The 5 to 4 Exchange

Subtracting with the 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 previous chapter, 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.  

Let’s look at some simple examples of how we use the 5 to 4 exchange: 

• Subtract:  6 - 2  

• Subtract:  7 - 3 

• Subtract:  8 - 4

• Subtract:  9 - 5

Examples

These examples we will use the 5 to 4 exchange in any column when no beads are available below the bar.  Here are some guidelines to follow: 

• Begin counting with the beads below the bar.

• Count one when we push each bead to the bar.

•  Never count when you clear.

• Clear all four beads simultaneously and continue counting.

Also, in these examples, each subtraction calculation will start in the left most column and continue in each column, moving to the right.

• Example:  36 - 23 

• Example:  89 - 63 

• Example: 595 - 274 

• Example: 787 - 464 

• Example: 8,279 – 6,138

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.