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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:
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.
Addendum:
I received email asking if I was actually recommending the use of calculators in early grades. I thought it was obvious that I was recommending learning arithmetic skills. Can this be done with calculators around? Maybe. But I must leave that up to the teachers who have to teach these skills. Calculators are important and useful to our society, and I think that kids need to learn about them, eventually. But, universal use of calculators probably prevents a student from learning arithmetic skills. So what? I don't need skills; I have a calculator. But, what happens when I multiply 17x37 (using a calculator) and get 663? If I have arithmetic skills, I can see that the answer is wrong (the right digit should be a 9). I pushed the wrong button, happens often.
Also, it is important to check your work, even when using a calculator. Mistakes happen. We skip a number; we misread a number; we put the decimal point in the wrong place; we do the wrong operation. So we still need to check our work.
This addendum is really a message to the student, not to the teacher. I wish people, including myself, would do what is good for them, even when it is a bother. You should see that practicing arithmetic skills (and many other skills) is good for you. You see that you have a weakness in mathematics. Instead of complaining or even bragging about it, it makes more sense to correct the situation. Work work work. Sorry. We are willing to work work work in athletics, but not mathematics. We should be smarter than that.