In a addition problem, the top number is called an addend, the number to be added is also called an addend, and the answer is called the sum.
1. Move the beads for the first number to the crosspiece starting from the left and making sure that the beads for the unit digit are placed on column 8.
2. Starting from the left, move the beads to the crosspiece for the number to be added. If there are not enough beads under the crosspiece or in a column to add the number, the concept of complementary numbers is used. There are two cases:
To add a number less than 4 when there are not enough beads under the crosspiece to move up and the five unit bead is not used, the five unit bead is moved down to the crosspiece and beads for the 5's complement of the number that is being added must be moved away (or subtracted*) to obtain the sum. See Example 1.
To add a number when there are not enough beads for the number, beads for the 10's complement of the number that is being added must be moved away (or subtracted*) and one bead must be added (or carried) to the column on the left to obtain the sum. See Example 2.
*For convenience we shall also use the word "subtract" to indicate that beads are being moved away from the crosspiece.
Example 1. Add: 4 +3
Enter first number (4) in col 8.
To add 3 in col 8; add 5,
and subtract 2. Sum is 7.
There are not enough beads under the crosspiece in column 8 to add 3 more, so we move a five unit bead down to the crosspiece and take away (subtract) the complement of 3 relative to 5, which is 2. (Case 1) Therefore we move 2 beads away (subtract 2 beads) in column 8 to obtain the sum.
Example 2. Add: 7+4
Enter first number (7) in col 8.
To add 4 in col 8, subtract the complement of 4 which is 6 and add 1 bead to the column on the left. Therefore, subtract 5,
Then subtract 1,
and carry 1 to col 7. Sum is 11.
There are not enough beads in column 8 to add 4 more, so we take the complement of 4 relative to 10 (which is 6), move away (or subtract) 6 from column 8 by moving the five unit bead and one unit bead away and carry (or add) one bead to the column on the left.
Example 3. Add: 72+86
Enter first number (72) in cols 7-8.
(Remember, numbers are entered and added from left to right when using the abacus.)
To add 8 in col 7; subtract 2,
and carry 1 to col 6.
To add 6 in col 8; add 5,
and add 1. Sum is 158.
Example 4. Add: 654+139
Enter first number (654) in cols 6-8.
Add 1 in col 6.
Add 3 in col 7.
To add 9 in col 8; subtract 1,
and carry 1 to col 7. Sum is 793.
Try solving the addition problems below and then do more of your own until you can perform addition quickly and easily without thinking "What do I do next?".