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
Step 2 Step 3
Step 1
A B C A B C
A B C . .
. 0 3 4 1 0 4
0 3 4 -3 Step 2 -2 Step 3
0 0 4 1 0 2
+1 Step 2a +1 Step 3a
1 0 4 1 1 2
Step 1: Set 34 on rods BC.
Step 2: Add 7 to tens rod B. Use the complement and subtract 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 3
Step 1 Step 2
A B C
A B C A B C .
. . 5 8 9
0 8 9 0 8 9 -4 Step 3
+5 Step 2 5 4 9
5 8 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.
算盤 ABACUS: MYSTERY OF THE BEAD - Addition Examples
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Example: 45.7 + 4.5 = 50.2
Step 3
Step 2
Step 1 A B C
A B C .
A B C . 4 9 7
. 4 5 7 -5 Step 3
4 5 7 +4 Step 2 4 9 2
4 9 7 -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 and 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
© 2004, 2005 by Totton Heffelfinge
算盤 ABACUS: MYSTERY OF THE BEAD - Addition Examples
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