Final answer:
To multiply the integers 21 and 12, you write them vertically, multiply each digit of one number by each digit of the other number corresponding to its place value, and then add the partial products to find the final answer.
Step-by-step explanation:
Steps for Multiplying the Integers 21 and 12 Vertically
To multiply the integers 21 and 12 vertically, we must follow these steps:
Write the two numbers with one above the other aligned by their right-hand digits.
Multiply the bottom right digit of the lower number (2) by each digit of the upper number, starting from the right (12 × 2).
Place the result of that multiplication directly below the second number, aligned with the digit that you used to multiply from the bottom number.
Next, multiply the bottom left digit of the lower number (1) by each digit of the upper number, starting from the right. Since we're now dealing with the tens place, place a 0 placeholder in the ones place of this row before writing the rest of the product (12 × 1).
Add the two products together to find the final answer.
Here is how it looks in action:
21
x 12
----
42 (21 × 2)
21x (21 × 1 with the placeholder)
----
252
This method involves adding the exponents of the base units when multiplying exponentials, but in this case, we are simply dealing with whole numbers.