Subtracting with the Abax (Lesson 2)

Subtracting with the Abax (Lesson 2)

This lesson is about subtraction with more then two columns. You can subtract numbers with as many columns as you want using this same system, (provided you have enough grooves, and marbles.)The lesson below illustrates how to do 227 - 89.

abax subtraction fig. 7
227

Here's the number 227 as represented on an abax. We are going to subtract 89 from it.

abax subtraction fig. 8
- 80

There is nothing in the hundreds column of 89 to subtract from 227, so we start with the next highest column - the tens. But you can't take 8 tens from 2 tens, so you take 1 hundred away, first.
1 hundred is 10 tens, but of course we only wanted to take away 8 tens (80). So we add two tens to make up for it.
To sum up this step: To subtract 80 from 227, subtract 1 hundred and add 2 tens.
That will give you...

abax subtraction fig. 9
= 147

...147, which looks like this. In the next step we will subtract the 9 from the ones column. Can you guess how we will do this, based on how we have done things so far?

abax subtraction fig. 10
147-9

This board shows how to subtract 9 from 147. Since there are not enough ones in the ones column to subtract 9 from, we take 1 from the tens column. That is the same as ten ones. But, as before, that is too many. This time it is 1 more than we needed to subtract. We only needed to subtract 9 ones, but we subtracted 10 ones (in the form of 1 ten). So we add 1 one, and we are done.
Doing that will give us the final answer, which is...

abax subtraction fig. 11
=138

...138.

In the next lesson, we will learn the a way to have saved us one step of what we did in this lesson. You should practice lots of examples like this, using the above system before you go to tackle the short-cut, though.

You may realize that, when it comes to the columns, you don't have to do subtraction in any particular order.

You may realize that, when it comes to the columns, you don't have to do subtraction in any particular order. This might seem to fly in the face of conventional theory, after all, we know that subtraction does not adhere to the commutative property. That means that it does matter which order you subtract numbers in. For example, 9 - 5 is not the same as 5 - 9.

So how can it be that the order of the columns doesn't matter? Click here to find out.

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