Unit Conversion

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Unit Conversion · Grade 6 · Worksheet 1

1. A construction company needs to mix concrete using a ratio of 3 parts cement to 5 parts sand to 2 parts gravel. If they need to make 2500 kilograms of concrete for a foundation, how many kilograms of sand should they use? Answer: 1250 Solution: Find the total number of parts in the ratio: 3 (cement) + 5 (sand) + 2 (gravel) = 10 total parts Determine what fraction of the mixture is sand: 5 parts sand out of 10 total parts = 5/10 = 1/2 Calculate the amount of sand needed: 1/2 of 2500 kg = 2500 × 1/2 = 1250 kg The answer is 1250 kilograms…
   Full step-by-step solution

   Step 1: Find the total number of parts in the ratio: 3 (cement) + 5 (sand) + 2 (gravel) = 10 total parts Step 2: Determine what fraction of the mixture is sand: 5 parts sand out of 10 total parts = 5/10 = 1/2 Step 3: Calculate the amount of sand needed: 1/2 of 2500 kg = 2500 × 1/2 = 1250 kg The answer is 1250 kilograms of sand.

2. Convert 2.4 kilometers to meters using the ratio 1:1000 = ? Answer: 2400 Solution: Identify the conversion ratio: 1 km = 1000 m Multiply the given kilometers by the conversion factor: 2.4 × 1000 Calculate: 2.4 × 1000 = 2400 The answer is 2400 meters.
   Full step-by-step solution

   Step 1: Identify the conversion ratio: 1 km = 1000 m Step 2: Multiply the given kilometers by the conversion factor: 2.4 × 1000 Step 3: Calculate: 2.4 × 1000 = 2400 Step 4: The answer is 2400 meters.

3. A triangular garden is drawn on a coordinate plane with vertices at (0,0), (15,0), and (0,8). The scale ratio for the drawing is 1 unit = 4 meters. What is the actual area of the garden in square meters? Answer: 960 Solution: Identify the base and height from the coordinates. The base extends from (0,0) to (15,0), so base = 15 units. The height extends from (0,0) to (0,8), so height = 8 units.
   Full step-by-step solution

   Step 1: Identify the base and height from the coordinates. The base extends from (0,0) to (15,0), so base = 15 units. The height extends from (0,0) to (0,8), so height = 8 units. Step 2: Calculate the area on the coordinate plane. Area of triangle = (1/2) × base × height = (1/2) × 15 × 8 = (1/2) × 120 = 60 square units. Step 3: Apply the scale ratio. 1 unit = 4 meters, so 1 square unit = (4 meters) × (4 meters) = 16 square meters. Step 4: Convert the area. Actual area = 60 square units × 16 square meters/square unit = 960 square meters. The answer is 960.

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. Sophia is looking at a scale drawing of a rectangular park on a coordinate grid. The corners of the park are at (1, 1), (11, 1), (11, 6), and (1, 6). The scale ratio is 1 unit = 16 meters. What is the actual area of the park in square meters? Answer: 12800 Solution: Find the length on the grid. The x-coordinates are 1 and 11, so length = 11 - 1 = 10 units. Step 2: Find the width on the grid.
   Full step-by-step solution

   Step 1: Find the length on the grid. The x-coordinates are 1 and 11, so length = 11 - 1 = 10 units. Step 2: Find the width on the grid. The y-coordinates are 1 and 6, so width = 6 - 1 = 5 units. Step 3: Convert to actual meters using the scale 1 unit = 16 meters. Actual length = 10 units * 16 meters/unit = 160 meters. Actual width = 5 units * 16 meters/unit = 80 meters. Step 4: Calculate area = length * width = 160 * 80 = 12800 square meters. The answer is 12800.

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. 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. A construction company is building a new highway and needs to convert between metric units. The blueprint shows that a bridge support must be 2.5 meters tall, but the construction materials are measured in centimeters. Additionally, the concrete mixture requires a water-to-cement ratio of 0.45:1. If the crew uses 1200 kilograms of cement, how many liters of water should they use? (Remember: 1 cubic meter of water = 1000 liters, and water has a density of 1 kg per liter) Answer: 540 Solution: Identify the water-to-cement ratio: 0.45:1 means 0.45 parts water to 1 part cement The crew uses 1200 kg of cement, so we multiply by the ratio: 1200 × 0.45 = 540 Since water has a density of 1 kg per liter, 540 kg of water equals 540 liters The bridge height information (2.5 meters = 250…
   Full step-by-step solution

   Step 1: Identify the water-to-cement ratio: 0.45:1 means 0.45 parts water to 1 part cement Step 2: The crew uses 1200 kg of cement, so we multiply by the ratio: 1200 × 0.45 = 540 Step 3: Since water has a density of 1 kg per liter, 540 kg of water equals 540 liters Step 4: The bridge height information (2.5 meters = 250 centimeters) is not needed for this specific calculation Step 5: The crew should use 540 liters of water