Multiply the following numbers using the box method:
a. 237 * 457
b. 2345 * 780
c. 1654 * 452
d. 673 * 547

Using the box method, the products of the four multiplications are: a. 237 * 457 = 108249, b. 2345 * 780 = 1826100, c. 1654 * 452 = 747028, and d. 673 * 547 = 367081.
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Answered by Anonymous | 2025-07-04

To multiply using the box method, also known as the area or grid method, we break down the numbers into smaller parts, multiply each part, and add the results. Let's demonstrate this with each of the given problems:
a. 237 × 457

Break down the numbers:

237: 200, 30, 7
457: 400, 50, 7


Create a box with the components:
40050720080000100001400301200015002107280035049

Calculate each box:

200 × 400 = 80,000
200 × 50 = 10,000
200 × 7 = 1,400
30 × 400 = 12,000
30 × 50 = 1,500
30 × 7 = 210
7 × 400 = 2,800
7 × 50 = 350
7 × 7 = 49


Add all the partial products:

Total = 80,000 + 10,000 + 1,400 + 12,000 + 1,500 + 210 + 2,800 + 350 + 49 = 108,309



b. 2345 × 780

Break down the numbers:

2345: 2000, 300, 40, 5
780: 700, 80, 0


Calculate each box and sum:

Use a similar process as shown in part (a) to populate the grid and sum the results.
Total = 1,827,300



c. 1654 × 452

Break down the numbers:

1654: 1000, 600, 50, 4
452: 400, 50, 2


Calculate each box and sum:

Follow the same steps to get the total.
Total = 748,808



d. 673 × 547

Break down the numbers:

673: 600, 70, 3
547: 500, 40, 7


Use the grid method:

Calculate each segment and add them.
Total = 368,731



This method helps visualize the multiplication process and ensures that each part is calculated accurately, leading to the final product.

Answered by OliviaLunaGracy | 2025-07-07