CARRYING

BORROWING

CARRYING AND BORROWING ON THE

PYTHABACUS

A story sequence similar to the 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 coins they get from the village merchants.

SUMING DIGITS TO TEENS AND CARRYING TENS ON THE

PYTHABACUS

Position all but the left-most bead in the middle of the frame. Count six beads starting at the left-most bead under the triangle. These are the copper coins one farmer brings the king, the top digit.

?+?

6

Then count right from the beginning of the three remaining beads. When you get to the last bead push it over against the right post.

6+?

Then continue counting from the adjacent bead back to the left until you reach seven and push to the right. This number is the number of copper coins a second farmer brings the king. This is the bottom digit.

6+ 7

7

Now leaving the column of four push the remaining triangle back to the left.

6+ 7

When the two farmers bring more than nine copper coins, the count takes ten and gives the the king one silver coin in its place. The king’s count notices that he needs four more copper coins to put with the six from the first farmer to make ten. So he takes four from the second farmer’s seven coins to put with the first farmer’s six.

6+ 7

+4

-4

One of the beads from the solution column is pushed to the left to reveal the representation of the correct sum.The king now has collected one silver and three copper coins

+4

-4

1

6+ 7 3

1 3

When a queen is rescued from an angry dragon it sets the villagers' crops and hamlets afire. A brave prince, the king and his knights drive the dragon from the kingdom. In the dragon’s lair they find bags of gold, silver and copper coins. The queen decides to give the coins to the villagers who lost their crops and hamlets. Each village received as many coins it needed to buy seed and straw.

Subtracting Digits From Teens and Borrowing

The first village master asked for seven copper coins for his village. The queen had a bag of treasure with one silver coin but only three copper coin. The three beads pushed against the right post on abacus ‘A’ represent the three copper coin and to the left of these three beads the one bead above the triangle represents the silver coin. There were not enough copper coins in the bag. So the queen took the silver coin and gave it to the king’s count and the count gave her ten copper coins in its place to put with the three from the treasure bag.

13 - 7

Now she had thirteen copper coins.The queen gave the village master seven of the ten copper coins.Start counting out the seven, to the right from the left-most bead of the triangle and when you get to the last bead continue to the left until you reach seven. Then push the next bead to the left.

1 3 - 7

10-7

(start counting here) -7

The queen had remaining three of the ten copper coins she got from the count plus the three she had in the treasure bag.Note the number of beads under the array in the middle of the abacus.

1 3 - 7

33+

10-7

She put all the remaining copper coins together in the treasure bag. There were six copper coins left in the bag.There are six beads in the solution row.

13 - 7 6

6