Multi-Digit Multiplication

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Answer Key & Explanations

Multi-Digit Multiplication · Grade 5 · Worksheet 3

1. 927 × 48 = ? Answer: 44496 Solution: Multiply 927 by the ones digit of 48, which is 8. 927 × 8 = 7416 Multiply 927 by the tens digit of 48, which is 4 (representing 40). 927 × 40 = 37080 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 927 by the ones digit of 48, which is 8. 927 × 8 = 7416 Step 2: Multiply 927 by the tens digit of 48, which is 4 (representing 40). 927 × 40 = 37080 Step 3: Add the two partial products together. 7416 + 37080 = 44496 The final answer is 44496.

2. 648 × 37 = ? Answer: 23976 Solution: Multiply 648 by 7 (ones place): 648 × 7 = 4536 Multiply 648 by 30 (tens place): 648 × 30 = 19440 Add the partial products: 4536 + 19440 = 23976 The answer is 23976.
   Full step-by-step solution

   Step 1: Multiply 648 by 7 (ones place): 648 × 7 = 4536 Step 2: Multiply 648 by 30 (tens place): 648 × 30 = 19440 Step 3: Add the partial products: 4536 + 19440 = 23976 The answer is 23976.

3. 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.

4. 1,358 × 74 = ? Answer: 100492 Solution: Multiply 1,358 by the ones digit of 74, which is 4. 1,358 × 4 = 5,432 Multiply 1,358 by the tens digit of 74, which is 7 (representing 70). 1,358 × 70 = 95,060 Add the two partial products together.
   Full step-by-step solution

   Step 1: Multiply 1,358 by the ones digit of 74, which is 4. 1,358 × 4 = 5,432 Step 2: Multiply 1,358 by the tens digit of 74, which is 7 (representing 70). 1,358 × 70 = 95,060 Step 3: Add the two partial products together. 5,432 + 95,060 = 100,492 The final answer is 100,492.

5. 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.

6. A community center is organizing a charity run and needs to provide water bottles for all participants. They have 48 cases of water, and each case contains 24 bottles. How many water bottles do they have in total? Answer: 1152 Solution: Identify the number of cases: 48 Identify the number of bottles per case: 24 Multiply to find the total number of bottles: 48 × 24 Break down the multiplication: 48 × 20 = 960 and 48 × 4 = 192 Add the partial products: 960 + 192 = 1152 The total number of water bottles is 1152.
   Full step-by-step solution

   Step 1: Identify the number of cases: 48 Step 2: Identify the number of bottles per case: 24 Step 3: Multiply to find the total number of bottles: 48 × 24 Step 4: Break down the multiplication: 48 × 20 = 960 and 48 × 4 = 192 Step 5: Add the partial products: 960 + 192 = 1152 Step 6: The total number of water bottles is 1152.

7. A community garden is planting tomato seedlings in rows. Each row has space for 28 tomato plants, and there are 47 rows in the garden. How many tomato seedlings are needed to fill the entire garden? Answer: 1316 Solution: Identify the numbers to multiply: 28 plants per row and 47 rows.
   Full step-by-step solution

   Step 1: Identify the numbers to multiply: 28 plants per row and 47 rows. Step 2: Set up the multiplication: 28 × 47 Step 3: Multiply 28 by 40: 28 × 40 = 1120 Step 4: Multiply 28 by 7: 28 × 7 = 196 Step 5: Add the partial products: 1120 + 196 = 1316 Step 6: The total number of tomato seedlings needed is 1316.

8. Emma is running a lemonade stand. Each pitcher of lemonade uses 187 lemons, and Emma makes 22 pitchers. How many lemons does Emma need in total? Answer: 4114 Solution: Identify the number of lemons per pitcher: 187. Identify the number of pitchers: 22. Multiply: 187 × 22 = 4114.
   Full step-by-step solution

   Step 1: Identify the number of lemons per pitcher: 187. Step 2: Identify the number of pitchers: 22. Step 3: Multiply: 187 × 22 = 4114. The answer is 4114 lemons.

9. A rectangular swimming pool is drawn on a coordinate grid where each unit represents 1 meter. The pool's corners are at coordinates (3, 2), (15, 2), (15, 8), and (3, 8). What is the area of the pool in square meters? Answer: 72 Solution: Find the length of the rectangle by calculating the horizontal distance between the x-coordinates. The x-coordinates are 3 and 15, so length = 15 - 3 = 12 meters.
   Full step-by-step solution

   Step 1: Find the length of the rectangle by calculating the horizontal distance between the x-coordinates. The x-coordinates are 3 and 15, so length = 15 - 3 = 12 meters. Step 2: Find the width of the rectangle by calculating the vertical distance between the y-coordinates. The y-coordinates are 2 and 8, so width = 8 - 2 = 6 meters. Step 3: Calculate the area using the formula: area = length × width. Area = 12 × 6 = 72 square meters. The answer is 72.