Mixed Number Multiplication

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Answer Key & Explanations

Mixed Number Multiplication · Grade 5 · Worksheet 3

1. A rectangular prism has a length of 8.5 cm, a width of 6.2 cm, and a height of 4.3 cm. What is the volume of this prism in cubic centimeters? Answer: 226.61 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given measurements. Length = 8.5 cm Width = 6.2 cm Height = 4.3 cm Multiply the length and the width first.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given measurements. Length = 8.5 cm Width = 6.2 cm Height = 4.3 cm Step 2: Multiply the length and the width first. 8.5 × 6.2 First, multiply 85 × 62 = 5270. Since 8.5 has one decimal place and 6.2 has one decimal place, the product must have two decimal places. So, 8.5 × 6.2 = 52.70 Step 3: Now multiply this result by the height. We have 52.70 × 4.3 First, multiply 5270 × 43 = 226610. Since 52.70 has two decimal places and 4.3 has one decimal place, the product must have three decimal places. So, 52.70 × 4.3 = 226.610 Step 4: Write the final answer. The volume is 226.61 cubic centimeters. (We drop the final zero as it is not needed after the decimal point). Final Answer: 226.61

2. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 1/4 feet by 1 3/5 feet. If Emma makes 8 identical blocks, what is the total area of fabric she will need for all the blocks in square feet? Answer: 28.8 Solution: Find the area of one quilt block. Area = length × width Area = 2 1/4 × 1 3/5 Convert the mixed numbers to improper fractions.
   Full step-by-step solution

   Step 1: Find the area of one quilt block. Area = length × width Area = 2 1/4 × 1 3/5 Step 2: Convert the mixed numbers to improper fractions. 2 1/4 = (2 × 4 + 1)/4 = 9/4 1 3/5 = (1 × 5 + 3)/5 = 8/5 Step 3: Multiply the fractions to find the area of one block. Area = (9/4) × (8/5) = (9 × 8)/(4 × 5) = 72/20 Step 4: Simplify the fraction. 72/20 = 18/5 = 3.6 square feet Step 5: Multiply the area of one block by the number of blocks. Total area = 3.6 × 8 = 28.8 square feet The answer is 28.8.

3. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 3/4 inches wide and 3 1/2 inches long. If Emma needs to calculate the area of one quilt block to determine how much fabric she needs, what is the area of one quilt block in square inches? Answer: 9.625 Solution: Width: 2 3/4 = (2 × 4 + 3)/4 = 11/4 Length: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Area = length × width = (11/4) × (7/2) (11 × 7)/(4 × 2) = 77/8 77 ÷ 8 = 9.625 The area of one quilt block is 9.625 square inches.
   Full step-by-step solution

   Step 1: Convert the mixed numbers to improper fractions Width: 2 3/4 = (2 × 4 + 3)/4 = 11/4 Length: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Step 2: Multiply the fractions to find the area Area = length × width = (11/4) × (7/2) Step 3: Multiply numerators and denominators (11 × 7)/(4 × 2) = 77/8 Step 4: Convert the improper fraction to a decimal 77 ÷ 8 = 9.625 The area of one quilt block is 9.625 square inches.

4. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 1/4 feet by 1 3/5 feet. If she needs to make 12 identical blocks, what is the total area of fabric she will use for all the blocks in square feet? Answer: 43.2 Solution: Find the area of one quilt block. Convert the mixed numbers to improper fractions: 2 1/4 = 9/4 and 1 3/5 = 8/5. Multiply the length and width: (9/4) * (8/5) = (9 * 8) / (4 * 5) = 72/20.
   Full step-by-step solution

   Step 1: Find the area of one quilt block. Convert the mixed numbers to improper fractions: 2 1/4 = 9/4 and 1 3/5 = 8/5. Multiply the length and width: (9/4) * (8/5) = (9 * 8) / (4 * 5) = 72/20. Simplify 72/20 by dividing numerator and denominator by 4: 72 ÷ 4 = 18, 20 ÷ 4 = 5, so 18/5 = 3.6 square feet per block. Step 2: Multiply the area of one block by the number of blocks: 3.6 * 12 = 43.2 square feet. The answer is 43.2.

5. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 1/4 feet long and 1 3/4 feet wide. If she needs to make 12 identical blocks for the quilt, what is the total area of fabric she needs for all the blocks in square feet? Answer: 47.25 Solution: Area = length × width = 2 1/4 × 1 3/4 2 1/4 = 9/4 1 3/4 = 7/4 9/4 × 7/4 = 63/16 63 ÷ 16 = 3.9375 square feet per block 3.9375 × 12 = 47.25 square feet The total fabric needed is 47.25 square feet.
   Full step-by-step solution

   Step 1: Find the area of one quilt block Area = length × width = 2 1/4 × 1 3/4 Step 2: Convert mixed numbers to improper fractions 2 1/4 = 9/4 1 3/4 = 7/4 Step 3: Multiply the fractions 9/4 × 7/4 = 63/16 Step 4: Convert to decimal 63 ÷ 16 = 3.9375 square feet per block Step 5: Multiply by number of blocks 3.9375 × 12 = 47.25 square feet Step 6: The total fabric needed is 47.25 square feet.

6. Zoe is training for a charity walk. Zoe walks 2 miles each day for 5 days. How many total miles does Zoe walk? Answer: 10 Solution: Miles walked per day: 2 miles. Number of days walked: 5 days. Multiply miles per day by number of days: 2 × 5 = 10.
   Full step-by-step solution

   Step 1: Miles walked per day: 2 miles. Step 2: Number of days walked: 5 days. Step 3: Multiply miles per day by number of days: 2 × 5 = 10. The answer is 10 miles.

7. Emma is making a quilt for her grandmother. Each quilt block is a rectangle that measures 2 3/4 inches by 1 1/2 inches. If Emma needs to make 12 identical blocks for her quilt pattern, what is the total area of fabric she needs for all the blocks combined? Answer: 49.5 Solution: Find the area of one quilt block. Area = length × width = (2 3/4) × (1 1/2) Convert mixed numbers to improper fractions. 2 3/4 = (2 × 4 + 3)/4 = 11/4 1 1/2 = (1 × 2 + 1)/2 = 3/2 Multiply the fractions.
   Full step-by-step solution

   Step 1: Find the area of one quilt block. Area = length × width = (2 3/4) × (1 1/2) Step 2: Convert mixed numbers to improper fractions. 2 3/4 = (2 × 4 + 3)/4 = 11/4 1 1/2 = (1 × 2 + 1)/2 = 3/2 Step 3: Multiply the fractions. (11/4) × (3/2) = (11 × 3)/(4 × 2) = 33/8 Step 4: Convert the improper fraction to a decimal. 33 ÷ 8 = 4.125 square inches for one block. Step 5: Multiply by the number of blocks. 4.125 × 12 = 49.5 Step 6: The total area needed is 49.5 square inches.