Subtracting Two Numbers Indirectly

 

As with addition, when the user does not have the needed beads to set and clear directly, the indirect method (or synthesis) needs to be used.  The problem 45-18=27 uses the indirect method.

The user begins by setting the number 45 on the abacus. She then asks, "Can I clear 10 directly?"  

The abacus shows four 1-beads set in the tens column and a 5-bead set in the ones column.

After clearing a 1-bead in the tens column the abacus reads 35 as shown in the photo below.  

The abacus has three 1-beads set in the tens column and a 5-bead set in the ones column.

The user then asks, "Can I clear 8 directly?"  There are not beads valuing 8 in the ones column to clear. The user must clear a 1-bead in the tens column because this is the next highest number that can be cleared. The abacus now reads 25.

 

The abacus has two 1-beads set in the tens column and a 5-bead set in the ones column

The user was only trying to clear beads totaling 8 but has cleared beads totaling 10.  Therefore, 2 more beads must be set so that the abacus reads 27 as shown in the final photo below.

The abacus shows two 1-beads in the tens column. Set a 5-bead and two 1-beads set in the ones column.