ABACUS: MYSTERY OF THE BEAD

The Bead Unbaffled - An Abacus Manual## Tutorial: negative numbers from subtraction

Example: Subtract 0 - 95 = - 95 (negative 95)## Note: This is an advanced operation. Before tackling this, it's suggested you have a good working knowledge of the chapters

Subtraction&Negative Numbers from Subtractionfound in the online manualAbacus: Mystery of the Bead.

Step 1: Begin byclearingthe soroban to start with 0 (zero)

## Step 1

## Step 2

## Step 3

## Step 4

Step 2: Since we are subtracting a larger two digit number from a smaller one (in this case subtracting 95 from zero) begin by borrowing 1 from the hundreds column. Although this step can also be done mentally, for learning purposes I'll actually show it. Place 100 onto the soroban.

Step 3 & 4: Subtract 90 (step 3) and 5 (step 4) for a total of 95 from 100 just as you normally would. This leaves 5. Notice the grey beads (step 4) - they are the beads that don't have value. They add up to 94. Following rules learned in the chapterNegative Numbers from Subtractionin the online manaulAbacus: Mystery of the Beadmentally add 1 grey bead to the last rod that has value. This leaves the answer -95 (negative 95).

REMEMBER TO GIVE BACK IF A NEGATIVE ANSWER BECOMES POSITIVE IN A SUBSEQUENT OPERATIONLets take this one step further and add a larger positive number to the negative answer. This will yield a positive answer.

Example:-95 + 118 = 23

## Step 5

## Step 6

Step 5: Add 118 to the negative answer on the soroban leaving 123. Since we borrowed 1 from the hundreds column in an earlier step we have to give it back if a subsequent operation yields a positive answer.

Step 6 and the answer: Give back the 100 borrowed in the earlier operation. This leaves 23, the correct answer.

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Abacus: Mystery of the Bead

▪Advanced Abacus Techniques## © March, 2011

Totton Heffelfinger Toronto Ontario Canada

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