Hand Calculations: addition, multiplication, and square root

Now we are going to start multiplying. We'll use the numbers from the first example above: 469 x 32. We begin with the ones place in the bottom number. This is the 2 in 32. We multiply 2x469 and write it down under the line.

Now we need to multiply by the next number to the left of the 2. This is the 3 in 32. Because the 3 is in the tens place we need to hold the tens place by placing a zero in the 1's place before we start multiplying.

Multiply the 3 by the top number (469) and write this number next to the zero

If there were more numbers we would add more rows and continue to add more zeros. For example, if there were a 4 in the hundreds spot (i.e. the number on the bottom was 432) we would add two zeros in the next row and then multiply 469 by 4

After we have multiplied all the numbers on the bottom, we add up the rows of numbers to get the answer. In this case there are two rows, but there would be more if the number we were multiplying by on the bottom (the 32) had more digits.