## 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 1

A B C .0 3 4Step2A B C.0 3 4-3Step 2 0 0 4 +1Step 2a 1 0 4Step3A B C .1 0 4-2Step 3 1 0 2+1Step 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 1A B C .0 8 9Step2A B C.0 8 9 +5Step 2 5 8 9Step3A B C.5 8 9-4Step 3 5 4 9 +1Step 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 1A B C .4 5 7Step2A B C .4 5 7+4Step 2 4 9 7Step3A B C.4 9 7-5Step 3 4 9 2-9Step 3a 4 0 2 +1Step 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.

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Abacus: Mystery of the Bead

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© 2004, 2005 by Totton Heffelfinge