Mixed Number Multiplication

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Mixed Number Multiplication · Grade 5 · Worksheet 1

1. Jordan is organizing a field trip. Each bus can hold 44 students. There are 3 buses going on the trip. How many students can go on the field trip in total? Answer: 132 Solution: Number of students per bus: 44. Number of buses: 3. Multiply students per bus by number of buses: 44 × 3 = 132.
   Full step-by-step solution

   Step 1: Number of students per bus: 44. Step 2: Number of buses: 3. Step 3: Multiply students per bus by number of buses: 44 × 3 = 132. The answer is 132 students.

2. A rectangular prism is drawn on a coordinate plane with vertices at (0,0,0), (5,0,0), (0,3,0), (0,0,4), (5,3,0), (5,0,4), (0,3,4), and (5,3,4). What is the volume of this prism in cubic units? Answer: 60 Solution: Find the length from the x-coordinates. Points (0,0,0) and (5,0,0) show the length is 5 - 0 = 5 units. Find the width from the y-coordinates.
   Full step-by-step solution

   Step 1: Find the length from the x-coordinates. Points (0,0,0) and (5,0,0) show the length is 5 - 0 = 5 units. Step 2: Find the width from the y-coordinates. Points (0,0,0) and (0,3,0) show the width is 3 - 0 = 3 units. Step 3: Find the height from the z-coordinates. Points (0,0,0) and (0,0,4) show the height is 4 - 0 = 4 units. Step 4: Calculate volume using the formula: volume = length × width × height Step 5: Volume = 5 × 3 × 4 = 15 × 4 = 60 The volume of the prism is 60 cubic units.

3. 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 for the quilt, what is the total area of fabric she will use for all the blocks in square feet? Answer: 28.8 Solution: Find the area of one quilt block by multiplying length and width. Area of one block = 2 1/4 × 1 3/5 Convert mixed numbers to improper fractions. 2 1/4 = 9/4 1 3/5 = 8/5 Multiply the fractions.
   Full step-by-step solution

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

4. 3 1/2 × 2 2/3 = ? Answer: 9 1/3 Solution: Convert 3 1/2 to an improper fraction: (3 × 2 + 1)/2 = 7/2 Convert 2 2/3 to an improper fraction: (2 × 3 + 2)/3 = 8/3 Multiply the fractions: 7/2 × 8/3 = (7 × 8)/(2 × 3) = 56/6 Simplify 56/6 by dividing numerator and denominator by 2: 28/3 Convert 28/3 to a mixed number: 28 ÷ 3 = 9 with…
   Full step-by-step solution

   Step 1: Convert 3 1/2 to an improper fraction: (3 × 2 + 1)/2 = 7/2 Step 2: Convert 2 2/3 to an improper fraction: (2 × 3 + 2)/3 = 8/3 Step 3: Multiply the fractions: 7/2 × 8/3 = (7 × 8)/(2 × 3) = 56/6 Step 4: Simplify 56/6 by dividing numerator and denominator by 2: 28/3 Step 5: Convert 28/3 to a mixed number: 28 ÷ 3 = 9 with remainder 1, so 9 1/3 The answer is 9 1/3.

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 Emma needs to make 8 identical blocks for the quilt, what is the total area of fabric she needs for all the blocks combined? Answer: 31.5 Solution: Find the area of one quilt block. Area = length × width = (2 1/4) × (1 3/4) Convert mixed numbers to improper fractions. 2 1/4 = 9/4 1 3/4 = 7/4 Multiply the fractions.
   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 the improper fraction to a mixed number or decimal. 63 ÷ 16 = 3.9375 square feet for one block. Step 5: Multiply by the number of blocks (8). 3.9375 × 8 = 31.5 Step 6: The total area of fabric needed is 31.5 square feet.

6. Tane is planting a vegetable garden. Tane plants 3 rows of carrots. Each row has 7 carrot plants. How many carrot plants does Tane have in total? Answer: 21 Solution: Number of rows of carrots: 3. Number of plants per row: 7. Multiply rows by plants per row: 3 × 7 = 21.
   Full step-by-step solution

   Step 1: Number of rows of carrots: 3. Step 2: Number of plants per row: 7. Step 3: Multiply rows by plants per row: 3 × 7 = 21. The answer is 21 carrot plants.

7. 2 1/2 × 3 3/4 = ? Answer: 9 3/8 Solution: Convert 2 1/2 to an improper fraction: (2 × 2 + 1)/2 = 5/2 Convert 3 3/4 to an improper fraction: (3 × 4 + 3)/4 = 15/4 Multiply the fractions: 5/2 × 15/4 = (5 × 15)/(2 × 4) = 75/8 Convert 75/8 to a mixed number: 75 ÷ 8 = 9 with remainder 3, so 9 3/8 The answer is 9 3/8.
   Full step-by-step solution

   Step 1: Convert 2 1/2 to an improper fraction: (2 × 2 + 1)/2 = 5/2 Step 2: Convert 3 3/4 to an improper fraction: (3 × 4 + 3)/4 = 15/4 Step 3: Multiply the fractions: 5/2 × 15/4 = (5 × 15)/(2 × 4) = 75/8 Step 4: Convert 75/8 to a mixed number: 75 ÷ 8 = 9 with remainder 3, so 9 3/8 The answer is 9 3/8.

8. A carpenter needs to cut a wooden board that is 2 3/4 feet long into 5 equal pieces. What is the length of each piece in feet? Answer: 0.55 Solution: Convert the mixed number to an improper fraction or decimal. 2 3/4 = 2 + 3/4 = 2 + 0.75 = 2.75 feet Divide the total length by the number of pieces: 2.75 ÷ 5 Perform the division: 2.75 ÷ 5 = 0.55 Check: 0.55 × 5 = 2.75, which confirms our answer.
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction or decimal. 2 3/4 = 2 + 3/4 = 2 + 0.75 = 2.75 feet Step 2: Divide the total length by the number of pieces: 2.75 ÷ 5 Step 3: Perform the division: 2.75 ÷ 5 = 0.55 Step 4: Check: 0.55 × 5 = 2.75, which confirms our answer. The length of each piece is 0.55 feet.