Unit Rate Applications

lessonbunny.com

Answer Key & Explanations

Unit Rate Applications · Grade 6 · Worksheet 3

1. (-18) × 2 ÷ (-4) = ? Answer: 9 Solution: Multiply -18 by 2: (-18) × 2 = -36 Divide -36 by -4: (-36) ÷ (-4) = 9 When dividing two negative numbers, the result is positive.
   Full step-by-step solution

   Step 1: Multiply -18 by 2: (-18) × 2 = -36 Step 2: Divide -36 by -4: (-36) ÷ (-4) = 9 When dividing two negative numbers, the result is positive. The answer is 9.

2. A triangular prism is drawn with a triangular base that is a right triangle. The legs of the triangular base measure 6 cm and 8 cm, and the prism has a height (length) of 15 cm. What is the volume of this prism in cubic centimeters? Answer: 360 Solution: Find the area of the triangular base. The base is a right triangle with legs of 6 cm and 8 cm. The area of a triangle is (1/2) * base * height.
   Full step-by-step solution

   Step 1: Find the area of the triangular base. The base is a right triangle with legs of 6 cm and 8 cm. The area of a triangle is (1/2) * base * height. Using the legs as the base and height, the area is (1/2) * 6 cm * 8 cm = (1/2) * 48 = 24 square cm. Step 2: Find the volume of the prism. The volume of any prism is the area of its base multiplied by its height (or length). Volume = Base Area * Height = 24 sq cm * 15 cm = 360 cubic cm. The volume of the prism is 360 cubic centimeters.

3. Olivia earns $1,575 for working 45 hours. What is her unit rate of pay in dollars per hour? Answer: 35 Solution: Identify the total earnings: $1,575. Identify the total hours worked: 45 hours. Divide earnings by hours: 1575 ÷ 45.
   Full step-by-step solution

   Step 1: Identify the total earnings: $1,575. Step 2: Identify the total hours worked: 45 hours. Step 3: Divide earnings by hours: 1575 ÷ 45. Step 4: 1575 ÷ 45 = 35. The unit rate is $35 per hour.

4. Aroha earns $1575 for working 45 hours. What is her hourly rate of pay? Answer: 35 Solution: Identify the total earnings: $1575 Identify the total hours worked: 45 hours Divide the total earnings by the total hours: 1575 ÷ 45 1575 ÷ 45 = 35 Aroha's hourly rate is $35 per hour.
   Full step-by-step solution

   Step 1: Identify the total earnings: $1575 Step 2: Identify the total hours worked: 45 hours Step 3: Divide the total earnings by the total hours: 1575 ÷ 45 Step 4: 1575 ÷ 45 = 35 Step 5: Aroha's hourly rate is $35 per hour. The answer is 35.

5. (-18) × (-5) ÷ 9 = ? Answer: 10 Solution: Start with (-18) × (-5) Multiply the numbers: 18 × 5 = 90 Apply the negative sign rules: negative × negative = positive, so (-18) × (-5) = 90 Now divide 90 ÷ 9 90 ÷ 9 = 10 Since we're dividing a positive by a positive, the result remains positive The answer is 10.
   Full step-by-step solution

   Step 1: Start with (-18) × (-5) Step 2: Multiply the numbers: 18 × 5 = 90 Step 3: Apply the negative sign rules: negative × negative = positive, so (-18) × (-5) = 90 Step 4: Now divide 90 ÷ 9 Step 5: 90 ÷ 9 = 10 Step 6: Since we're dividing a positive by a positive, the result remains positive The answer is 10.

6. Noah buys 16 kilograms of apples for $56. What is the unit price per kilogram? Answer: 3.5 Solution: Total cost = $56, total weight = 16 kilograms. Unit price = total cost ÷ total weight = 56 ÷ 16. 56 ÷ 16 = 3.5.
   Full step-by-step solution

   Step 1: Total cost = $56, total weight = 16 kilograms. Step 2: Unit price = total cost ÷ total weight = 56 ÷ 16. Step 3: 56 ÷ 16 = 3.5. The unit price is $3.50 per kilogram.

7. A rectangular prism is drawn with dimensions: length = 12 cm, width = 8 cm, and height = 5 cm. The prism is then scaled up proportionally so that its new volume is exactly 8 times larger than the original volume. What is the length of the scaled-up prism? Answer: 24 cm Solution: Volume = length × width × height = 12 cm × 8 cm × 5 cm = 480 cubic cm The new volume is 8 times the original volume New volume = 8 × 480 = 3840 cubic cm When scaling proportionally, all dimensions are multiplied by the same scale factor New length = k × 12 New width = k × 8 New height = k × 5 (k…
   Full step-by-step solution

   Step 1: Find the original volume of the prism Volume = length × width × height = 12 cm × 8 cm × 5 cm = 480 cubic cm Step 2: The new volume is 8 times the original volume New volume = 8 × 480 = 3840 cubic cm Step 3: When scaling proportionally, all dimensions are multiplied by the same scale factor Let k be the scale factor New length = k × 12 New width = k × 8 New height = k × 5 Step 4: Set up the volume equation for the scaled prism (k × 12) × (k × 8) × (k × 5) = 3840 k³ × (12 × 8 × 5) = 3840 k³ × 480 = 3840 Step 5: Solve for k³ k³ = 3840 ÷ 480 = 8 Step 6: Find k by taking the cube root k = cube root of 8 = 2 Step 7: Calculate the new length New length = k × original length = 2 × 12 cm = 24 cm The length of the scaled-up prism is 24 cm.

8. At a lemonade stand, Olivia pours 20 fluid ounces of lemonade equally into 4 glasses. How many fluid ounces are in each glass? Answer: 5 Solution: There are 20 fluid ounces total and 4 glasses. To find the amount per glass, divide the total ounces by the number of glasses: 20 oz ÷ 4 = 5 oz per glass.
   Full step-by-step solution

   Step 1: There are 20 fluid ounces total and 4 glasses. Step 2: To find the amount per glass, divide the total ounces by the number of glasses: 20 oz ÷ 4 = 5 oz per glass. The answer is 5 fluid ounces per glass.

9. Sophia drives 1,176 miles in 21 hours. What is her unit rate in miles per hour? Answer: 56 Solution: Identify the total distance: 1,176 miles. Identify the total time: 21 hours. Divide distance by time to find the unit rate: 1,176 ÷ 21.
   Full step-by-step solution

   Step 1: Identify the total distance: 1,176 miles. Step 2: Identify the total time: 21 hours. Step 3: Divide distance by time to find the unit rate: 1,176 ÷ 21. Step 4: 1,176 ÷ 21 = 56. The unit rate is 56 miles per hour.