Addition by Counting
Counting and Setting Numbers
The first step to learning to use the abacus is to learn to count, first with our fingers and then with the Cranmer or Japanese abacus (in the future, other types of abaci will be added). Then we will learn how to set (enter) and clear numbers. Click on this link, Counting and Setting Numbers to learn these basic skills.
Direct Addition
Direct addition can take place when a digit needs to added and all of the beads are available. One motion of your hand will complete the addition. Click on the link, Direct Addition, to learn this skill.
The 4 to 5 Exchange
Adding by counting is simply pushing 1 bead at a time to the bar in each column. However, what do we do when you want to continue adding but all of the beads below the bar have been pushed to the bar? The answer is to exchange the four beads for the 5 bead. Click on this link, The 4 to 5 Exchange, to learn this technique in detail.
The 9 to 10 Exchange
Another situation can occur when all the beads in a column have been pushed to the bar but we want to continue adding. We handle this situation by exchanging all the beads in the column (9) for 10. Follow the link, The 9 to 10 Exchange, to learn more about this technique.
The 49 to 50 Exchange
If you want to add 1 to 49, you will need to do an exchange in two columns using the 4 to 5 exchange and the 9 to 10 exchange. The technique to do this is called the the 49 to 50 exchange. Learn this technique in detail by clicking on this link, The 49 to 50 Exchange.
The 99 to 100 Exchange
The last steps to learning to add by counting is to learn to count to 99 with our fingers and with our abacus. When we exchange from ninety-nine (99) to one hundred (100), this is called the Rule of 99. Click on the link, The 99 to 100 Exchange, to learn this procedure.
Putting it all Together - Adding Multiple Columns
Now you are ready to put it all together, that is, add any size number to any other number. To do this, you will need to use one or more of the rules (Rule of 4, Rule of 9, Rule of 49 and Rule of 99) from the previous pages. Click on the link, Putting it All Together to study the examples.
Adding Decimals and Columns of Decimals
To conclude our study of adding numbers by counting with the Cranmer abacus, we need to understand how to enter decimal numbers. There are special markings on the Cranmer abacus that we will make use of to correctly position our decimals. Click on the link, Adding Decimals and Columns of Decimals , to learn to correctly align your decimal numbers and correctly add them.
Abacus Addition by Counting Text
You can view the full text of this material by clicking on the link, Abacus Addition by Counting.