The 10 to 9 Exchange

Subtracting with the 10 to 9 Exchange

In the previous section, we practiced direct subtraction and using the 5 to 4 exchange.  However, sometimes, during a subtraction, all the beads have been cleared but we still need to continue the subtraction calculation.  When we have this situation, we will clear 1 bead from the column to left and then set all 9 beads in the current column. This is called the 10 to 9 exchange.  

Let’s look at some simple examples of how we use the 10 to 9 exchange: 

• Subtract:  10 – 1 

• Subtract:  11 – 2 

• Subtract:  12 – 3

• Subtract:  13 – 4 

Examples

These examples we will use the 10 to 9 exchange in any column when no beads are available below the bar.  Each subtraction will start in the left most column and continue in each column moving to the right until all the columns have been subtracted. 

• Example:  131 – 53 

• Example:  122 – 47 

• Example: 144 – 58

• Example: 943 – 368  

• Example: 1341 – 476 

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.