When there are no beads that can be set directly (moved to the horizontal bar), then the indirect method of addition has to be used. This is also called synthesis. Think of a scale. If there are 5 balls sitting on the left side and only 2 balls on the right side then the scale is not balanced. By adding 3 more balls to the right side you can balance the scale.
It is important for children to learn what combinations make partners...e.g., you can make a 7 by the following:
0+7 = 7
1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7
7+0 = 7
When a user doesn't have the needed number of beads to set, then knowing the partner number is important. Here's an illustration of adding 3+3 = 6:
The first step is for the user to set 3. The user then asks herself, "Do I have 3 beads I can set directly?" The answer is "no."
The user then asks herself, "What is the next highest number I can set?" The answer is 5 so the user sets a 5-bead and the abacus reads 8.
However, the user only wanted to set 3 beads so she must clear 2 of the beads below the horizontal bar. After doing this the abacus reads 6.