Add With Complements



The basic rule for the new technique is this:

To "add" over ten, subtract the complement of the larger digit from the smaller digit - and record a ten.

First we need to learn what complements are. Then we will take up how to record tens. Both are easy.

What is a complement? A complement is simply the digit that, added to the digit you have, adds up to ten. You might say that a complement is that digit needed (in addition to the one you have) to complete a ten.

For example: The complement of 9 is 1, because 9 + 1 is ten. The complementt of 8 is 2, because 8 + 2 is ten. The complement of 7 is 3, and the complement of 6 is 4, because 7 + 3 is ten and 6 + 4 is ten. Even in your sleep you would answer that the complement of 5 is 5.

Those are all the complements you ever have to remember in adding the longest column of figures. There are only five of them: five pairs, you will note, that add up to ten in the table of possible combinations.

Before learning how to add with complements, make doubly sure that you have the idea by looking at the following digits and giving their complements. Try to "read" the complement of each.

7 6 9 5 8

The way you add with complements takes a bit of getting used to. But it is one of the most fascinating and fruitful approaches known to short-cut arithmetic. You "add" two digits that total more than ten by subtracting the complement of the larger digit from the smaller digit and recording a ten.

In order to add 6 + 7, you subtract the complement of 7(3) from 6, and record a ten. 6 - 3 gives 3. The recorded ten makes it 13.

Or to add 8 + 4, you subtract the complement of 8 (2) from 4 and record a ten. 4 - 2 gives 2. The recorded ten makes it 12.

It is useful to subtract the complement of the larger digit rather than the complement of the smaller. In this way you cut in half the number of complements you have to remember at this stage - though the other half of the complements are really only the same pairs of digits that add up to ten turned around. Just as 2 is the complement of 8, so is 8 the complement of 2.

Try it yourself, before going any further. Add 7 9 by subtracting the complement of the larger digit from the smaller digit. The complement of The complement of 9 is - 7 - is -Remember to record a ten. So the answer is 16. I hope that is what you arrived at through the new method, even the first time. If not, then it hasn't become clear yet. Another reading of the article is indicated.

Now add 3 + 8. Would you subtract the complement of 8 from 3? What is the complement of 8? Don't forget to record a ten.

Strange and complex as this system undoubtedly seems at the moment, it is really far faster. This is because you are working with only the easier half of the forty-five digit combinations, the half that add up to less than ten.

Each time you use it, the system will become a little easier and more natural.

Add 6 + 5. The complement of 6 is - 5 minus - is - Record a ten.

As you incorporate this method into your life you will see what a difference it makes.