Unit Rates

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Unit Rates · Grade 6 · Worksheet 2

1. If a car travels 360 km in 4 hours, what is its unit rate in km/h? Answer: 90 Solution: To find the unit rate in km/h, we need to determine how many kilometers the car travels in one hour. Identify the total distance and total time. The car travels 360 km in 4 hours.
   Full step-by-step solution

   To find the unit rate in km/h, we need to determine how many kilometers the car travels in one hour. Step 1: Identify the total distance and total time. The car travels 360 km in 4 hours. Step 2: The unit rate is found by dividing the total distance by the total time. Unit rate = Total distance / Total time Unit rate = 360 km / 4 hours Step 3: Perform the division. 360 divided by 4 equals 90. Step 4: State the final answer with units. The car's unit rate is 90 km/h. This means the car travels 90 kilometers every hour.

2. A rectangular prism is drawn with dimensions 12 cm by 8 cm by 5 cm. If you were to paint all the outside faces of this prism, what is the total surface area in square centimeters? Answer: 392 Solution: Identify the dimensions: length = 12 cm, width = 8 cm, height = 5 cm Calculate area of front and back faces: 2 × (12 × 5) = 2 × 60 = 120 cm² Calculate area of left and right faces: 2 × (8 × 5) = 2 × 40 = 80 cm² Calculate area of top and bottom faces: 2 × (12 × 8) = 2 × 96 = 192 cm² Add all…
   Full step-by-step solution

   Step 1: Identify the dimensions: length = 12 cm, width = 8 cm, height = 5 cm Step 2: Calculate area of front and back faces: 2 × (12 × 5) = 2 × 60 = 120 cm² Step 3: Calculate area of left and right faces: 2 × (8 × 5) = 2 × 40 = 80 cm² Step 4: Calculate area of top and bottom faces: 2 × (12 × 8) = 2 × 96 = 192 cm² Step 5: Add all areas: 120 + 80 + 192 = 392 cm² The answer is 392.

3. Mere is making lemonade for a party. The recipe uses 22 lemons to make 2 cups of lemonade. How many lemons are needed for one cup of lemonade? Answer: 11 Solution: To find lemons per cup, divide the total lemons by the total cups. 22 lemons ÷ 2 cups = 11 lemon per cup. So, Mere needs 11 lemon for each cup of lemonade.
   Full step-by-step solution

   Step 1: To find lemons per cup, divide the total lemons by the total cups. Step 2: 22 lemons ÷ 2 cups = 11 lemon per cup. Step 3: So, Mere needs 11 lemon for each cup of lemonade.

4. Olivia earns $1,125 for working 45 hours. What is her hourly rate of pay? Answer: 25 Solution: Identify the total earnings and total hours. Total earnings = $1,125, Total hours = 45. Divide the total earnings by the total hours to find the hourly rate: 1125 ÷ 45.
   Full step-by-step solution

   Step 1: Identify the total earnings and total hours. Total earnings = $1,125, Total hours = 45. Step 2: Divide the total earnings by the total hours to find the hourly rate: 1125 ÷ 45. Step 3: 45 × 20 = 900, remainder 225. Step 4: 45 × 5 = 225, so 20 + 5 = 25. Step 5: Check: 45 × 25 = 1125. The hourly rate is $25 per hour.

5. A car travels 360 miles on 12 gallons of gas. What is the unit rate in miles per gallon? Answer: 30 Solution: We are asked to find the unit rate in miles per gallon. Unit rate means how many miles the car travels per 1 gallon of gas. Identify the given quantities.
   Full step-by-step solution

   We are asked to find the unit rate in miles per gallon. Unit rate means how many miles the car travels per 1 gallon of gas. Step 1: Identify the given quantities. The car travels 360 miles using 12 gallons of gas. Step 2: Unit rate in miles per gallon is found by dividing total miles by total gallons. So, miles per gallon = 360 miles / 12 gallons. Step 3: Perform the division. 360 ÷ 12 = 30. Step 4: Interpret the result. The car travels 30 miles for each 1 gallon of gas. Step 5: Write the final answer with units. The unit rate is 30 miles per gallon. ANSWER: 30

6. If a car travels 420 miles on 14 gallons of gas, what is the unit rate in miles per gallon? Answer: 30 Solution: Identify the total distance traveled: 420 miles Identify the total gallons used: 14 gallons Calculate the unit rate by dividing total miles by total gallons: 420 ÷ 14 Perform the division: 420 ÷ 14 = 30 The unit rate is 30 miles per gallon.
   Full step-by-step solution

   Step 1: Identify the total distance traveled: 420 miles Step 2: Identify the total gallons used: 14 gallons Step 3: Calculate the unit rate by dividing total miles by total gallons: 420 ÷ 14 Step 4: Perform the division: 420 ÷ 14 = 30 Step 5: The unit rate is 30 miles per gallon.

7. If 3.75 kilograms of coffee cost $45.00, what is the unit rate per kilogram? Answer: 12 Solution: Identify the total cost and the total amount. Total cost = $45.00, Total amount = 3.75 kg To find the unit rate (cost per kilogram), divide the total cost by the total amount.
   Full step-by-step solution

   Step 1: Identify the total cost and the total amount. Total cost = $45.00, Total amount = 3.75 kg Step 2: To find the unit rate (cost per kilogram), divide the total cost by the total amount. Step 3: Perform the division: 45.00 ÷ 3.75 Step 4: 45.00 ÷ 3.75 = 12 Step 5: The unit rate is $12 per kilogram.

8. If a car travels 480 miles on 15 gallons of gas, what is the unit rate in miles per gallon? Answer: 32 Solution: Identify the total distance traveled: 480 miles Identify the total gallons used: 15 gallons Calculate the unit rate by dividing total miles by total gallons: 480 ÷ 15 Perform the division: 480 ÷ 15 = 32 The unit rate is 32 miles per gallon.
   Full step-by-step solution

   Step 1: Identify the total distance traveled: 480 miles Step 2: Identify the total gallons used: 15 gallons Step 3: Calculate the unit rate by dividing total miles by total gallons: 480 ÷ 15 Step 4: Perform the division: 480 ÷ 15 = 32 Step 5: The unit rate is 32 miles per gallon.