Putting it All Together - Adding Multiple Columns

Addition Counting Exchanges

Let’s review each of the exchanges we have learned in the previous sections:

4 to 5 Exchange

The 4 to 5 exchange  is needed when all the beads below the bar is set but the 5 bead is available.  This exchange adds 1 by pushing the 5 bead to the bar and clearing all the beads below the bar.

This is an example of how the exchange works: 

•   Example:  4 + 1

9 to 10 Exchange

The 9 to 10 exchange is used when all the beads have been set in a column.  To add 1 in the column where all beads are set, push 1 bead to the bar in the column immediately to the left of the 9 and clear all the beads in the column with a 9.  This is an example of the 9 to 10 exchange:

•   Example:  9 + 1

49 to 50 Exchange

The "49 to 50 exchange uses both the 4 to 5 exchange and the 9 to 10 exchange. It is needed when all the beads below the bar are set (but not the 5 bead) in a column and all the beads are set in the column immediately to its right. With this exchange, we push the 5 bead to the bar in the column with 4 set and clear the beads below the bar in this column and clear all the beads in the column immediately to the right, the column with a 9. Here is an example of the 49 to 50 exchange:

•   Example:  49 + 1

99 to 100 Exchange

The 99 to 100 exchange uses the 9 to 10 exchange twice. This occurs when both the current column and the column immediately to its left have all 9 beads set.  Push 1 bead to the bar in the column immediately to the left of the 99 and clear all the beads in the columns with 99 to add 1.

This is how the exchange works:

•   Example:  96 + 6

Examples

These examples we will use any of the exchanges from the previous sections to add columns of numbers and larger numbers. Each addition will start in the left most column and continue in each column moving to the right until all the columns have been added. 

• Example:  3 + 8 + 6 + 5

• Example:  7 + 4 6 + 8 + 3

• Example:  62 + 303 + 52

• Example:  751 + 96

• Example: 872 + 542

• Example: 542 + 459 + 896

• Example: 2,918 + 2,534

• Example: 13,238 + 21,918

• Example: 252,237 + 1,733,302

Build Your Skill

Now you are ready to try some calculations on your own. Click on this link for some problems and their solutions to test your skill.