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ABACUS: MYSTERY OF THE BEAD |
ADDITION EXAMPLES
**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
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Step 1 A B C
.
0 3 4
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Step 2
A B C
.
0 3 4
-3 Step 2
0 0 4
+1 Step 2a
1 0 4
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Step 3
A B C
.
1 0 4
-2 Step 3
1 0 2
+1 Step 3a
1 1 2
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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
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Step 1
A B C
.
0 8 9
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Step 2
A B C
.
0 8 9
+5 Step 2
5 8 9
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Step 3
A B C
.
5 8 9
-4 Step 3
5 4 9
+1 Step 3a
6 4 9
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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
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Step 1
A B C
.
4 5 7
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Step 2
A B C
.
4 5 7
+4 Step 2
4 9 7
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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
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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
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Exercise sheets - Addition
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Abacus: Mystery of the Bead
© 2004, 2005 by Totton Heffelfinge