Unit Conversion

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Unit Conversion · Grade 6 · Worksheet 2

1. A map of a national park uses a scale where 1 centimeter represents 2.5 kilometers of actual distance. If the hiking trail from the visitor center to the waterfall measures 8.4 centimeters on the map, how many meters long is the actual hiking trail? Answer: 21000 Solution: The map scale is 1 cm : 2.5 km. The trail on the map is 8.4 cm long.
   Full step-by-step solution

   Step 1: The map scale is 1 cm : 2.5 km. The trail on the map is 8.4 cm long. Step 2: Calculate the actual distance in kilometers: 8.4 cm × 2.5 km/cm = 21 km Step 3: Convert kilometers to meters: 1 km = 1000 m, so 21 km = 21 × 1000 = 21000 m Step 4: The actual hiking trail is 21000 meters long.

2. A recipe for making fruit punch requires mixing 2 cups of orange juice with 5 cups of pineapple juice. If Emma wants to make a larger batch using 8 cups of orange juice, how many cups of pineapple juice should she use to maintain the same flavor ratio? Answer: 20 Solution: Identify the original ratio of orange juice to pineapple juice: 2 cups orange juice to 5 cups pineapple juice Set up a proportion to find the new amount of pineapple juice: 2/5 = 8/x Cross-multiply: 2 × x = 5 × 8 Simplify: 2x = 40 Divide both sides by 2: x = 40 ÷ 2 Calculate: x = 20 Emma should…
   Full step-by-step solution

   Step 1: Identify the original ratio of orange juice to pineapple juice: 2 cups orange juice to 5 cups pineapple juice Step 2: Set up a proportion to find the new amount of pineapple juice: 2/5 = 8/x Step 3: Cross-multiply: 2 × x = 5 × 8 Step 4: Simplify: 2x = 40 Step 5: Divide both sides by 2: x = 40 ÷ 2 Step 6: Calculate: x = 20 Emma should use 20 cups of pineapple juice.

3. A construction company needs to mix concrete using cement, sand, and gravel in a ratio of 1:2:4. If they need 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 number of ratio parts: 1 + 2 + 4 = 7 parts Cement represents 1 part out of 7 total parts, so fraction for cement = 1/7 Calculate cement needed in cubic meters: 3.5 cubic meters × (1/7) = 0.5 cubic meters Convert cubic meters to liters: 0.5 cubic meters × 1000 liters/cubic meter =…
   Full step-by-step solution

   Step 1: Find the total number of ratio parts: 1 + 2 + 4 = 7 parts Step 2: Cement represents 1 part out of 7 total parts, so fraction for cement = 1/7 Step 3: Calculate cement needed in cubic meters: 3.5 cubic meters × (1/7) = 0.5 cubic meters Step 4: Convert cubic meters to liters: 0.5 cubic meters × 1000 liters/cubic meter = 500 liters The answer is 500 liters.

4. Convert 2.5 kilometers to meters using the ratio 1 km : 1000 m = ? Answer: 2500 Solution: We know that 1 kilometer is equal to 1000 meters. So, 1 km = 1000 m. Write the given value that we need to convert.
   Full step-by-step solution

   Step 1: Understand the relationship between kilometers and meters. We know that 1 kilometer is equal to 1000 meters. So, 1 km = 1000 m. Step 2: Write the given value that we need to convert. We have 2.5 kilometers. Step 3: Set up the conversion using the ratio 1 km : 1000 m. Since 1 km = 1000 m, to convert kilometers to meters, we multiply the number of kilometers by 1000. Step 4: Perform the multiplication. 2.5 km × 1000 m/km = 2.5 × 1000 m Step 5: Calculate the result. 2.5 × 1000 = 2500 Step 6: Write the final answer with units. So, 2.5 kilometers = 2500 meters. ANSWER: 2500

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. 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.

7. Convert 15.5 pounds to kilograms using the ratio 1 kg = 2.2 lb = ? Answer: 7.045 Solution: Write the conversion ratio as a fraction: 1 kg / 2.2 lb Set up a proportion: 1 kg / 2.2 lb = x kg / 15.5 lb Cross-multiply: 1 × 15.5 = 2.2 × x Simplify: 15.5 = 2.2x Divide both sides by 2.2: x = 15.5 ÷ 2.2 Calculate: 15.5 ÷ 2.2 = 7.04545...
   Full step-by-step solution

   Step 1: Write the conversion ratio as a fraction: 1 kg / 2.2 lb Step 2: Set up a proportion: 1 kg / 2.2 lb = x kg / 15.5 lb Step 3: Cross-multiply: 1 × 15.5 = 2.2 × x Step 4: Simplify: 15.5 = 2.2x Step 5: Divide both sides by 2.2: x = 15.5 ÷ 2.2 Step 6: Calculate: 15.5 ÷ 2.2 = 7.04545... Step 7: Round to three decimal places: 7.045 The answer is 7.045 kilograms.

8. Lily is creating a scale model of her city's new library building. The actual library will be 45 meters tall, and her model uses a scale ratio of 1:150. If she needs to convert the model height from meters to centimeters for her display, how many centimeters tall will her model be? Answer: 30 Solution: Find the model height in meters using the scale ratio 1:150 Model height = Actual height ÷ Scale factor Model height = 45 meters ÷ 150 Model height = 0.3 meters Since 1 meter = 100 centimeters 0.3 meters × 100 = 30 centimeters The answer is 30 centimeters.
   Full step-by-step solution

   Step 1: Find the model height in meters using the scale ratio 1:150 Model height = Actual height ÷ Scale factor Model height = 45 meters ÷ 150 Model height = 0.3 meters Step 2: Convert meters to centimeters Since 1 meter = 100 centimeters 0.3 meters × 100 = 30 centimeters The answer is 30 centimeters.