Stacking multiplications 2

This multiplication, 23 times 3, can be solved by using stacking, and calculating digit by digit. And here, below the bar, the product will appear, one digit at a time. 3 times 3 equals 9. 2 times 3 equals 6. Now we have calculated all digits of the product.

23 times three equals 69. What about this? 23 times 4. We stack the factors like before. 23 and 4.

23 has the most digits, so we write it on top. And a bar below. 4 times 3 equals 12. 4 times 2 is 8. Hmm, now it got tricky.

8 and 12? Simply writing 8 and 12 in a row won’t work. It’s wrong. 23 times 4 does not equal 812. Instead we need to do it like this: The number 12 contains 2 digits, and does not fit in this little box.

So we write only the last digit there, 2. The one is saved here, and we will remember it for later. 1 is our memory digit. And then there was the next calculation. 2 times 4, which is 8.

And now we fetch our memory digit, 1, and add it to 8. Yes, we will do addition, even though it’s a multiplication we’re carrying out. 8 plus 1 is 9, and this is the number we write here, to the left of the two. And now we are done. 23 times 4 equals 92.

So there were several steps we had to follow here: Stack the numbers. Multiply. Check if we need to save a memory digit. Note the memory digit. Multiply again.

Add the new number with the memory digit. After this we got the product we were looking for. These are many steps, and the only way to learn is, as usual, to practise. 35 times 4? Let’s start by stacking.

Then we calculate, digit by digit. 4 times 5 is 20. This does not fit into a box, so we write zero below the bar and save the two as memory digit. 4 times 3 is 12. And the memory digit is 2.

12 plus 2 is 14. Now we are done calculating and need only to write the product. 1, 4, 0. 140! One more example.

A bit of a harder one, which you cannot easily calculate in your head. We’ll go slowly and steadily. 324 times 6. First the stacking. The number with the most digits goes on top.

And we start from the right. 6 times 4 is 24. We write the 4 below the bar, and 2 is our memory digit. 6 times 2 is 12. This will be added to the memory digit 2.

This is 14. And now remember: we are not done multiplying, because we have a three left to multiply. 14 does not fit into one box. No problem. Write 4 below the bar, and save a new memory digit.

Cross out the last one. The new memory digit is 1. Last calculation. 6 times 3 is 18, and we have a memory digit of 1. 18 plus 1 is 19.

And we are done. 1, 9, 4, 4. The product is 1944. These are advanced multiplications with large numbers, and now you know how to calculate them. Not with calculators, but with stacking and memory digits.