## Multiplication in columns

Multiplying vertically (in columns) helps us when counting with higher numbers. As the example below (75×7) shows, we have to write the numbers below each other so that the larger number is above the smaller one. The numbers must be aligned to the right, so the ones are under the ones, the tens under the tens, etc. We will multiply the ones and tens of the larger number (75) with the smaller number (here 7). We start the calculation from the right hand side. In our case, we multiply 7×5, which is 35. Under the ones, we write only 5 as the final digit from the number 35, and we remember the carry over (3) for the next multiplication. Next, we calculate 7×7 and add the carry over 3 from the previous calculation operation to the result 49 (49+3=52). There is no more digit in the hundreds position, so we write 52 at the beginning of the result. The final result is 525.

If we look at the 348×3 example, we will proceed in the same way as in the previous problem. We must multiply all ones, tens and hundreds of the higher number (348) by the lower number (3). We start from the right hand side by multiplying 3×8 and from the result 24 we write only 4 in the ones position and remember to carry over 2 for the next operation. We continue 3×4 and to the result of 12 we carry over and add the 2 we have from the previous round. From the result 14, we again write down only the final number 4 under the tens and keep the rest (1) in our memory until the next calculation operation. This is a 3×3 multiplication, to which we carry over the 1. Then we write 10 at the beginning of the result, because we no longer have another digit in the thousands position that needs to be multiplied. The final result is 1044.

### Multiplication by a two-digit number

When multiplying with a two-digit number in writing, we use the same procedure as when using a one-digit number. We write the numbers below each other so that the right is aligned. As we can see in the example below, we start again from the right hand side. First, we multiply all the digits in the upper number by the number 2. Then we multiply the digits of the upper number by the digit 3. We write this result in the next line. We will write it from the right hand side, starting at the tens position, i.e. at the position where 3 is located. If we have both products calculated, we add a plus sign, underline and add both results.