Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Unit Conversion

Grade 6 · Mathematics · Worksheet 3

  1. 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: ______________
  2. 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: ______________
  3. Convert 3.25 kilometers to meters using the ratio 1:1000 = ? Answer: ______________
  4. Convert 4.75 kilometers to meters using the ratio 1:1000 = ? Answer: ______________
  5. Convert 4.8 kilometers to meters using the ratio 1 km : 1000 m = ? Answer: ______________
  6. Emma is examining a scale drawing of a rectangular hiking trail map on a coordinate grid. The map shows a straight trail segment connecting point A at (3, 5) to point B at (11, 5). The scale on the map says: 1 unit = 7 miles. What is the actual length of the trail segment in miles? Answer: ______________
  7. Noah is examining a scale drawing of a rectangular playground on a coordinate grid. The corners of the playground are at points (3,4), (19,4), (19,12), and (3,12). The scale of the drawing is 1 unit = 8 feet. What is the actual perimeter of the playground in feet? Answer: ______________
  8. Mere is planning a trip to Japan and needs to convert some currency. She has $1,250 New Zealand dollars (NZD) to convert to Japanese yen (JPY). The exchange rate is 1 NZD = 85 JPY. However, the currency exchange booth charges a 2% fee on the total amount of yen she receives. How many yen will Mere actually receive after the fee is deducted? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Unit Conversion · Grade 6 · Worksheet 3

  1. 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.

  2. 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.

  3. Convert 3.25 kilometers to meters using the ratio 1:1000 = ? Answer: 3250 Solution: We know that 1 kilometer = 1000 meters Multiply 3.25 kilometers by the conversion factor 1000 meters/kilometer 3.25 × 1000 = 3250 Therefore, 3.25 kilometers equals 3250 meters The answer is 3250.
    Full step-by-step solution

    Step 1: We know that 1 kilometer = 1000 meters Step 2: Multiply 3.25 kilometers by the conversion factor 1000 meters/kilometer Step 3: 3.25 × 1000 = 3250 Step 4: Therefore, 3.25 kilometers equals 3250 meters The answer is 3250.

  4. Convert 4.75 kilometers to meters using the ratio 1:1000 = ? Answer: 4750 Solution: The ratio 1:1000 means 1 kilometer equals 1000 meters Multiply the number of kilometers by the conversion factor: 4.75 × 1000 Calculate: 4.75 × 1000 = 4750 Therefore, 4.75 kilometers equals 4750 meters The answer is 4750.
    Full step-by-step solution

    Step 1: The ratio 1:1000 means 1 kilometer equals 1000 meters Step 2: Multiply the number of kilometers by the conversion factor: 4.75 × 1000 Step 3: Calculate: 4.75 × 1000 = 4750 Step 4: Therefore, 4.75 kilometers equals 4750 meters The answer is 4750.

  5. 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.

  6. Emma is examining a scale drawing of a rectangular hiking trail map on a coordinate grid. The map shows a straight trail segment connecting point A at (3, 5) to point B at (11, 5). The scale on the map says: 1 unit = 7 miles. What is the actual length of the trail segment in miles? Answer: 56 Solution: Find the distance between A(3, 5) and B(11, 5) on the coordinate grid. Since the y-coordinates are the same, the distance is the difference in x-coordinates: 11 - 3 = 8 units.
    Full step-by-step solution

    Step 1: Find the distance between A(3, 5) and B(11, 5) on the coordinate grid. Since the y-coordinates are the same, the distance is the difference in x-coordinates: 11 - 3 = 8 units. Step 2: Use the scale ratio 1 unit = 7 miles to set up a proportion: 1 unit / 7 miles = 8 units / x miles. Step 3: Cross-multiply: 1 * x = 7 * 8, so x = 56. The actual length of the trail segment is 56 miles.

  7. Noah is examining a scale drawing of a rectangular playground on a coordinate grid. The corners of the playground are at points (3,4), (19,4), (19,12), and (3,12). The scale of the drawing is 1 unit = 8 feet. What is the actual perimeter of the playground in feet? Answer: 384 Solution: Find the length of the rectangle on the coordinate plane. The x-coordinates are 3 and 19, so the length is 19 - 3 = 16 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 3 and 19, so the length is 19 - 3 = 16 units. Step 2: Find the width of the rectangle on the coordinate plane. The y-coordinates are 4 and 12, so the width is 12 - 4 = 8 units. Step 3: Convert the drawing dimensions to actual dimensions using the scale ratio. The scale is 1 unit = 8 feet, so: Actual length = 16 units × 8 feet/unit = 128 feet Actual width = 8 units × 8 feet/unit = 64 feet Step 4: Calculate the actual perimeter of the playground. Perimeter = 2 × (length + width) = 2 × (128 feet + 64 feet) = 2 × 192 feet = 384 feet. The answer is 384.

  8. Mere is planning a trip to Japan and needs to convert some currency. She has $1,250 New Zealand dollars (NZD) to convert to Japanese yen (JPY). The exchange rate is 1 NZD = 85 JPY. However, the currency exchange booth charges a 2% fee on the total amount of yen she receives. How many yen will Mere actually receive after the fee is deducted? Answer: 104125 Solution: Set up a proportion using the exchange rate: 1 NZD / 85 JPY = 1250 NZD / x JPY. Cross-multiply: 1 * x = 1250 * 85, so x = 106250 JPY (before fee). Calculate the 2% fee: 2% of 106250 = 0.02 * 106250 = 2125 JPY.
    Full step-by-step solution

    Step 1: Set up a proportion using the exchange rate: 1 NZD / 85 JPY = 1250 NZD / x JPY. Cross-multiply: 1 * x = 1250 * 85, so x = 106250 JPY (before fee). Step 2: Calculate the 2% fee: 2% of 106250 = 0.02 * 106250 = 2125 JPY. Step 3: Subtract the fee from the total: 106250 - 2125 = 104125 JPY. Mere will receive 104125 yen.