The 50 to 49 Exchange

Subtracting with the 50 to 49 Exchange

The 50 to 49 exchange uses both the 5 to 4 exchange and the 10 to 9 exchange. We will need to use this exchange when we need to subtract 1 in a column with no beads set and where only the 5-bead set in the column to its left.  To subtract 1 from 50, we will first clear the 5-bead (in the column to the left) and push the 5-bead and all 4 beads below the bar, to the bar (in the current column).  This is the 50 to 49 exchange. 

Let’s look at some simple examples of how we use the 50 to 49 exchange: 

• Subtract:  50 – 1 

• Subtract:  51 – 2 

• Subtract:  52 – 3 

• Subtract:  52 – 4 

Examples

In these examples we will use the exchanges learned in the preceding sections and the 50 to 49 exchange. The 50 to 49 exchange will be used when we need to subtract in a column without any beads and only the 5-bead is set in the column to the left.  To subtract 1 from 50 (getting 49) we will use the 5 to 4 exchange in the column to the left and set 9 in the current column. 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:   62 – 13 

• Example:  74 – 29 

• Example:  823 - 362 

• Example:  7,467 – 2,518 

• Example:  47,158 – 32,409 

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.