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 Subtraction found in the online manual Abacus: Mystery of the Bead.
Step 1: Begin by clearing the soroban to start with 0 (zero)
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 chapter Negative Numbers from Subtraction in the online manaul Abacus: Mystery of the Bead mentally 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 OPERATION
Lets 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: 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.
▪ Abacus: Mystery of the Bead
▪ Advanced Abacus Techniques
© March, 2011
Totton Heffelfinger Toronto Ontario Canada