tiny soroban gif  SUBTRACTION EXAMPLES

ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual


**All of the following examples will require using complementary numbers. In order to fully understand the technique, it's best to work these examples using your abacus.**


Example: 102 - 78 = 24

1s gif
Step 1

A B C
    .
1 0 2 
 
2s gif
 Step 2

 A B C
     .
 1 0 2
-1      Step 2
 0 0 2
  +3    Step 2a
 0 3 2
3s gif
Step 3

A B C
    .
0 3 2
 -1    Step 3
0 2 2
   +2  Step 3a
0 2 4

Step 1: Set 102 on rods ABC.

Step 2: Subtract 7 from tens rod B. Use the complement. Begin by subtracting 1 from hundreds rod A, then....
Step 2a: Add the complementary 3 to rod B leaving 32 on rods BC.

Step 3: Subtract 8 from units rod C. Use the complement again. Begin by subtracting 1 from hundreds rod A, then....
Step 3a and the answer: Add the complementary 2 to rod C leaving the answer 24 on rods BC.

 

Example: 146 - 57 = 89

4s gif
Step 1

A B C
    .
1 4 6 
 
5s gif
 Step 2

 A B C
     .
 1 4 6 
-1      Step 2
 0 4 6 
  +5    Step 2a
 0 9 6
6s gif
Step 3

A B C
    .
0 9 6
 -1    Step 3
0 8 6
   +3  Step 3a
0 8 9

Step 1: Set 146 on rods ABC.

Step 2: Subtract 5 from tens rod B. Use the complement. Begin by subtracting 1 from hundreds rod A, then....
Step 2a: Add the complementary 5 to rod B, leaving 96 on rods ABC.

Step 3: Subtract 7 from units rod C. Use the complement again. Begin by subtracting 1 from hundreds rod A, then....
Step 3a and the answer: Add the complement 3 to rod C leaving the answer 89 on rods ABC.


Note the decimal numbers in the following example. Rod B is the designated unit rod.


Example: 22.3 - 2.8 = 19.5

Step 1

A B C
  .  
2 2 3 
 
Step 2

A B C
  .  
2 2 3 
 -2    Step 2
2 0 3
 
 Step 3

 A B C
   .  
 2 0 3
-1       Step 3
 1 0 3
  +9     Step 3a
 1 9 3
    +2   Step 3b
 1 9 5


Step 1: Designate rod B as the unit rod. Set 22.3 on rods ABC.

Step 2: Subtract 2 from units rod B leaving 20.3 on rods ABC.

Step 3: Subtract 8 from tenths rod C. Use the complement. Begin by subtracting 1 from units rod on B...There's a problem. Rod B is empty. There's nothing there to subtract so we have to go all the way over to rod A for help.
Step 3a: Subtract 1 from tens rod A. Add 9 to rod B, *then*
Step 3b and the answer: Add the complementary 2 to rod C leaving 19.5 on rods ABC.
 

**Something like this last example may seem a stretch at first.**
But with a little practice, solving problems of this sort soon becomes second nature.

 

 

Abacus: Mystery of the Bead
Exercise sheets - Subtraction

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Abacus: Mystery of the Bead
2004, 2005 by Totton Heffelfinger