CARRYING

BORROWING

CARRYING AND BORROWING ON THE

PYTHABACUS

END

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 coins, they get from the village merchants.

SUMING DIGITS TO TEENS AND CARRYING TENS ON THE

PYTHABACUS

Position entire array of beads in the middle of the frame. Push to the left a column of beads equal the copper coins one farmer brings the king, the top digit.

?+?

Then push to the right a column of beads equal the number of copper coins a second farmer brings the king, the bottom digit.

7+?

The king’s count notices that he needs three more copper coins to put with the seven from the first farmers coins to make ten. So he takes three from the second farmers six coins to put with the first farmers seven.

7+ 6

When the farmers bring more than nine copper coins the count takes ten and gives the the king one silver coin in its place.

7+ 6

+3

-3

The king now has collected one silver

and three copper coins.

7+ 6 3

+3

-3

1

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 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 piece but only three copper pieces. Abacus A represents the number of copper pieces with beads pushed against the right post and the silver piece to the left of the copper. There were not enough copper pieces in the bag. So the Queen took the silver piece and gave it to the kings count and he gave her ten copper pieces in its place.

13 - 7

Now, she had thirteen copper pieces.The Queen gave the village master seven of the ten copper pieces.

3 - 7

10+

The queen had three of the ten copper pieces she got from the count remaining plus the three she had in the treasure bag.

3 - 7

10+

33+

She put all the remaining copper pieces together in the treasure bag. There were six copper pieces left in the bag.

13 - 7 6