Final answer:
Vertically multiplying the integers 21 and 12 involves stacking the numbers, multiplying each digit in turn, using placeholders, and adding the results to get the final product of 252.
Step-by-step explanation:
To vertically multiply the integers 21 and 12, we stack the numbers one on top of the other and multiply each digit of the bottom number by each digit of the top number, just like we would do with a single digit number.
- We write 21 on top and 12 underneath, aligning the digits by place value.
- Multiply the 2 (from 12) by 1 (from 21) and write 2 below the line, under the ones column. Next, multiply the 2 (from 12) by the 2 (from 21) and write 4 next to the 2, but this time in the tens column.
- Now, we write a 0 under the 2 (we're essentially moving to the tens place, so this is a placeholder).
- Multiply the 1 (from 12, but now representing 10 because it is in the tens place) by 1 (from 21) and write the result, 1, next to the placeholder. Then, multiply the same 1 by the 2 (from 21) and write 2 next to the result of the previous step, again shifting one column to the left.
- Add the two rows of numbers together. The 2 stays the same since nothing is on top of it, the 4 and 1 add to make a 5, and the 2 carries down since nothing is above it either.
- The final result is 252.
Therefore, when you multiply 21 by 12 vertically, you get 252 as the final product.