Unit Conversion

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Unit Conversion · Grade 6 · Worksheet 2

1. A car's fuel efficiency is 32 miles per gallon. If the car's gas tank holds 15.5 gallons, how many kilometers can the car travel on a full tank? (Use the conversion: 1 mile = 1.6 kilometers) Answer: 793.6 Solution: Calculate how many miles the car can travel on a full tank Miles = fuel efficiency × tank capacity Miles = 32 × 15.5 Miles = 496 Convert miles to kilometers using the conversion factor Kilometers = miles × 1.6 Kilometers = 496 × 1.6 Kilometers = 793.6 The car can travel 793.6 kilometers on a…
   Full step-by-step solution

   Step 1: Calculate how many miles the car can travel on a full tank Miles = fuel efficiency × tank capacity Miles = 32 × 15.5 Miles = 496 Step 2: Convert miles to kilometers using the conversion factor Kilometers = miles × 1.6 Kilometers = 496 × 1.6 Kilometers = 793.6 The car can travel 793.6 kilometers on a full tank.

2. Liam is building a model of the Eiffel Tower using a scale ratio of 1:150. If the actual Eiffel Tower is 330 meters tall, how many centimeters tall should Liam's model be? Answer: 220 Solution: The scale ratio 1:150 means that 1 unit on the model represents 150 units on the actual tower. Write the relationship between model height and actual height. Let the model height be \( h \) meters.
   Full step-by-step solution

   Step 1: Understand the scale ratio. The scale ratio 1:150 means that 1 unit on the model represents 150 units on the actual tower. Step 2: Write the relationship between model height and actual height. Let the model height be \( h \) meters. From the scale: \( h / 330 = 1 / 150 \) Step 3: Solve for \( h \) in meters. \( h = 330 / 150 \) \( h = 33 / 15 \) \( h = 11 / 5 \) \( h = 2.2 \) meters. Step 4: Convert meters to centimeters. We know 1 meter = 100 centimeters. So \( 2.2 \) meters = \( 2.2 \times 100 = 220 \) centimeters. Step 5: Final answer. Liam's model should be 220 centimeters tall.

3. A map of the United States uses a scale where 1 inch represents 150 miles. The actual distance between Chicago and New York City is 790 miles. How many inches apart should these cities be on the map? Round your answer to the nearest hundredth of an inch. Answer: 5.27 Solution: Identify the scale ratio: 1 inch on the map represents 150 miles in reality.
   Full step-by-step solution

   Step 1: Identify the scale ratio: 1 inch on the map represents 150 miles in reality. Step 2: Set up a proportion where the map distance (in inches) is to the actual distance (in miles) as the scale is: map_distance / 790 = 1 / 150 Step 3: Solve for the map distance: map_distance = 790 / 150 Step 4: Calculate the division: 790 ÷ 150 = 5.2666... Step 5: Round to the nearest hundredth: 5.2666... rounds to 5.27 Therefore, the cities should be 5.27 inches apart on the map.

4. 1 kilogram = 2.2 pounds. Convert 15 kilograms to pounds using the ratio 1 kg : 2.2 lb = ? Answer: 33 Solution: Write the ratio as a proportion: 1 kg / 2.2 lb = 15 kg / x lb Cross-multiply: 1 * x = 15 * 2.2 Calculate: 15 * 2.2 = 33 So x = 33 The answer is 33 pounds.
   Full step-by-step solution

   Step 1: Write the ratio as a proportion: 1 kg / 2.2 lb = 15 kg / x lb Step 2: Cross-multiply: 1 * x = 15 * 2.2 Step 3: Calculate: 15 * 2.2 = 33 Step 4: So x = 33 The answer is 33 pounds.

5. A rectangular swimming pool is drawn on a coordinate plane with corners at (1,2), (11,2), (11,7), and (1,7). The scale ratio is 1 unit = 2.5 meters. What is the actual area of the swimming pool in square meters? Answer: 312.5 Solution: Find the length of the rectangle using the x-coordinates: 11 - 1 = 10 units Find the width of the rectangle using the y-coordinates: 7 - 2 = 5 units Convert length to actual meters: 10 units × 2.5 meters/unit = 25 meters Convert width to actual meters: 5 units × 2.5 meters/unit = 12.5 meters…
   Full step-by-step solution

   Step 1: Find the length of the rectangle using the x-coordinates: 11 - 1 = 10 units Step 2: Find the width of the rectangle using the y-coordinates: 7 - 2 = 5 units Step 3: Convert length to actual meters: 10 units × 2.5 meters/unit = 25 meters Step 4: Convert width to actual meters: 5 units × 2.5 meters/unit = 12.5 meters Step 5: Calculate actual area: 25 meters × 12.5 meters = 312.5 square meters The answer is 312.5.

6. Kaia is looking at a scale drawing of a rectangular playground on a coordinate grid. The corners of the playground are marked at points (3, 2), (18, 2), (18, 12), and (3, 12). The scale ratio for the drawing is 1 unit = 9 meters. What is the actual perimeter of the playground in meters? Answer: 450 Solution: Find the length on the grid. The x-coordinates are 3 and 18, so the length is 18 - 3 = 15 units. Find the width on the grid.
   Full step-by-step solution

   Step 1: Find the length on the grid. The x-coordinates are 3 and 18, so the length is 18 - 3 = 15 units. Step 2: Find the width on the grid. The y-coordinates are 2 and 12, so the width is 12 - 2 = 10 units. Step 3: Convert the length to actual meters using the scale. 1 unit = 9 meters, so actual length = 15 units * 9 meters/unit = 135 meters. Step 4: Convert the width to actual meters. Actual width = 10 units * 9 meters/unit = 90 meters. Step 5: Calculate the actual perimeter. Perimeter = 2 * (length + width) = 2 * (135 + 90) = 2 * 225 = 450 meters. The answer is 450.

7. Charlotte is looking at a scale drawing of a rectangular playground on a coordinate grid. The corners of the playground are at (2, 2), (17, 2), (17, 12), and (2, 12). The scale ratio is 1 unit = 7 meters. What is the actual area of the playground in square meters? Answer: 7350 Solution: Find the length of the rectangle in grid units. The x-coordinates are 2 and 17, so length = 17 - 2 = 15 units. Find the width of the rectangle in grid units.
   Full step-by-step solution

   Step 1: Find the length of the rectangle in grid units. The x-coordinates are 2 and 17, so length = 17 - 2 = 15 units. Step 2: Find the width of the rectangle in grid units. The y-coordinates are 2 and 12, so width = 12 - 2 = 10 units. Step 3: Convert grid units to actual meters using the scale 1 unit = 7 meters. Actual length = 15 units × 7 meters/unit = 105 meters Actual width = 10 units × 7 meters/unit = 70 meters Step 4: Calculate the actual area. Area = length × width = 105 × 70 = 7350 square meters. The answer is 7350.

8. 1 kilogram = 2.2 pounds. Convert 7 kilograms to pounds using the ratio 1:2.2 = ? Answer: 15.4 Solution: The conversion ratio is 1 kilogram = 2.2 pounds. Set up a proportion: 1/2.2 = 7/x Cross-multiply: 1 * x = 7 * 2.2 Calculate: x = 15.4 The answer is 15.4 pounds.
   Full step-by-step solution

   Step 1: The conversion ratio is 1 kilogram = 2.2 pounds. Step 2: Set up a proportion: 1/2.2 = 7/x Step 3: Cross-multiply: 1 * x = 7 * 2.2 Step 4: Calculate: x = 15.4 Step 5: The answer is 15.4 pounds.