Subtracting by Counting
Direct Subtraction
To directly subtract a number or a digit in a number, the all the beads need to be present in the column. Click on the link, Direct Subtraction to learn this skill.
The 5 to 4 Exchange
Subtracting by counting is simply pulling 1 bead at a time from the bar in each column. However, what do we do when you want to continue subtracting but all of the beads below the bar have been pulled from the bar? The answer is to exchange the 5-bead for the four beads below the bar. Click on this link, The 5 to 4 Exchange, to learn this technique in detail.
The 10 to 9 Exchange
Another situation can occur when all the beads in a column have been pulled from the bar but we want to continue subtracting We handle this situation by exchanging one bead from the column to the left and push all the beads in the column to the bar. This is the 10 to 9 exchange. Follow the link, The 10 to 9 Exchange, to learn more about this technique.
The 50 to 49 Exchange
If you want to subtract 1 from 50, you will need to do an exchange in two columns using the 5 to 4 exchange and the 10 to 9 exchange. The technique to do this is called the the 50 to 49 exchange. Learn this technique in detail by clicking on this link, The 50 to 49 Exchange.
The 100 to 99 Exchange
The last steps to learning to subtract by counting is to learn to subtract 99 from 100. To do this, we will pull one bead from the hundreds column and then push all of the beads in the tens and units column. This is called the 100 to 99 exchange. Click on the link, The 100 to 99 Exchange, to learn this procedure.
Putting it All Together
Now you are ready to put it all together, that is, subtract any size number from any other smaller number. To do this, you will need to use one or more of the exchanges (5 to 4, 10 to 9, 50 to 49 and 100 to 99) from the previous chapters. If you don’t feel comfortable with any of the exchanges, please go back and review the page for that exchange. Click on the link, Putting it All Together, to learn to subtract any size numbers.
Subtracting Decimals and Columns of Decimals
To conclude our study of subtracting numbers with the Cranmer abacus, we need to understand how to enter decimal numbers. There are special markings on the Cranmer abacus that we will use to correctly position our decimals. This will ensure that all the numbers are aligned correctly, making it easier to calculate the correct difference for several numbers. Click on the link, Subtracting Decimals and Columns of Decimals , to learn to correctly align your decimal numbers and correctly subtract them.
Abacus Subtraction by Counting Text
You can view the full text of this material by clicking on the link, Abacus Subtraction by Grouping text.