Multi-Digit Multiplication

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Answer Key & Explanations

Multi-Digit Multiplication · Grade 5 · Worksheet 1

1. 1,729 × 83 = ? Answer: 143507 Solution: Multiply 1,729 by the ones digit of 83, which is 3. 1,729 × 3 = 5,187 Multiply 1,729 by the tens digit of 83, which is 8 (representing 80). 1,729 × 80 = 138,320 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,729 by the ones digit of 83, which is 3. 1,729 × 3 = 5,187 Step 2: Multiply 1,729 by the tens digit of 83, which is 8 (representing 80). 1,729 × 80 = 138,320 Step 3: Add the two partial products together. 5,187 + 138,320 = 143,507 The final answer is 143,507.

2. 3,215 × 78 = ? Answer: 250770 Solution: Multiply 3,215 by the ones digit of 78, which is 8. 3,215 × 8 = 25,720 Multiply 3,215 by the tens digit of 78, which is 7 (representing 70). 3,215 × 70 = 225,050 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 3,215 by the ones digit of 78, which is 8. 3,215 × 8 = 25,720 Step 2: Multiply 3,215 by the tens digit of 78, which is 7 (representing 70). 3,215 × 70 = 225,050 Step 3: Add the two partial products together. 25,720 + 225,050 = 250,770 The final answer is 250,770.

3. 1,836 × 74 = ? Answer: 135864 Solution: Multiply 1,836 by the ones digit of 74, which is 4. 1,836 × 4 = 7,344 Multiply 1,836 by the tens digit of 74, which is 7 (representing 70). 1,836 × 70 = 128,520 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,836 by the ones digit of 74, which is 4. 1,836 × 4 = 7,344 Step 2: Multiply 1,836 by the tens digit of 74, which is 7 (representing 70). 1,836 × 70 = 128,520 Step 3: Add the two partial products together. 7,344 + 128,520 = 135,864 The final answer is 135,864.

4. A rectangular garden is drawn on a grid where each unit square represents 1 square meter. The garden has corners at coordinates (2, 1), (8, 1), (8, 5), and (2, 5). What is the area of the garden in square meters? Answer: 24 Solution: Identify the length from the x-coordinates. The bottom corners are at (2,1) and (8,1). The length is 8 - 2 = 6 meters.
   Full step-by-step solution

   Step 1: Identify the length from the x-coordinates. The bottom corners are at (2,1) and (8,1). The length is 8 - 2 = 6 meters. Step 2: Identify the width from the y-coordinates. The left corners are at (2,1) and (2,5). The width is 5 - 1 = 4 meters. Step 3: Calculate the area using the formula: area = length × width. Step 4: Area = 6 × 4 = 24. The area of the garden is 24 square meters.

5. 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.

6. 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.

7. 1,357 × 64 = ? Answer: 86848 Solution: Multiply 1,357 by the ones digit of 64, which is 4. 1,357 × 4 = 5,428 Multiply 1,357 by the tens digit of 64, which is 6 (representing 60). 1,357 × 60 = 81,420 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,357 by the ones digit of 64, which is 4. 1,357 × 4 = 5,428 Step 2: Multiply 1,357 by the tens digit of 64, which is 6 (representing 60). 1,357 × 60 = 81,420 Step 3: Add the two partial products together. 5,428 + 81,420 = 86,848 The final answer is 86,848.

8. A school is organizing a field trip and needs to transport 348 students. Each school bus can carry 24 students. How many buses are needed to transport all the students? Answer: 15 Solution: We have 348 students, and each bus can carry 24 students. We need to find how many buses are needed. Divide the total number of students by the number of students per bus.
   Full step-by-step solution

   Step 1: Understand the problem. We have 348 students, and each bus can carry 24 students. We need to find how many buses are needed. Step 2: Divide the total number of students by the number of students per bus. 348 ÷ 24 Step 3: Perform the division. 24 × 14 = 336 348 − 336 = 12 Step 4: Interpret the result. 14 buses would carry 336 students, but we have 348 students, so 12 students would be left without a seat. Step 5: Since we cannot leave any student behind, we need one more bus for the remaining 12 students. So, 14 + 1 = 15 buses. Step 6: Final check. 15 buses × 24 students = 360 seats, which is enough for 348 students. Answer: 15 buses are needed.

9. A community garden is planting tomato seedlings in rows. Each row contains 28 seedlings, and there are 36 rows in the garden. How many tomato seedlings are being planted in total? Answer: 1008 Solution: Identify the number of seedlings per row: 28 Identify the number of rows: 36 Multiply to find the total number of seedlings: 28 × 36 Break down the multiplication: (20 × 36) + (8 × 36) Calculate 20 × 36 = 720 Calculate 8 × 36 = 288 Add the partial products: 720 + 288 = 1008 The answer is 1008.
   Full step-by-step solution

   Step 1: Identify the number of seedlings per row: 28 Step 2: Identify the number of rows: 36 Step 3: Multiply to find the total number of seedlings: 28 × 36 Step 4: Break down the multiplication: (20 × 36) + (8 × 36) Step 5: Calculate 20 × 36 = 720 Step 6: Calculate 8 × 36 = 288 Step 7: Add the partial products: 720 + 288 = 1008 The answer is 1008.