Mixed Number Multiplication

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Answer Key & Explanations

Mixed Number Multiplication · Grade 5 · Worksheet 2

1. 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

2. 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

3. A rectangular garden is drawn on a coordinate plane with corners at (2, 3), (8, 3), (8, 7), and (2, 7). Each unit on the grid represents 1 meter. What is the area of the garden in square meters? Answer: 24 Solution: Find the length of the rectangle by calculating the difference in x-coordinates between two points on the same horizontal line. Points (2, 3) and (8, 3) have the same y-coordinate, so the length is 8 - 2 = 6 meters.
   Full step-by-step solution

   Step 1: Find the length of the rectangle by calculating the difference in x-coordinates between two points on the same horizontal line. Points (2, 3) and (8, 3) have the same y-coordinate, so the length is 8 - 2 = 6 meters. Step 2: Find the width of the rectangle by calculating the difference in y-coordinates between two points on the same vertical line. Points (2, 3) and (2, 7) have the same x-coordinate, so the width is 7 - 3 = 4 meters. Step 3: Calculate the area using the formula: area = length × width Area = 6 × 4 = 24 square meters. The answer is 24.

4. 2 1/2 × 3 1/4 = ? Answer: 8 1/8 Solution: Convert 2 1/2 to an improper fraction: 2 × 2 + 1 = 5, so 2 1/2 = 5/2 Convert 3 1/4 to an improper fraction: 3 × 4 + 1 = 13, so 3 1/4 = 13/4 Multiply the fractions: 5/2 × 13/4 = (5 × 13)/(2 × 4) = 65/8 Convert 65/8 to a mixed number: 65 ÷ 8 = 8 with remainder 1, so 65/8 = 8 1/8 The final answer…
   Full step-by-step solution

   Step 1: Convert 2 1/2 to an improper fraction: 2 × 2 + 1 = 5, so 2 1/2 = 5/2 Step 2: Convert 3 1/4 to an improper fraction: 3 × 4 + 1 = 13, so 3 1/4 = 13/4 Step 3: Multiply the fractions: 5/2 × 13/4 = (5 × 13)/(2 × 4) = 65/8 Step 4: Convert 65/8 to a mixed number: 65 ÷ 8 = 8 with remainder 1, so 65/8 = 8 1/8 Step 5: The final answer is 8 1/8

5. 2 1/4 × 3 1/3 = ? Answer: 7 1/2 Solution: Convert each mixed number to an improper fraction. 2 1/4 = (2 × 4 + 1)/4 = (8 + 1)/4 = 9/4 3 1/3 = (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Multiply the improper fractions.
   Full step-by-step solution

   Let's solve 2 1/4 × 3 1/3 step by step. Step 1: Convert each mixed number to an improper fraction. 2 1/4 = (2 × 4 + 1)/4 = (8 + 1)/4 = 9/4 3 1/3 = (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Step 2: Multiply the improper fractions. (9/4) × (10/3) = (9 × 10) / (4 × 3) = 90 / 12 Step 3: Simplify the fraction 90/12. First, divide numerator and denominator by 6: (90 ÷ 6) / (12 ÷ 6) = 15/2 Step 4: Convert the improper fraction 15/2 back to a mixed number. 15 ÷ 2 = 7 remainder 1, so 15/2 = 7 1/2 Final Answer: 7 1/2

6. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 3 1/4 inches wide and 2 1/2 inches tall. If Emma needs to make 8 identical blocks for her quilt pattern, what is the total area of fabric she needs for all the blocks combined? Answer: 65 Solution: Area = width × height = 3 1/4 × 2 1/2 3 1/4 = 13/4 2 1/2 = 5/2 13/4 × 5/2 = (13 × 5)/(4 × 2) = 65/8 65/8 = 8 1/8 square inches per block 8 1/8 × 8 = (65/8) × 8 = 65 square inches The answer is 65 square inches.
   Full step-by-step solution

   Step 1: Find the area of one quilt block Area = width × height = 3 1/4 × 2 1/2 Step 2: Convert mixed numbers to improper fractions 3 1/4 = 13/4 2 1/2 = 5/2 Step 3: Multiply the fractions 13/4 × 5/2 = (13 × 5)/(4 × 2) = 65/8 Step 4: Convert back to mixed number 65/8 = 8 1/8 square inches per block Step 5: Multiply by number of blocks 8 1/8 × 8 = (65/8) × 8 = 65 square inches The answer is 65 square inches.