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Unit Conversion

Grade 6 · Mathematics · Worksheet 3

  1. Convert 3.6 kilometers to meters using the ratio 1:1000 = ? Answer: ______________
  2. Convert 6.25 kilometers to meters using the ratio 1:1000 = ? Answer: ______________
  3. 1 mile = 1.6 km. Convert 16 miles to km using the ratio 1:1.6 = ? Answer: ______________
  4. 1 pound = 0.45 kilograms. Convert 20 pounds to kilograms using the ratio 1:0.45 = ? Answer: ______________
  5. A construction company is building a new bridge with a scale model for planning. The actual bridge will be 1.2 kilometers long, and the model uses a scale ratio of 1:150. If the model bridge is made from materials measured in centimeters, how many centimeters long should the model bridge be? Answer: ______________
  6. Convert 4.8 kilometers to meters using the ratio 1 km : 1000 m = ? Answer: ______________
  7. A construction company needs to mix concrete using cement, sand, and gravel in a ratio of 1:2:4. If they want to make 3.5 cubic meters of concrete, how many liters of cement do they need? (Remember: 1 cubic meter = 1000 liters) Answer: ______________
  8. 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 1500 kilograms of concrete for a foundation, how many kilograms of sand should they use? Answer: ______________
  9. A rectangular swimming pool is being filled with water. The pool measures 12.5 meters long, 8.4 meters wide, and 1.8 meters deep. If water flows into the pool at a rate of 0.25 cubic meters per minute, how many hours will it take to completely fill the pool? Answer: ______________
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Answer Key & Explanations

Unit Conversion · Grade 6 · Worksheet 3

  1. Convert 3.6 kilometers to meters using the ratio 1:1000 = ? Answer: 3600 Solution: Identify the conversion ratio: 1 km = 1000 m Multiply the given kilometers by the conversion factor: 3.6 × 1000 Calculate: 3.6 × 1000 = 3600 The answer is 3600 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: 3.6 × 1000 Step 3: Calculate: 3.6 × 1000 = 3600 Step 4: The answer is 3600 meters.

  2. Convert 6.25 kilometers to meters using the ratio 1:1000 = ? Answer: 6250 Solution: Identify the conversion ratio: 1 km = 1000 m Multiply the given kilometers by the conversion factor: 6.25 km × 1000 m/km Calculate: 6.25 × 1000 = 6250 The answer is 6250 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: 6.25 km × 1000 m/km Step 3: Calculate: 6.25 × 1000 = 6250 Step 4: The answer is 6250 meters.

  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: x = 25.6. The answer is 25.6 km.

  4. 1 pound = 0.45 kilograms. Convert 20 pounds to kilograms using the ratio 1:0.45 = ? Answer: 9 Solution: Identify the conversion ratio: 1 pound = 0.45 kilograms. Multiply the given pounds by the conversion factor: 20 × 0.45. Calculate: 20 × 0.45 = 9.
    Full step-by-step solution

    Step 1: Identify the conversion ratio: 1 pound = 0.45 kilograms. Step 2: Multiply the given pounds by the conversion factor: 20 × 0.45. Step 3: Calculate: 20 × 0.45 = 9. Step 4: The answer is 9 kilograms.

  5. A construction company is building a new bridge with a scale model for planning. The actual bridge will be 1.2 kilometers long, and the model uses a scale ratio of 1:150. If the model bridge is made from materials measured in centimeters, how many centimeters long should the model bridge be? Answer: 800 Solution: Convert the actual bridge length from kilometers to centimeters. Since 1 km = 1000 m and 1 m = 100 cm, then 1 km = 1000 * 100 = 100,000 cm. Actual bridge length in cm = 1.2 km * 100,000 cm/km = 120,000 cm.
    Full step-by-step solution

    Step 1: Convert the actual bridge length from kilometers to centimeters. Since 1 km = 1000 m and 1 m = 100 cm, then 1 km = 1000 * 100 = 100,000 cm. Step 2: Actual bridge length in cm = 1.2 km * 100,000 cm/km = 120,000 cm. Step 3: Apply the scale ratio 1:150. This means 1 cm on the model represents 150 cm in reality. Step 4: Model length = Actual length / Scale factor = 120,000 cm / 150 = 800 cm. The model bridge should be 800 centimeters long.

