Multi-Digit Multiplication — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Using the area model, 46 × 23 is broken into four parts: 40 × 20, 40 × 3, 6 × 20, and 6 × 3. What is the sum of all four parts?
A) 1,038
B) 1,048
C) 1,058
D) 1,068
Calculate each rectangle: 40 × 20 = 800, 40 × 3 = 120, 6 × 20 = 120, and 6 × 3 = 18. Adding all four gives 800 + 120 + 120 + 18 = 1,058.
2. A delivery service makes 1,375 deliveries each week. How many deliveries does it make in 4 weeks?
A) 5,400
B) 5,500
C) 5,600
D) 5,700
Multiply 1,375 × 4: 5 × 4 = 20, 7 × 4 = 28 + 2 = 30, 3 × 4 = 12 + 3 = 15, 1 × 4 = 4 + 1 = 5. The product is 5,500 deliveries in 4 weeks.
3. Which pair of partial products correctly solves 58 × 34?
A) 58 × 4 = 232 and 58 × 3 = 174
B) 58 × 4 = 232 and 58 × 30 = 1,740
C) 58 × 4 = 222 and 58 × 30 = 1,740
D) 58 × 34 = 1,962 and 58 × 0 = 0
To use partial products for 58 × 34, break 34 into 4 and 30. Then 58 × 4 = 232 and 58 × 30 = 1,740, and 232 + 1,740 = 1,972.
4. A concert hall has 38 rows of 52 seats. How many seats are in the hall?
A) 1,876
B) 1,926
C) 1,976
D) 2,026
Multiply 38 × 52 using partial products: 38 × 2 = 76 and 38 × 50 = 1,900, so 76 + 1,900 = 1,976 seats in the concert hall.
Part B: Fill in the Blank
Write the correct answer on each line.
1. 1,862 × 4 = 7,448
Multiply column by column: 2 × 4 = 8, 6 × 4 = 24 (write 4, carry 2), 8 × 4 = 32 + 2 = 34 (write 4, carry 3), 1 × 4 = 4 + 3 = 7. The product is 7,448.
2. 79 × 63 = 4,977
Using partial products: 79 × 3 = 237 and 79 × 60 = 4,740. Adding gives 237 + 4,740 = 4,977.
3. An orchard has 45 rows with 37 trees in each row. The orchard has 1,665 trees.
Multiply 45 × 37: 45 × 7 = 315 and 45 × 30 = 1,350, so 315 + 1,350 = 1,665 trees in the orchard.
4. Using partial products, 96 × 15 = 96 × 5 + 96 × 10 = 480 + 960 = 1,440
Adding the two given partial products: 480 + 960 = 1,440. This confirms 96 × 15 = 1,440.
5. 2,507 × 3 = 7,521
Multiply each digit by 3: 7 × 3 = 21 (write 1, carry 2), 0 × 3 = 0 + 2 = 2, 5 × 3 = 15 (write 5, carry 1), 2 × 3 = 6 + 1 = 7. The product is 7,521.