## A New Look at Subtraction

Subtraction is pretty simple, right? Well, no matter how simple it seems to you, you may enjoy this article.

What is 137-88?

Traditional method: The following is the traditional way to do it. I used dots (over the 1 and 3) to indicate borrows. You may mark them differently, or not mark them at all.

```     ..
137
-88
49```

I started at the right column. 7 is less than 8, so I borrowed from the three (making it 2) and changing the 7 into 17. 17-8=9, which I wrote as the right digit of the answer. In the next column, our 3 is now a 2, and it is less than 8. So I had to borrow from the 1 (making it 0) and the two became 12. 12-8=4. Our answer is 49.

Second method: Another method (slightly easier, in my opinion) is to add when we borrow:

```     137
.
-88
49```

Here I put the dot over the left 8. Instead of making the 3 above it into a 2, I made the 8 into a 9. We still have 17-8=9 in the right column. But now, we have 13-9=4 in the second column. This method is easier when some of the top digits are zero.

Third method: Now let's look at a method which involves addition, but very little actual subtraction:

```     137  +2 = 139  +10 =  149
-88  +2 = -90  +10 = -100
49```

Normally, most of this would be done mentally, without writing it down. But this also works well if you do write it down, in some manner (you may leave out the +2's and +10's). This method works because adding the same number to both numbers of a subtraction problem doesn't change the answer. We add numbers which make the eventual subtraction easier. We could have stopped after step #1 (139-90), as that is fairly easy to subtract. Personally, I think that this method is the easiest of the three methods, especially when I'm doing the work in my head. You may disagree.

Calculators: So why do we even want to know how to subtract, in a world filled with calculators? I can think of three reasons:

1. You may not be able to find your calculator. This happens to me often.
2. Some subtractions are so easy that you can do them in your head faster. Try it. 137-88 turned out to be fairly easy with the above third method.
3. What if you make a mistake while using your calculator. If you are skilled at subtraction, you can say, "That doesn't look right," and recalculate the answer.

Of course, we should use calculators. They are more accurate. And they simplify difficult arithmetic. But we do need to know how to do arithmetic without calculators.