  6. Convert 4.8 kilometers to meters using the ratio 1 km : 1000 m = ? Answer: 4800 Solution: Identify the conversion ratio: 1 kilometer = 1000 meters. Multiply the number of kilometers by the number of meters in one kilometer. 4.8 km × 1000 m/km = 4800 m.
    Full step-by-step solution

    Step 1: Identify the conversion ratio: 1 kilometer = 1000 meters. Step 2: Multiply the number of kilometers by the number of meters in one kilometer. Step 3: 4.8 km × 1000 m/km = 4800 m. The answer is 4800 meters.

  7. A construction company needs to mix concrete using cement, sand, and gravel in a ratio of 1:2:4. If they want to make 3.5 cubic meters of concrete, how many liters of cement do they need? (Remember: 1 cubic meter = 1000 liters) Answer: 500 Solution: Find the total ratio parts: 1 (cement) + 2 (sand) + 4 (gravel) = 7 parts total Determine what fraction represents cement: 1/7 of the total mixture is cement Calculate cement volume in cubic meters: 1/7 × 3.5 m³ = 0.5 m³ Convert cubic meters to liters: 0.5 m³ × 1000 L/m³ = 500 L The construction…
    Full step-by-step solution

    Step 1: Find the total ratio parts: 1 (cement) + 2 (sand) + 4 (gravel) = 7 parts total Step 2: Determine what fraction represents cement: 1/7 of the total mixture is cement Step 3: Calculate cement volume in cubic meters: 1/7 × 3.5 m³ = 0.5 m³ Step 4: Convert cubic meters to liters: 0.5 m³ × 1000 L/m³ = 500 L Step 5: The construction company needs 500 liters of cement.

  8. 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 1500 kilograms of concrete for a foundation, how many kilograms of sand should they use? Answer: 750 Solution: Find the total number of parts in the ratio: 3 (cement) + 5 (sand) + 2 (gravel) = 10 parts total. Determine what fraction of the mixture is sand: 5 parts sand / 10 total parts = 5/10 = 1/2.
    Full step-by-step solution

    Step 1: Find the total number of parts in the ratio: 3 (cement) + 5 (sand) + 2 (gravel) = 10 parts total. Step 2: Determine what fraction of the mixture is sand: 5 parts sand / 10 total parts = 5/10 = 1/2. Step 3: Calculate the amount of sand needed: 1/2 × 1500 kg = 750 kg. The answer is 750 kilograms of sand.

  9. A rectangular swimming pool is being filled with water. The pool measures 12.5 meters long, 8.4 meters wide, and 1.8 meters deep. If water flows into the pool at a rate of 0.25 cubic meters per minute, how many hours will it take to completely fill the pool? Answer: 12.6 Solution: Volume = length × width × depth Volume = 12.5 m × 8.4 m × 1.8 m 12.5 × 8.4 = 105 105 × 1.8 = 189 cubic meters Time = Volume ÷ Rate Time = 189 ÷ 0.25 189 ÷ 0.25 = 756 minutes Hours = Minutes ÷ 60 Hours = 756 ÷ 60 756 ÷ 60 = 12.6 hours The answer is 12.6.
    Full step-by-step solution

    Step 1: Calculate the volume of the pool Volume = length × width × depth Volume = 12.5 m × 8.4 m × 1.8 m 12.5 × 8.4 = 105 105 × 1.8 = 189 cubic meters Step 2: Calculate the time in minutes to fill the pool Time = Volume ÷ Rate Time = 189 ÷ 0.25 189 ÷ 0.25 = 756 minutes Step 3: Convert minutes to hours Hours = Minutes ÷ 60 Hours = 756 ÷ 60 756 ÷ 60 = 12.6 hours The answer is 12.6.