Mixed Number Multiplication

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Answer Key & Explanations

Mixed Number Multiplication · Grade 5 · Worksheet 3

1. A rectangular garden is drawn on a coordinate plane with corners at (1, 1), (7, 1), (7, 5), and (1, 5). Each unit on the grid represents 1 meter. A pathway that is 1 1/2 meters wide runs along the entire length of the garden. What is the area of the garden in square meters that is NOT covered by the pathway? Answer: 15 Solution: Find the total area of the garden. The length is the distance from x=1 to x=7, which is 7 - 1 = 6 meters. The width is the distance from y=1 to y=5, which is 5 - 1 = 4 meters.
   Full step-by-step solution

   Step 1: Find the total area of the garden. The length is the distance from x=1 to x=7, which is 7 - 1 = 6 meters. The width is the distance from y=1 to y=5, which is 5 - 1 = 4 meters. Total area = 6 × 4 = 24 square meters. Step 2: The pathway runs along the entire length (6 meters) and has a width of 1 1/2 meters. Write 1 1/2 as an improper fraction: 1 1/2 = (1×2+1)/2 = 3/2. Step 3: Area of the pathway = length × width = 6 × 3/2 = (6 × 3)/2 = 18/2 = 9 square meters. Step 4: Area not covered by pathway = total area - pathway area = 24 - 9 = 15 square meters. The answer is 15.

2. A rectangular prism has a length of 7.5 cm, a width of 5.2 cm, and a height of 3.8 cm. What is the volume of this prism in cubic centimeters? Answer: 148.2 Solution: Recall the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 7.5 × 5.2 × 3.8 First multiply 7.5 × 5.2 = 39.0 Then multiply 39.0 × 3.8 = 148.2 The volume is 148.2 cubic centimeters
   Full step-by-step solution

   Step 1: Recall the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 7.5 × 5.2 × 3.8 Step 3: First multiply 7.5 × 5.2 = 39.0 Step 4: Then multiply 39.0 × 3.8 = 148.2 Step 5: The volume is 148.2 cubic centimeters

3. A rectangular prism has a length of 7.5 cm, a width of 4.8 cm, and a height of 6.2 cm. What is the volume of this prism in cubic centimeters? Answer: 223.2 Solution: Write down the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 7.5 × 4.8 × 6.2 First multiply 7.5 × 4.8 = 36 Then multiply 36 × 6.2 = 223.2 The volume is 223.2 cubic centimeters
   Full step-by-step solution

   Step 1: Write down the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 7.5 × 4.8 × 6.2 Step 3: First multiply 7.5 × 4.8 = 36 Step 4: Then multiply 36 × 6.2 = 223.2 Step 5: The volume is 223.2 cubic centimeters

4. A rectangular prism has a length of 12.5 cm, a width of 8.4 cm, and a height of 6.2 cm. What is the volume of this prism? Answer: 651 Solution: To find the volume of a rectangular prism, we multiply its length, width, and height. Write down the formula for volume. Volume = length × width × height Substitute the given values into the formula.
   Full step-by-step solution

   To find the volume of a rectangular prism, we multiply its length, width, and height. Step 1: Write down the formula for volume. Volume = length × width × height Step 2: Substitute the given values into the formula. Volume = 12.5 cm × 8.4 cm × 6.2 cm Step 3: Multiply the first two numbers. First, multiply 12.5 by 8.4. 12.5 × 8.4 = (12.5 × 8) + (12.5 × 0.4) = 100 + 5 = 105 So, 12.5 × 8.4 = 105 Step 4: Now multiply this result by the height. We have 105 × 6.2 105 × 6.2 = (105 × 6) + (105 × 0.2) = 630 + 21 = 651 Step 5: State the final answer with units. The volume is 651 cubic centimeters. Therefore, the volume of the rectangular prism is 651.