## 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

Step 1A B C .1 0 2Step2A B C.1 0 2 -1Step 2 0 0 2+3Step 2a 0 3 2Step3A B C .0 3 2-1Step 3 0 2 2+2Step 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

Step 1A B C .1 4 6Step2A B C.1 4 6 -1Step 2 0 4 6+5Step 2a 0 9 6Step3A B C .0 9 6-1Step 3 0 8 6+3Step 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 1A B C .2 2 3Step2A B C .2 2 3-2Step 2 2 0 3Step3A B C.2 0 3 -1Step 3 1 0 3+9Step 3a 1 9 3+2Step 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.

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Abacus: Mystery of the Bead

▪Exercise sheets - Subtraction

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© 2004, 2005 by Totton Heffelfinger