**SECTION FIVE.ADDITION**

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.*

__General Procedure__

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:

**CASE 1.**

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.

**CASE 2.**

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?".

**Practice Exercises**

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