In a subtraction problem, the top number is called the __minuend__, the number to be
subtracted is called the __subtrahend__ and the answer is calls the __difference__.

__General Procedure__

1. Move the beads for the top number (minuend) to the crosspiece making sure that the beads for the unit digit are located on column 8.

2. Starting from the __left__, move the beads for the number to be subtracted (the
subtrahend) away from the crosspiece using the correct digit placement (100's, 10's
unit). If there are not enough beads available under the crosspiece or in a column, the
concept of complementary numbers is used to subtract the number.

To subtract two numbers when a digit in the minuend is smaller than a digit in the
subtrahend, one bead is borrowed (subtracted) from the column on the left. Then the
beads for the 10's complement of the number you are subtracting are __added__ to the current
column to obtain the difference. See example 7. Negative numbers, however, are not used
on the abacus.

Example 5. Subtract: 8-2

Eenter minuend (8) in col 8.Subtract 2 in col 8.

Difference is 6.

Example 6. Subtract: 97-15

Enter minuend (97) in cols 7-8

Subtract 1 in col 7.

Subtract 5 in col 8.

Difference is 82.

Example 7. Subtract: 12-6

Enter minuend (12) in cols 7-8.

Borrow 1 in col 7.

To subtract 6 in col 8; add 5

and subtract 1.

Difference is 6.

In order to subtract 6 in column 8, borrow 1 bead from column 7 and add the 10's complement of 6 (which is 4) to column 8. There are 2 beads under the crosspiece in this column so in order to add 4 more, the concept of complementary numbers is used again. A 5 unit bead is moved down to the crosspiece and 1 bead (the 5's complement of 4) is subtracted in column 8.

Example 8. Subtract: 5,253-148

Enter minuend (5,253) in cols 5-8.

Subtract 1 in col 6.

To subtract 4 in col 7;

add 1,

and subtract 5.

To subtract 8 in col 8,

borrow 1 in col 7,

add 5 in col 8,

and subtract 3 (5's complement of 2).

Difference is 5,105.

__Practice Exercises__

5 - 3 15 - 9 50 - 27 150 - 76 115 - 56 7,951 - 963

9 - 8 32 - 19 86 - 29 487 - 98 517 - 99 4,715 - 4,269

6 - 4 48 - 37 69 - 25 926 - 58 119 - 97 15,613 - 7,815

5 - 2 32 - 19 71 - 23 334 - 84 876 - 68 49,136 - 1,382

4 - 1 27 - 17 43 - 75 851 - 75 722 - 54 89,724 - 9,176

7 - 2 51 - 38 23 - 16 683 - 25 283 - 95 37,153 - 8,239

8 - 5 93 - 57 81 - 57 720 - 65 333 - 77 25,734 - 3,476

9 - 8 75 - 46 34 - 28 245 - 19 415 - 36 64,284 - 5,045

6 - 2 66 - 58 57 - 39 554 - 27 536 - 58 70,463 - 6,198

**Points to Remember:**

**When using complementary numbers in addition, you subtract the 10's complement
of the number you are adding, and add one bead to the column on the left.**

**In subtraction, you borrow a bead from the column on the left and add the 10's
complement of the number you are subtracting.**

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