2.5 × 1000 = 2500 Step 5: Write the answer with units. 2.5 kilometers = 2500 meters. Final answer: 2500