Left-to-Right (L2R) Mental Subtraction with-more-than-one-carry-in-a-row Mojo

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What would happen if you had to carry in two or more columns in a row? For example:

Here is interactive clip which should clear that up for you.
(If for some reason the clip is distorted, hit the refresh button on your browser).

  A curious reader wrote to ask about the following:

I'm enchanted by your lessons, but your interactive lesson about "looking ahead" in subtractions only deals with an easy problems. How do you figure out this one:

How do you deal with the next set of RNs, which are zeroes. And
where do you deduct and switch a ten to deal with 7 - 8 in the third column? It is driving me nuts. Can you help?

Professor Homunculus repies:

I think I can. It is a great question. There are always new examples that come up with things I never thought about. Thank goodness for astute readers like you!
Here goes -

If, while you are looking at the neighbor to the right (RN), you notice that upper RN is the same as the lower one, keep looking to the right at the next RN, because that set may have an upper one is smaller than the lower one.
If that is the case, do this:

You will have to borrow from the column to the left of it, which will make that column’s minuend smaller than the subtrahend. (In the particular case of your example, there is nothing (zero) in that column, so you can’t borrow from it.) In either case, you will now have a problem. So...as soon as you see that this problem will exist, you must reduce the minuend of the first column by one, and carry that one to the next column (all this is done in your mind, you don’t need paper for it.)

Let’s do this together so I can make it clear.

When we go to subtract the ten-thousands, we notice that the RNs are the same. So we must look over to the next RN, where we notice that the minuend is too small to subtract from. We also notice that we can’t borrow from the thousands, because there is nothing (zero) there.

So we have to go back to the ten-thousands and borrow one from the minuend. That makes the 7 a 6, so when we subtract the ten-thousands, we get nothing. Now there is a “10” in the thousands place.

The situation so far:

Of course, you can’t have a two-digit number in any of the places, but it is only there temporarily, because we will immediately turn it into a “9” when we borrow from that column to put a “1” in front of the 7 in minuend of the hundreds column.

The new situation:

Now you subtract 0 from 9 to get the answer to the thousands column. (The answer to that is obviously 9).

The new situation:

The hundreds column is now 17 – 8, which should pose no problem.
Then continue on as usual.

Actually, this kind of problem is addressed in “Change for the Better,” which is a booklet about making change, but is basically a great lesson in speed-subtraction.

The more of your own effort you put into learning, the more meaningful it will be to you. That's why textbooks usually are only a very limited way to learn.

   There are other secrets to turbo-charging your subtraction skills. They will also be included here a.s.a.p. Check back occasionally. Until then, practice at least 10 examples a day. Make them up yourself (and don't make 'em too easy!)

Soon there will be an interactive test here, like the one on the page for subtraction without multiple carries.

return to page for subtraction without more than one carry in a row