ADDITION SUBTRACTION MECHANICAL MATH ON THE ABACUS MENU

A story sequence similar to the one following might be used to guide the solution process for mechanical addition on the abacus. There is a king who owns all the land around his castle. He lets the village farmers grow crops on his land, but they have to pay him with copper and silver coins, they get from the village merchants. MECHANICAL ADDITION ON THE PYTHAGOREAN ABACUS

The farmers bring the coins to the count. One farmer brings three silvers and eight copper coins, and another farmer brings two silvers and seven copper coins. The count collects the copper coins, and puts them in stacks. Count eight beads starting at the left-most bead under the triangle, push these a little to the left, then continue counting seven more beads starting with the next bead after the eight. When you get to the last bead reverse direction and continue counting to the left until you reach seven

Push the seventh bead to the right until the triangle rest against the right post. Then push the second bead from the post to the left leaving the solution column over the right-most bead

Once the coins are collected, the count counts the copper coins. If there are more than nine copper coins, the king gets ten, and the count gets the remaining coins.To get the kings ten, two coins from the bottom seven are taken to add to the top eight. Push the top bead of the solution column to the right

The king had decreed that one silver coin equals ten copper coins, so he exchanged the ten copper coins for one silver coin.The solution is represented by the column of five beads and one above it representing ten

Now the count collects the three coins. Note that the one bead representing the silver coin has been carried over to the left-side post. Push three beads from the left-most column to the left

Then push two beads from the left-most column to the left

Now the solution is arrayed with the six tens to the left and the five ones to the right

BLANK

When a queen is rescued from an angry dragon it sets the villagers' crops and hamlets a fire. A brave Prince, the King and his knights drive the dragon from the kingdom. In the dragons lair they find bags of treasure. The Queen decides to give the treasure to the villagers who lost their crops and hamlets. Each village received as many silver and copper coins it needed to buy seed and straw. Each silver piece was counted as was counted as ten copper coins. SUBTRACTION ON THE ABACUS

To begin a subtraction problem first position the triangle of beads in the middle with a resting bead pushed against the left and right post. The first village master asked for seventeen copper coins for his village. The Queen chose a bag of treasure with three silver coins but only five copper coins. Push three beads to the left for the silver coins and five beads to the right for the copper coins

She took one silver piece from the bag, leaving two sliver coins in the bag, and exchanged it for ten silver coins

The abacus shows one bead pushed to the left of the five against the right post to represent ten copper for one silver and two beads against the left post to represent the remaining silver coins. The queen now had enough to give the village master the seven copper coins he needed. These seven coins are taken from the ten. Start counting, out the seven, to the right from the bottom bead of the column of the borrowed silver When you reach seven push the next bead to the left Start count here 7

Now the remainder from the ten, three, is added to the five to make eight. The answer is given by the number of beads pushed together under the triangle. Since there are no hundreds or gold coins the one silver needed may simply be subtracted from the remaining two by pushing one bead from the left post column

Now there is one bead in the left post column representing the remaining tens or silver coins in the bag