Final answer:
Using an area model, 21 and 23 are broken down into tens and ones, creating a rectangle divided into smaller areas that sum up to the product, which is 483. The standard algorithm confirms this multiplication with the same result.
Step-by-step explanation:
To illustrate the concept of multiplication using an area model, we'll solve the problem 21 × 23. First, we break the numbers 21 and 23 into tens and ones. 21 can be expressed as 20 + 1 and 23 as 20 + 3. Next, we draw a rectangle divided into four smaller rectangles. The top side represents 20 + 1, and the side represents 20 + 3. This creates individual areas of 20×20, 20×3, 1×20, and 1×3 to sum up.
Calculating each area, we have:
- 20×20 = 400
- 20×3 = 60
- 1×20 = 20
- 1×3 = 3
The sum of these areas gives us the total product: 400 + 60 + 20 + 3 = 483.
Now for the standard algorithm:
21
× 23
----
63 (3×21)
+420 (20×21, shifted one position to the left)
----
483
Through both the area model and the standard algorithm, we find the product of 21 and 23 is 483.