Mixed Number Multiplication

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Answer Key & Explanations

Mixed Number Multiplication · Grade 5 · Worksheet 1

1. A carpenter needs to cut a board that is 4 3/8 feet long into 5 equal pieces. What is the length of each piece in feet? Answer: 0.875 Solution: Convert 4 3/8 to an improper fraction 4 3/8 = (4 × 8 + 3)/8 = (32 + 3)/8 = 35/8 Divide the total length by 5 to find the length of each piece 35/8 ÷ 5 = 35/8 × 1/5 = 35/40 35/40 = 7/8 7/8 = 0.875 The answer is 0.875 feet.
   Full step-by-step solution

   Step 1: Convert 4 3/8 to an improper fraction 4 3/8 = (4 × 8 + 3)/8 = (32 + 3)/8 = 35/8 Step 2: Divide the total length by 5 to find the length of each piece 35/8 ÷ 5 = 35/8 × 1/5 = 35/40 Step 3: Simplify the fraction 35/40 = 7/8 Step 4: Convert the fraction to a decimal 7/8 = 0.875 The answer is 0.875 feet.

2. 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.

3. 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.

4. A carpenter needs to cut a board that is 2 3/4 feet long into pieces that are each 1 1/8 feet long. How many complete pieces can the carpenter cut from the board? Answer: 2 Solution: Convert the mixed numbers to improper fractions. The board length is 2 3/4 feet = 11/4 feet. Each piece is 1 1/8 feet = 9/8 feet.
   Full step-by-step solution

   Step 1: Convert the mixed numbers to improper fractions. The board length is 2 3/4 feet = 11/4 feet. Each piece is 1 1/8 feet = 9/8 feet. Step 2: To find how many pieces fit, divide the total length by the piece length: 11/4 ÷ 9/8 Step 3: When dividing fractions, multiply by the reciprocal: 11/4 × 8/9 Step 4: Multiply the fractions: (11 × 8)/(4 × 9) = 88/36 Step 5: Simplify the fraction: 88/36 = 22/9 Step 6: Convert to a mixed number: 22/9 = 2 4/9 Step 7: Since we need complete pieces, we take the whole number part: 2 The carpenter can cut 2 complete pieces from the board.

5. 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.

6. Aroha is training for a charity walk. Aroha walks 4 miles each day for 5 days. How many total miles does Aroha walk? Answer: 20 Solution: Miles walked per day: 4 miles. Number of days walked: 5 days. Multiply miles per day by number of days: 4 × 5 = 20.
   Full step-by-step solution

   Step 1: Miles walked per day: 4 miles. Step 2: Number of days walked: 5 days. Step 3: Multiply miles per day by number of days: 4 × 5 = 20. The answer is 20 miles.

7. 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.

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.