Unit Rates

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Unit Rates · Grade 6 · Worksheet 3

1. If a car travels 528 miles on 16 gallons of gas, what is the unit rate in miles per gallon? Answer: 33 Solution: Identify the total distance traveled: 528 miles Identify the total gallons used: 16 gallons Calculate the unit rate by dividing total miles by total gallons: 528 ÷ 16 Perform the division: 528 ÷ 16 = 33 The unit rate is 33 miles per gallon.
   Full step-by-step solution

   Step 1: Identify the total distance traveled: 528 miles Step 2: Identify the total gallons used: 16 gallons Step 3: Calculate the unit rate by dividing total miles by total gallons: 528 ÷ 16 Step 4: Perform the division: 528 ÷ 16 = 33 Step 5: The unit rate is 33 miles per gallon.

2. If 2.5 kilograms of flour costs $8.75, what is the unit rate per kilogram? Answer: 3.5 Solution: Identify the total cost and the total amount. Total cost = $8.75, Total amount = 2.5 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 = $8.75, Total amount = 2.5 kg Step 2: To find the unit rate (cost per kilogram), divide the total cost by the total amount. Step 3: Perform the division: 8.75 ÷ 2.5 Step 4: 8.75 ÷ 2.5 = 3.5 Therefore, the unit rate is $3.50 per kilogram.

3. Liam is making a large batch of lemonade for a school event. His recipe requires 8 cups of lemon juice for every 12 cups of water. If Liam uses a total of 45 cups of liquid for his lemonade, how many cups of lemon juice did he use? Answer: 18 Solution: The recipe says: 8 cups lemon juice to 12 cups water. 8 + 12 = 20 cups. Find the fraction of lemon juice in the total liquid Lemon juice fraction = lemon juice / total liquid = 8 / 20.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Understand the ratio** The recipe says: 8 cups lemon juice to 12 cups water. That means the total liquid in the recipe is: 8 + 12 = 20 cups. --- **Step 2: Find the fraction of lemon juice in the total liquid** Lemon juice fraction = lemon juice / total liquid = 8 / 20. Simplify: 8/20 = 2/5. So, 2/5 of the total liquid is lemon juice. --- **Step 3: Apply this fraction to the actual total liquid used** Liam used 45 cups of liquid in total. Lemon juice = (2/5) × 45. --- **Step 4: Calculate** (2/5) × 45 = (2 × 45) / 5 = 90 / 5 = 18. --- **Step 5: Conclusion** Liam used 18 cups of lemon juice. --- **Final answer:** 18

4. A rectangular prism is drawn with dimensions 12 cm by 8 cm by 5 cm. If the prism is completely filled with identical cubes that have whole-number side lengths, what is the largest possible volume of each cube in cubic centimeters? Answer: 1 Solution: Identify the dimensions of the rectangular prism: length = 12 cm, width = 8 cm, height = 5 cm To fill the prism completely with identical cubes, the side length of each cube must be a common factor of all three dimensions Find the greatest common factor (GCF) of 12, 8, and 5 Factors of 12: 1, 2,…
   Full step-by-step solution

   Step 1: Identify the dimensions of the rectangular prism: length = 12 cm, width = 8 cm, height = 5 cm Step 2: To fill the prism completely with identical cubes, the side length of each cube must be a common factor of all three dimensions Step 3: Find the greatest common factor (GCF) of 12, 8, and 5 Step 4: Factors of 12: 1, 2, 3, 4, 6, 12 Step 5: Factors of 8: 1, 2, 4, 8 Step 6: Factors of 5: 1, 5 Step 7: The only common factor of all three numbers is 1 Step 8: Therefore, the largest possible cube side length is 1 cm Step 9: Volume of each cube = side length × side length × side length = 1 cm × 1 cm × 1 cm = 1 cubic cm The answer is 1.

5. A printing company is running a special promotion where they print 1,200 flyers for every 3 hours of operation. If they need to print 8,400 flyers for a client's order, how many hours will the printing take at this constant rate? Answer: 21 Solution: The company prints 1,200 flyers in 3 hours Flyers per hour = 1,200 ÷ 3 = 400 flyers/hour Calculate the time needed for 8,400 flyers Time = Total flyers ÷ Rate Time = 8,400 ÷ 400 Time = 21 hours The printing will take 21 hours to complete the order of 8,400 flyers.
   Full step-by-step solution

   Step 1: Find the unit rate (flyers per hour) The company prints 1,200 flyers in 3 hours Flyers per hour = 1,200 ÷ 3 = 400 flyers/hour Step 2: Calculate the time needed for 8,400 flyers Time = Total flyers ÷ Rate Time = 8,400 ÷ 400 Time = 21 hours The printing will take 21 hours to complete the order of 8,400 flyers.

6. If a car travels 360 km in 4 hours, what is its speed in km/h? Answer: 90 Solution: To find the speed in kilometers per hour (km/h), we use the formula: Speed = Distance / Time Identify the given values from the problem.
   Full step-by-step solution

   To find the speed in kilometers per hour (km/h), we use the formula: Speed = Distance / Time Step 1: Identify the given values from the problem. Distance traveled = 360 km Time taken = 4 hours Step 2: Substitute the given values into the formula. Speed = 360 km / 4 hours Step 3: Perform the division. 360 divided by 4 equals 90. Step 4: Write the answer with the correct units. The car's speed is 90 km/h. This means the car travels 90 kilometers for every hour it is driving.

7. If 2.5 kilograms of flour costs $8.75, what is the unit rate in dollars per kilogram? Answer: 3.5 Solution: Identify the total cost and the total amount. Total cost = $8.75, Total amount = 2.5 kg Calculate the unit rate by dividing the total cost by the total amount: 8.75 ÷ 2.5 Perform the division: 8.75 ÷ 2.5 = 3.5 The unit rate is $3.5 per kilogram.
   Full step-by-step solution

   Step 1: Identify the total cost and the total amount. Total cost = $8.75, Total amount = 2.5 kg Step 2: Calculate the unit rate by dividing the total cost by the total amount: 8.75 ÷ 2.5 Step 3: Perform the division: 8.75 ÷ 2.5 = 3.5 Step 4: The unit rate is $3.5 per kilogram.