Short Multiplication: Click here for Chalkboard Lesson

The following story can motivate the short multiplication process. The people of the kingdom of Clotheah are weavers of the finest cloth in many lands. With the fine cloth they make beautiful cloaks. The king appointed his daughter, Princess Clotheah, mistress of the sewing circles. One of her duties is to attend the great bazaar and buy thread to make the beautiful cloaks. At the bazaar, thread is sold on single spools and in wraps of ten spools.

Each cloak requires three single spools of thread. Princess Clotheah must buy thread for two village sewing circle and three farm sewing circles. For each village sewing circle she must buy enough thread to make ten cloaks and for each farm circle enough thread for one cloak. Therefore the princess must buy enough thread for twenty-three cloaks. So she will need twenty-three times three spools of thread.

First reset beads to the right on the Pythabacus. The digits of twenty-three are represented by the base beads of triangles pushed to the left. Push two beads against the left post to represent the village sewing circle or the tens digit and three beads to left close to the first two to represent the farm circles or the ones digit.

Then push three beads midway to the left post to represent the spools of thread needed for each cloak. Push the three beads back into the array against the right post leaving an array of columns in the middle of the Pythabacus.

   PLACE MOUSE OVER PICTURE

Now to multiply the ones, push the three beads representing the farm circles to the right into the array of columns just enough to separate three columns from the others. Do not push these columns into the array against the right post. Then push the three-bead triangle back to the left. The left most array of columns represents the number of wraps of ten spools of thread the princess must buy and the rightward array of columns represents the number of single spools of thread the princess must buy. Therefore the princess must buy 69 spools of the thread for each mistress and master of the sewing circles to make one cloak.

If the rightward array of columns or product is greater than nine the ones digit of the product is placed in the ones column and the tens digit is written small to the left of the ones digit then added to the tens product which is placed in the tens column.

The reverse process of short division can be motivated by the task of the Prince of Clotheah, dividing vegetables from the royal gardens among the village grocers.  The prince in his stand has shelves with bags of vegetables, (ten vegetables in each bag) and shelves with single vegetables. In the illustrated problem, the prince has three bags and four single vegetables to divide equally between two grocers.

Reset beads right on the Pythabacus then push two base beads over against the left post to represent the grocers or divisor.  Then push midway to the left post in columns of two three brown beads to represent the three bags of vegetables.

  PLACE MOUSE OVER PICTURE

Now push from the right side the largest regular triangle you can into the array of columns. Push the separated columns just a little bit toward the left post. The number of beads in the base of the regular triangle (gold beads) is equal the number of bags the prince gave each grocers and the tens value of the quotient (1).  Push this triangle or bead back against the array at the right post. The bead remaining to the right of the separated columns represents the leftover bag of vegetables.

Since the prince takes the vegetables out of this bag and puts them on the shelf with the other single vegetables join nine beads in columns of two to this bead to make ten (the number of vegetables in a bag). Join four more beads to this ten to represent the total number of single vegetables the prince has to divide among the grocers.

Push from the right side the largest regular triangle you can until it touches the rightmost array of columns. Push the regular triangle representing the tens or number of bags each grocer received from the prince to the left until it touches the leftmost columns.

The base beads remaining under the rightmost column represents the number of single vegetables the prince gave each grocer (the ones of the quotient 7). Note that a small one is written to the left of the ones digit to indicate the leftover bag of tens.