small soroban gif  ADDITION 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: 34 + 78 = 112

1a gif
Step 1
A B C
    .
0 3 4 
 
2a gif
 Step 2

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

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

Step 1: Set 34 on rods BC.

Step 2: Add 7 to tens rod B. Subtract complement 3, then....
Step 2a: Carry 1 to hundreds rod A leaving 104 on rods ABC.

Step 3: Add 8 to units Rod C. Subtract the complement 2, then....
Step 3a and the answer: Carry 1 to tens rod B leaving 112 on rods ABC.
 

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

Example: 8.9 + 56 = 64.9

Step 1

A B C
  .  
0 8 9 
 
 Step 2

 A B C
   .  
 0 8 9
+5       Step 2
 5 8 9
Step 3

 A B C
  .   
 5 8 9
  -4    Step 3
 5 4 9
+1      Step 3a
 6 4 9

Step 1: Designate rod B as the unit rod. Set 8.9 on rods BC.

Step 2:  Add 5 to tens rod A leaving 58.9

Step 3: Add 6 to units rod B. Subtract the complement 4, then....
Step 3a and the answer: Carry1 to tens rod A leaving 64.9 on rods ABC.


This next example will be a little bit more difficult. With a little practice, solving problems of this type soon becomes second nature.
 

Example: 45.7 + 4.5 = 50.2

Step 1

A B C
  .  
4 5 7
 
Step 2

A B C
  .  
4 5 7
 +4    Step 2
4 9 7
 
 Step 3

 A B C
   .  
 4 9 7
    -5  Step 3
 4 9 2
  -9    Step 3a
 4 0 2
+1      Step 3b
 5 0 2

Step 1: Designate rod B as the unit rod. Set 45.7 on rods ABC.

Step 2: Add 4 to units rod B. This leaves 49.7 on rods ABC.

Step 3: Add 5 to tenths rod C. Use the complement. Subtract 5, then....
Step 3a: Carry 1 to units rod B. Rod B is full. Subtract the complement 9, then....
Step 3b and the answer: Carry 1 to tens rod A. This leaves 50.2 on rods ABC.

 

Abacus: Mystery of the Bead
Exercise sheets - Addition

Print Page (.pdf format,96kb)

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