# How To Use An Abacus

## Reading Numbers on the Abacus

The decimal number system is represented on the abacus using beads and columns. Each column displays a digit between 0 and 9 (depending on the bead combination). The single top bead has a value of 5 and the four bottom beads have a value of 1 each. The abacus has a 1's column, a 10's column to its left, a 100's column and so on. In the image below, the abacus is showing the number 17,539. ## Small Friend and Big Friend Concepts

When a number has a small friend or a big friend, it is just a fun way of describing its complementary number. Each number 0 to 5 has a small friend number and when they are summed together they equal 5. For example, the small friend of 2 is 3 because they sum to make 5. Similarly, each number, 0 to 10, has a big friend number and when they sum together they make 10. Here are some examples: 1's big friend is 9, 4's big friend is 6 and 0's big friend is 10. A solid understanding of these basic math concepts is required to progress in abacus.

## Direct Movements on the Abacus

A direct movement is the most simple abacus action as it occurs when neither the small friend or big friend value are required for the calculation. The example below demonstrates the direct movements needed for summing 5 and 3 on the abacus. First, the top bead, with a value of 5, is pulled down to show number 5. Then three bottom beads, with a value of 1 each, are pulled up to give the answer 8. Direct movements can be practiced in Part 1: Sum to Nine on the Abacus where students learn to add and subtract on the abacus. ## The Pull-5 Movement on the Abacus ## The Break-5 Movement on the Abacus ## The Carry Movement on the Abacus

The carry movement is used on the abacus when two numbers are added and the answer flows over into the next column. The image below demonstrates how the carry movement uses the big friend concept for 9 + 3. First, 9 is added by pulling down the top bead and pulling up four bottom beads. Adding 3 will cause an overflow into the 10's column so carry is required. The big friend of 3 is 7 so 7 is subtracted from the 1's column while one bottom bead is added to the 10's column. This gives the answer 12. Practice questions are available in Part 3: The Borrow and Carry Movements where kids learn to add and subtract on the abacus. ## The Borrow Movement on the Abacus

When subtracting two numbers on the abacus and there are not enough available beads to subtract from one column, the borrow movement is used. In the example below, the borrow movement uses the big friend concept to calculate 14 - 5. To show 14 on the abacus, four bottom beads are pulled up in the 1's column and one bottom bead is pulled down in the 10's column. Now there is no top bead to subtract 5 so the borrow movement is used. The big friend of 5 is 5; therefore, the top bead is pulled in the 1's column and one bottom bead is subtracted from the 10's column. This leaves the answer 9 on the abacus. Practice questions are available in Part 3: The Borrow and Carry Movements where kids learn to add and subtract on the abacus. 