Subtracting with the Abax (Lesson 1)

Subtracting with the Abax (Lesson 1)
This lesson on subtractions is very easy. It only deals with one column, and does not deal with any negative numbers. It is here for the sake of completion. You can probably already subtract simple numbers, but this is here just in case you need to be reminded how that works, visually.In previous lessons, you learned how to add from left-to-right with the abax if you have more than one column. You probably suspected that you could subtract from left-to-right also. Of course you can! You can do all of the operations that way. The next pages will deal with left-to-right subtraction with more than one column. There is also an interactive lesson about doing that without an abax. That is more advanced than this, but once you are good at it on the abax, that will be easy. If you are curious to check it out now, click here.

Pay particular attention to the lesson in figure. 4.

abax subtraction fig. 1
8

This abax represents the number 8. We are going to subtract 6 from it.

abax subtraction fig. 2
- 6

You see the 6 which we are removing moved out of the groove and off to the side.

abax subtraction fig. 3
= 2

When you get rid of those six marbles, you end up with 2. Nothing could be simpler.

As you might imagine, tens-complements will play a part in subtraction, as well as addition. You can use them when you have to subtract a number in a column which is higher than the amount of marbles you have in that column.

abax subtraction fig. 4
15

This board represents the number 15. If we want to subtract 7 from it, you'll notice that there are not enough units to take seven marbles from.

abax subtraction fig. 5
- 7

Traditionally, we "borrow" from the next highest column. We are going to do something like that here, but not quite the same way. We will look at it like this:
If you take away 1 from the next highest column(the tens), that is the same as taking away 10 ones. But you really only wanted to take away 7 ones. In effect, you took away 3 too many.
So you replace those three by adding them to the ones column.
What you have done is remove the marble in the tens column, and added the ten-remainder of the number subtracted from the ones column to the ones column.

abax subtraction fig. 6
= 8

After having taken away the tens marble, and added three to the five remaining in the ones column, you end up with 8, which is the final answer.

Try to do all your subtraction problems without thinking in the traditional terms of "carrying." Use the tens-complement method instead. It will make your subtractions go faster.

Make sure you understand the Idea behind why the tens-complements work. It makes no sense to just "do it."

Would you like to learn this on your own Abax?
To order an abax and instruction booklets for more detailed speedmath lessons, click here.

on to the next lesson on subtraction with more columns

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