# How to Learn the Chinese Abacus

Written by martin malcolm
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A Chinese abacus, or "suan-pan," is an ancient kind of calculator, dating from around the year 1200. It is made up of 12 rods, mounted in a wooden frame, with seven beads threaded on each rod. A bar across the abacus divides the rods into two sections. In the lower section, there are five beads on each rod. In the upper section, there are two beads on each rod. To learn how to use a Chinese abacus, start by modelling numbers and counting, before proceeding to basic addition and subtraction calculations.

Skill level:
Moderate

### Things you need

• Stick of chalk
• Grocery bill receipt

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## Setting Up

1. 1

Turn the abacus so that the section holding two beads on each rod is at the top, and the section holding five beads on each rod is at the bottom.

2. 2

Draw a large dot on the dividing bar of the abacus, using chalk. Place the chalk dot between the second and third rods from the right. This shows where a decimal point appears in written figures. Whole numbers can be modelled on the abacus to the left of your decimal point chalk mark. The two rods to the right of your decimal point chalk mark can be used to model tenths and hundredths respectively.

3. 3

Slide all the beads back as far as they will go, away from the dividing bar of the abacus. When the beads are in rows against the top and bottom edges of the frame, the abacus is set at zero and ready to use.

## Counting

1. 1

Slide a bead up the third rod from the right, until that bead meets the dividing bar. You have modelled the number one on the abacus. Slide three more beads up the rod to join your first bead. Now the abacus models the number four. Each bead on the lower section of the rod is worth one unit.

2. 2

Slide one bead from the top down the third rod, until it meets the dividing bar. Slide your original four beads back to their starting point. Now the abacus models the number five. Each bead on the top section of the rod is worth five units. Leave your number-five bead in place and slide a single bead up from the bottom of the third rod to meet the dividing bar. Now the abacus models the number six. Slide all the beads back to their starting points, to reset the abacus to zero.

3. 3

Slide both beads down from the top section of the third rod. Now the abacus models the number 10. This is the maximum value allowed. To model numbers bigger than 10, the fourth rod from the right comes into play. You could show numbers up to 15 by just using beads on the third rod, but this is not regarded as "proper form" and should be avoided. Aim to use the fewest beads possible to represent the number you wish to show. Reset the abacus to zero.

4. 4

Slide a bead up from the bottom of the fourth rod from the right. Each bead from here is worth 10 units. Slide up two beads from the bottom section of the third rod. Together, the beads now clustered around the dividing bar model the number 12. Slide up beads on the fourth rod to make successively: 22, 32 and then 42. Make 52 by sliding the beads on the lower section of the fourth rod back to the start, and sliding down a single bead from the top section. Beads from here are worth 50 units.

5. 5

Reset the abacus and practice making numbers such as your age, the year of your birth, and your house, street or apartment number. The fifth rod from the right on the abacus shows hundreds, the sixth rod shows thousands and so on. The two beads at the top of each rod are worth five times the value of the beads at the bottom. Always aim to use the fewest beads possible to represent the number you wish to show.

## Calculating

1. 1

Calculate the sum 8 + 3 on the abacus by first making the number eight on the third row, using a bead from the top and three beads from the bottom. The layout of the abacus does not give you enough beads to simply add on three more by sliding them up from the bottom, so to do the calculation you must add on five--another bead from the top--and then move two of your lower beads back to the start to compensate. This will give you the answer 11, shown as two top beads and one bead from below.

2. 2

Adjust your answer into "proper form," by sliding back the top beads on the third rod to their starting point and using instead a single bead from the bottom of the fourth rod. This will show the number 11 using the fewest beads possible.

3. 3

Reset the abacus and practice adding together numbers such as your age and apartment number, until the process of calculating and adjusting your answer to show "proper form" becomes familiar.

4. 4

Add together items from a grocery bill receipt to practice using the rods to the right of your chalk mark decimal point. The process of calculating is exactly the same: Model the starting number on the abacus, add on extra beads, using higher-value beads and compensating where necessary, then adjust the answer to display it in "proper form."

5. 5

Subtract items from a grocery bill receipt when you are confident with using the abacus for addition. Simply reverse the calculating process: Model the starting number on the abacus and take away beads, using higher-value beads and compensating where necessary, then adjust the answer to display it in "proper form."

#### Tips and warnings

• If you do not have a Chinese abacus, use an online version, such as one of those mentioned in the "Resources" section. Alternatively, draw a diagram of the abacus in a tray of sand: the Latin word "abacus" literally translates to "sand tray."

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