How to Add and Subtract Using an Abacus

The Chinese people have used abaci for thousands of years, and many still use them because they're faster than handheld calculators. (Competitions between the two prove this.) An abacus can be used to add, subtract, multiply, divide, calculate square roots and deal with negative numbers. However, this article will only deal with addition and subtraction.

Difficulty: Moderate

Instructions

Things You'll Need:

• Chinese abacus

Reading an Abacus

1. Lay the abacus on a flat surface in front of you with the rods vertical and the large section of beads closest to you.

2. Move all the beads away from the center divider, called the bar. The top section of beads will be at the top of the rods and the bottom section will be at the bottom of the rods.

3. Study the beads. Those in the bottom section represent the numbers 1 through 4, called units or earth beads. Those at the top represent the numbers 5 and 10, called fives or heaven beads. For the purposes of adding and subtracting, use only one fives bead and ignore the other.

4. Enter a three-digit number into the abacus. Start with the rightmost rod. For numbers 1 through 4 move only the unit beads against the bar. For numbers between 5 and 10, move a fives bead against the bar, then add unit beads. For instance, the number 163 will have three unit beads against the bar on the rightmost rod followed by a five bead and a unit bead, and then by a unit bead.

Adding and Subtracting

5. Add a number less than five. To do this, move unit beads against the bar on the rightmost rod. If necessary, move a fives bead also. For instance, to add the number 3 to 163, the rightmost rod will have a five bead and a unit bead against the bar. Your abacus now reads 166.

6. Add a number greater than 5. To do this, it's best to think of the number as some number less than 10. For instance, to add 7 to the number on the abacus, first add a unit bead to the second rod, then subtract 3 beads from the first rod. Continue adding units of 10 then subtracting the appropriate number to get the right results.

7. When all the unit beads and one five bead has been moved to a bar, add a unit bead to the next rod and move the first group of beads back to their starting positions. For example, if you have the number 9 on the abacus, the rightmost rod has 4 unit beads and 1 five bead against the bar. To add 1, move a unit bead on the next rod and set the first rod to 0.

8. Subtract a number greater than 5. To do this first subtract 10 and then add back the appropriate number. For example, to subtract 8, first subtract 10 and then add 2. Continue in this manner for numbers greater than 10.

Tips & Warnings

• Once you feel comfortable adding and subtracting whole numbers, try inserting a decimal. To do this, find the rightmost dot on the bar. The rod running beneath the dot is a whole number and the rods to the right are places to the right of the decimal. Add and subtract as before. If your abacus doesn't have a dot, and if it has more than 10 rods, place a dot over the 4th rod.