Stacking multiplications 4

Let’s multiply two numbers: 328 times 34. We'll solve it by stacking. Let’s go! First we stack the numbers. 328 has the most digits, so it goes on top.

Let’s calculate. We start here, to the very right. 4 times 8 is 32. 32 doesn’t have enough room in the box, so we need to separate the digits. We write the three here.

This is our memory digit. We’ll keep it in mind for later. 2 we write here, right below the four. 4 times 2 is 8. Remember the memory digit.

This one we add, right? 8 plus 3 is 11. This too doesn’t fit one box. Then we need to write the first one here, and save the other one as a memory digit. 4 times 3 is 12.

Then we add the memory digit: 1. 12 plus 1 is 13. This is the last multiplication with the four, so we write it below the bar here and get 1312. Nice! But we’re not done.

Now we’ll multiply the three also. 3 times 8 is 24. The four goes here, right below the three. And we save a two as - that’s right! - a memory digit. Then we continue to calculate.

3 times 2 is 6. Plus the memory digit 2, this is 8. We write that here, and 8 is a one-digit-number. Now we don’t have a memory digit. And finally, 3 times 3.

This is 9, and we did not have a memory digit from before. The number 9 only has one digit, so we write 9 here. Good! Now we have multiplied all digits in both numbers. We have one last step to do.

We have to add these two numbers. 1312 and 9840. Wait, 9840? Yes, because this box is empty, so we need to add a zero. 2 plus zero is 2.

1 plus 4 is 5. 3 plus 8 is 11. Write 1 and add 1 here. We get 1 plus 1 plus 9. This is 11.

The product is ready: 328 times 34 equals 11 152. Let’s look at another example. Two large numbers, but with stacking we can calculate nicely, step by step. 546 times 48. First we stack.

546 has more digits, so it goes on top. Then we calculate. 8 times 6 is 48. We get the memory digit 4, while we write the eight here. 8 times 4 is 32, and then we add the memory digit which is also 4.

32 plus 4 equals 36, so the new memory digit is 3. The six goes here. And then 8 times 5. This is 40. Plus the memory digit 3.

This is 43. Write the whole number here, because this is the last calculation for the eight. Next digit. The four: 4 times 6 is 24. The memory digit is two, and the four goes here.

4 times 4 is 16, and we have a memory digit from before: 2. 16 plus 2 is 18. The new memory digit is 1, and the eight goes here. 4 times 5 is 20. Plus the memory digit 1, equals 21.

We write that here, because it was the last multiplication. One more thing. These two numbers need to be added. 4368 plus 21 840. 26 208.

This is the product we were looking for in the beginning. There are a lot of steps, and you have to be cautious in each step, but with practice it will get easier and easier. Good luck!