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Equal Addend Subtraction Algorithm. The term “borrow” was dropped from elementary math books about fifteen years ago because we are not really borrowing, we regroup or trade. The object that we took out for trading will never be returned. Hence the new terminology “regrouping” is introduced.
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Equal Addend Subtraction Algorithm The term “borrow” was dropped from elementary math books about fifteen years ago because we are not really borrowing, we regroup or trade. The object that we took out for trading will never be returned. Hence the new terminology “regrouping” is introduced. However, this term “borrow”, no matter how incorrect it is, is stuck to everyone’s mind. Even if the teachers are not using it, the parents will still do. It is therefore desirable to create an algorithm that allows us to borrow and return. This is called the Equal Addend (Subtraction) Algorithm
The standard algorithm for subtraction can become quite complicated when there are several zeros in the minuend (the 1st number in the subtraction problem). For instance, in the problem 9 9 3 10 10 16 • 4 0 0 6 • 1 3 2 8 • ¯¯¯¯¯¯¯¯ 2 6 7 8 we don’t have anything in the tens column hence we need to go to the thousands column to regroup and bring something back to the ones column. (click to see animation) Most students will not be able to memorize the long process correctly.
Method: The major feature of the “Equal Addend” method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 1 When we try to subtract 3 by 5, we can easily see that there is not enough to do so, hence we borrow 10 (perhaps using a credit card) and we change the 3 to13.(click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 2 After we borrow, our debt will increase. We then cross out the 7 and change it to 8.(click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 8 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 3 Perform the subtraction 13 – 5. (click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 8 8 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 4 In the ten’s column, 4 is not big enough to be subtracted by 8, so we borrow again.(click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 1 8 8 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 5 Increase the debt by crossing out the 6 and change it to a 7.(click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 1 7 8 8 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 6 Perform the subtraction 14 – 8. (click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 1 7 8 6 8 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 7 In the hundred’s column, 0 is not big enough to be subtracted by 7, so we borrow again and change the 0 to 10. (click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 1 1 7 8 6 8 Click to see the next step.
Method: The major feature of this method is that we increase the subtrahend whenever we borrow, hence whatever we borrowed will be returned in the next step. This is sometimes nicknamed as the “credit card method”. Step 8 Increase the debt by adding a 1 under the 2.(click to see animation) Example: • 2 0 4 3 • 6 7 5 • ¯¯¯¯¯¯¯¯ 1 1 1 1 7 8 1 3 6 8 Click to see the next step.
Another example Let’s first review the standard method. Now we look at the Equal Addend method Standard Method 9 9 10 10 16 3 10 10 16 • 4 0 0 6 • 1 3 2 8 • ¯¯¯¯¯¯¯¯ • 4 0 0 6 • 1 3 2 8 • ¯¯¯¯¯¯¯¯ 3 2 4 2 6 7 8 2 6 7 8
Conclusions: Just like learning anything new, the beginning is difficult. You may criticize this algorithm just because it is different from the one that you are familiar with. We hope you can be more open minded and give it a chance. Compare it with the standard algorithm fairly. Even if you really don’t like it, you should still thoroughly understand it just in case someday, one of your students likes it.
