Multi-Digit Multiplication

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Answer Key & Explanations

Multi-Digit Multiplication · Grade 5 · Worksheet 1

1. 847 × 56 = ? Answer: 47432 Solution: Multiply 847 by the ones digit of 56, which is 6. 847 × 6 = 5,082 Multiply 847 by the tens digit of 56, which is 5 (representing 50). 847 × 50 = 42,350 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 847 by the ones digit of 56, which is 6. 847 × 6 = 5,082 Step 2: Multiply 847 by the tens digit of 56, which is 5 (representing 50). 847 × 50 = 42,350 Step 3: Add the two partial products together. 5,082 + 42,350 = 47,432 The final answer is 47,432.

2. A school is organizing a field trip and needs to transport 324 students. Each school bus can carry 36 students. How many buses are needed to transport all the students? Answer: 9 Solution: We have 324 students in total. Each bus can carry 36 students. We need to find how many buses are needed for all students.
   Full step-by-step solution

   Step 1: Understand the problem. We have 324 students in total. Each bus can carry 36 students. We need to find how many buses are needed for all students. Step 2: Set up the division. To find the number of buses, divide the total number of students by the number of students per bus: 324 ÷ 36. Step 3: Perform the division. First, check how many times 36 fits into 324. 36 × 9 = 324. So, 324 ÷ 36 = 9. Step 4: Interpret the result. Since 324 divided by 36 equals exactly 9, we need 9 buses to carry all students. There are no leftover students, so no extra bus is needed. Final Answer: 9 buses.

3. 1,728 × 45 = ? Answer: 77760 Solution: Multiply 1,728 by the ones digit of 45, which is 5. 1,728 × 5 = 8,640 Multiply 1,728 by the tens digit of 45, which is 4 (representing 40). 1,728 × 40 = 69,120 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,728 by the ones digit of 45, which is 5. 1,728 × 5 = 8,640 Step 2: Multiply 1,728 by the tens digit of 45, which is 4 (representing 40). 1,728 × 40 = 69,120 Step 3: Add the two partial products together. 8,640 + 69,120 = 77,760 The final answer is 77,760.

4. A community garden is planting tomato seedlings in rows. Each row contains 48 seedlings, and there are 36 rows in the garden. How many tomato seedlings are being planted in total? Answer: 1728 Solution: Identify the number of seedlings per row: 48 Identify the number of rows: 36 Multiply to find the total: 48 × 36 Break down the multiplication: 48 × 30 = 1440 Calculate the second part: 48 × 6 = 288 Add the partial products: 1440 + 288 = 1728 The answer is 1728.
   Full step-by-step solution

   Step 1: Identify the number of seedlings per row: 48 Step 2: Identify the number of rows: 36 Step 3: Multiply to find the total: 48 × 36 Step 4: Break down the multiplication: 48 × 30 = 1440 Step 5: Calculate the second part: 48 × 6 = 288 Step 6: Add the partial products: 1440 + 288 = 1728 The answer is 1728.

5. A school is organizing a field trip and needs to transport 347 students. Each school bus can carry 28 students. How many buses are needed to transport all the students? Answer: 13 Solution: We have 347 students, and each bus can carry 28 students. We need to find how many buses are needed for all students.
   Full step-by-step solution

   Step 1: Understand the problem We have 347 students, and each bus can carry 28 students. We need to find how many buses are needed for all students. Step 2: Divide total students by bus capacity Number of buses = Total students ÷ Students per bus Number of buses = 347 ÷ 28 Step 3: Perform the division 28 × 12 = 336 347 − 336 = 11 So 347 ÷ 28 = 12 remainder 11. Step 4: Interpret the result 12 full buses carry 336 students, but there are 11 students left over. These 11 students also need a bus, so we need one more bus for them. Step 5: Total buses needed 12 buses + 1 bus = 13 buses Step 6: Check 13 buses × 28 students = 364 seats 364 seats is enough for 347 students. Final answer: 13 buses

6. A community center is organizing a summer reading program and needs to provide books for 625 students. Each student will receive 3 books for the program. How many books does the community center need to prepare in total? Answer: 1875 Solution: Identify the number of students: 625 Identify the number of books per student: 3 Multiply to find the total number of books: 625 × 3 Calculate 600 × 3 = 1800 Calculate 25 × 3 = 75 Add the partial products: 1800 + 75 = 1875 The community center needs to prepare 1875 books in total.
   Full step-by-step solution

   Step 1: Identify the number of students: 625 Step 2: Identify the number of books per student: 3 Step 3: Multiply to find the total number of books: 625 × 3 Step 4: Calculate 600 × 3 = 1800 Step 5: Calculate 25 × 3 = 75 Step 6: Add the partial products: 1800 + 75 = 1875 The community center needs to prepare 1875 books in total.

7. A community garden is planting rows of tomato plants. Each row contains 48 plants, and there are 26 rows in the garden. How many tomato plants are being planted in total? Answer: 1248 Solution: Identify the numbers to multiply: 48 plants per row and 26 rows Set up the multiplication: 48 × 26 Multiply 48 by 20: 48 × 20 = 960 Multiply 48 by 6: 48 × 6 = 288 Add the partial products: 960 + 288 = 1248 The total number of tomato plants is 1248
   Full step-by-step solution

   Step 1: Identify the numbers to multiply: 48 plants per row and 26 rows Step 2: Set up the multiplication: 48 × 26 Step 3: Multiply 48 by 20: 48 × 20 = 960 Step 4: Multiply 48 by 6: 48 × 6 = 288 Step 5: Add the partial products: 960 + 288 = 1248 Step 6: The total number of tomato plants is 1248

8. 1,728 × 56 = ? Answer: 96768 Solution: Multiply 1,728 by the ones digit of 56, which is 6. 1,728 × 6 = 10,368 Multiply 1,728 by the tens digit of 56, which is 5 (representing 50). 1,728 × 50 = 86,400 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,728 by the ones digit of 56, which is 6. 1,728 × 6 = 10,368 Step 2: Multiply 1,728 by the tens digit of 56, which is 5 (representing 50). 1,728 × 50 = 86,400 Step 3: Add the two partial products together. 10,368 + 86,400 = 96,768 The final answer is 96,768.

9. 1,847 × 56 = ? Answer: 103432 Solution: Multiply 1,847 by the ones digit of 56, which is 6. 1,847 × 6 = 11,082 Multiply 1,847 by the tens digit of 56, which is 5 (representing 50). 1,847 × 50 = 92,350 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,847 by the ones digit of 56, which is 6. 1,847 × 6 = 11,082 Step 2: Multiply 1,847 by the tens digit of 56, which is 5 (representing 50). 1,847 × 50 = 92,350 Step 3: Add the two partial products together. 11,082 + 92,350 = 103,432 The final answer is 103,432.