Math 300

Alternative Subtraction Algorithms

Borrow First and Then Subtract

Dr. Wilson

When subtracting long numbers where there are several places where you have to borrow, most people borrow as they go along. For example

When you borrow from the tens to get enough ones to take away 8 ones you get

Next we go to the ten's place where we also have to borrow or regroup.

When we go to the hundred's place, in this example, we need to borrow or regroup again.

Finally, in the thousand's place we don't need to borrow.

That is the way most people use the standard algorithm. But some people do all of their borrowing or regrouping before they do any subtracting. When you look at the problem

you can see that you are going to need to borrow ones from the ten's place

At this point you can see that you are going to need to borrow tens from the hundred's place.

And now you can see that you are going to need to borrow hundreds from the thousand's place.

A nice thing about this method is that, while you will need to do the regrouping from right to left, after you have gotten the regrouping together, you can do the subtraction either from right to left as in the standard algorithm or from left to right. The advantage of algorithms that allow you to procede from left to right is that if you are going to do a subtraction to see if you have overdrawn your bank account, you are probably more interested in how many thousands of dollars you have than in the number which appears in the one's place which is the first thing you find with standard right to left algorithms.