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The pictures show how to add 387+495.
Step 1. Put 387 on the abacus.

Step 2. Move a 5-bead to the center on the ones string.

Step 3. Trade in 2 5-beads on the ones string for a 1 on the tens string.

Step 4. Start adding 9 tens by moving a 5-bead on the tens string to the center.

Step 5. Trade two 5-beads on the tens string for a 1-bead on the hundreds string.

Step 6. So far you've added 5 tens. You need to add the rest of the 9 tens by moving 5-bead to the center on the tens string and moving a 1-bead away from the center.

Step 7. Add 4 on the hundreds string by moving a 5-bead to the center and a 1-bead away from the center.

The answer is 882.

ABACUS ARITHMETIC

During the Middle Ages in Europe Roman numerals were used to write numbers. Arithmetic with Roman numerals is difficult to do on paper. Computations were done using an abacus or a counting table. Arithmetic was a specialized skill until about the 16th century, when our current numeration system was developed. Today Chinese children learn arithmetic using an abacus, and it is still used in banks and shops throughout China.




Using an abacus



Each of the wires on the abacus represents a place value: the right-most wire represents the ones place, the next to the left the tens place, then hundreds, etc. The abacus shown has 7 wires on it; it goes up to the millions place.

There are five beads below the central bar: these each represent one of that place value. The two beads above the bar each represent 5 of that place value.


Here's how the number 286,417 is represented on the abacus:





Addition on the abacus is straightforward. To add 231 + 315 on the abacus you place 231 on the abacus (move 1 1-bead to the center on the right-hand string, 3 on the next string to the left, and 2 on the 3rd string to the left). Then move a 5-bead to the center on the right-hand string, one 1-bead on the next and 3 1-beads on the next. You can trade in the 5 1-beads on the 3rd from the lowest string for a 5-bead. You should be able to read 546 on the abacus.

Abacus Activities

1. Read the number on the abacus.





2. Use the abacus to do these addition problems.

2,425 + 1,373 =

120,721 + 612,135 =

531,327 + 839,438 =



3. Challenge activity: subtract using the abacus

589 - 232 =

973,678 - 851,254 =

827 - 384 =

956,386 - 673,734 =