Putting it All Together

Putting it All Together

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

5 to 4 Exchange

Each subtraction problem starts by setting the first (larger) number. Then we pull (clear) the beads in the column, one at a time or directly in one motion.  In the first section, we practiced direct subtraction.  However, most often, you will need to pull (clear) the beads individually. When the first number is set with the 5 bead and beads below the bar, we pull (clear) the beads below the bar. If we need to continue subtracting but have cleared all the beads below the bar, we will need to exchange the 5 bead for 4 beads below the bar.  In this situation, we pull the 5 bead away from the bar and push 4 beads from below the bar to the bar.  This is called the 5 to 4 exchange.   

This is an example of how the exchange works: 

•   Subtract:  6 - 2 

10 to 9 Exchange

In the previous sections, we practiced direct subtraction and learned how to use 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.  This is an example of the 10 to 9 exchange:

•   Subtract:  10 – 1

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.  Here is an example of how this exchange works:

•   Subtract:   50 – 1 

100 to 99 Exchange1.

The 100 to 99 exchange involves using the current column and the two columns to its left. You will need to use this exchange when you subtract 1 in the current column when the current column and the column to its left have no beads are available. This means if you are subtracting 1 from 100, 200, 300 … 900, then you will need to use this exchange. 

This is how the exchange works:

•   Example:  104 – 6  

Examples

These examples we will use any of the exchanges from the previous sections to subtract columns of numbers and larger numbers. 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:   9 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1  

• Example:  75 – 16 

• Example:  64 – 27 

• Example:  478 – 369

• Example:  2,621 – 864  

• Example:  25,229 – 777

• Example:  65,253 – 26,854   

• Example:  47,595 – 39,841    

• Example:  969,095 – 203,618   

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.