How To Use A Chinese Abacus

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The abacus (the suanpan is the most useful variety) is a deceptively elementary computing tool still used all over the world. It'southward a useful learning device for the visually impaired, as well every bit for anyone who wants to larn the roots of the mod reckoner. After learning the nuts of counting on the abacus, you can quickly perform arithmetic similar improver, subtraction, multiplication, and sectionalization.

1

Orient your abacus properly. Each cavalcade in the top row should have one or two chaplet per row, while each column in the lesser row should take iv. When you start, all of the beads should be upwardly in the acme row, and down in the bottom row. The beads in the top row represent the number value 5 and each bead in the bottom row represents the number value ane.^[one]
2
Assign each column a place value. As on a mod computer, each column of beads represents a "place" value from which yous build a numeral. So, the farthest column on the right would exist the "ones" place (one-nine), the second uttermost the "tens" place (x-99), the third uttermost the hundreds (100-999), and so on.^[2]
- You can also assign some columns to be decimal places if necessary.
- For case, if you are representing a number like x.5, then the furthest correct cavalcade would be the tenths place (the first decimal identify), the second column would be the ones place, and the third column the tens identify.
- Likewise, to stand for a number like 10.25, the furthest correct column would be the hundredths place, the second column would be the tenths place, the tertiary the ones place, and the fourth the tens place.
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3
First counting with the chaplet in the lower row. To count a digit, push i bead to the "up" position. "One" would be represented by pushing a single bead from the bottom row in the farthest column on the correct to the "up" position, "two" by pushing two, etc.^[three]
- You'll find it easiest to employ your thumb to move the beads in the bottom row, and your index finger to motility the beads in the top row.
4

Complete the "4/5 commutation." Since there are only four beads on the bottom row, to go from "4" to "5," you push the bead on the height row to the "downward" position and push button all four beads from the bottom row down. The abacus at this position is correctly read "v." To count "half dozen," button ane dewdrop from the bottom row up, so the dewdrop in the acme row is down (representing a value of 5) and ane dewdrop from the bottom row is up.^[four]
5
Echo the pattern for college numbers. The process is essentially the same across the abacus. Go from "nine," in which all the beads in the ones identify are pushed up and the bead in the top row is pushed downwardly, to "x," in which a unmarried dewdrop from the bottom row of the tens identify is pushed up (while the beads in the ones identify are pushed back to their starting or "0" position).
- For example, 11 would have one bead in the 2d column pushed upward, and another in the first cavalcade pushed up, all on the bottom row. Twelve would accept 1 in the second column and ii in the first cavalcade, all pushed up, and all on the bottom row.
- Two hundred and 20 six would take two in the third cavalcade pushed upward in the lesser row, and two in the second cavalcade pushed up in the bottom row. In the first column, one bead on the lesser row would be pushed upward, and the bead on the meridian row would be pushed down.
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1

Input your first number. Say yous've got to add 1234 and 5678. Enter 1234 on the abacus by pushing upwards four beads in the ones place, 3 in the tens place, two in the hundreds place, and one in the thousands place.^[5]
ii

Offset calculation from the left. The first numbers yous'll add are the one and the 5 from the thousands identify, in this case moving the single bead from the top row of that column down to add together the 5, and leaving the lower bead up for a full of vi. Too, to add together vi in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row upwards to get a total of viii.
iii
Complete an exchange. Since adding the two numbers in the tens identify will upshot in 10, you lot'll carry over a ane to the hundred place, making information technology a 9 in that column. Next, put all the beads downwards in the tens place, leaving it nada.
- In the ones cavalcade, you lot'll practise essentially the same thing. Eight plus 4 equals 12, so you'll carry the one over to the tens place, making it 1. This leaves you with 2 in the ones place.
4

Count your chaplet to get the answer. Y'all're left with a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a ii in the ones: 1,234 + v,678 = 6,912.
5
Decrease past doing the addition process in reverse. Borrow digits from the previous cavalcade instead of carrying them over. Say you're subtracting 867 from 932. Later entering 932 into the abacus, start subtracting column-by-column starting on your left.
- Eight from ix is one, and so you'll leave a single bead up in the hundreds place.
- In the tens place, you lot tin't subtract 6 from three, then you'll borrow the 1 in the hundreds identify (leaving it zero) and subtract 6 from thirteen, making it 7 in the tens place (the upper bead up and 2 lower beads).
- Practise the same affair in the ones place, "borrowing" a dewdrop from the tens place (making information technology 6) to subtract 7 from 12 instead of ii.
- At that place should be a 5 in the ones column: 932 - 867 = 65.
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1
Record the trouble on the abacus. Start at the farthest left cavalcade of the abacus. Say you lot're multiplying 34 and 12. You demand to assign columns to "3", "four", "10", "i", "ii", and "=". Leave the rest of the columns to the right open for your production.^[half-dozen]
- The "Ten" and "=" will be represented by blank columns.
- The abacus should accept iii beads upwards in the uttermost column left, four up in the next farthest, a bare cavalcade, a cavalcade with i bead upwards, two beads upward in the next, and some other bare column. The rest of the columns are open.
2
Multiply by alternating columns. The gild here is critical. You need to multiply the beginning column by the first column subsequently the break, and so the first cavalcade by the second column later on the interruption. Next, you'll multiply the second column earlier the break by the beginning column afterwards the break, then the second column before the break by the second cavalcade later on the break.^[7]
- If you are multiplying larger numbers, proceed the aforementioned pattern: kickoff with the leftmost digits, and piece of work to the correct.
3
Record the products in the correct order. First recording in the outset answer cavalcade, after the blank one for the "=" sign. Y'all will go along moving beads on the right paw portion of the abacus equally you multiply the private digits. For the problem 34 x 12:^[8]
- Kickoff, multiply iii and 1, recording their production in the commencement answer cavalcade. Button three chaplet up in that seventh column.
- Next, multiply the iii and the two, recording their product in the eighth column. Push button ane bead from the upper department downwards, and one bead from the lower department up.
- When you multiply the iv and the one, add that production (4) to the eighth column, the second of the reply columns. Since you're adding a 4 to a vi in that cavalcade, bear one bead over to the outset answer column, making a 4 in the seventh column (four beads from the bottom section pushed up to center bar) and a 0 in the eighth (all beads in their original starting position: the top section bead pushed upwards, bottom section beads pushed down).
- Record the product of the terminal two digits 4 and 2 (8), in the final of the answer columns. They should at present read iv, blank, and 8, making your answer 408.
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one
Leave space for your answer to the right of the divisor and the dividend. When dividing on an abacus, you lot will put the divisor in the left-about column(south). Leave a couple blank columns to the right, then put the dividend in the columns next to those. The remaining columns to the right will be used to do the work leading to the reply. Leave those blank for now.^[9]
- For example, to separate 34 past 2, count two in the left-nigh cavalcade, exit ii blank columns, then put 34 over to the right. Leave the other columns blank for the reply section.
- To practice this, push two lower beads from the lesser portion up in the left-well-nigh cavalcade. Leave the next ii columns alone. In the quaternary column, push 3 beads from the bottom portion up. In the fifth column from the left, button iv chaplet from the bottom portion upwardly.
- The blank columns between the divisor and the dividend are simply to visually separate the numbers so you don't lose runway of what'due south what.
ii
Tape the caliber. Divide the commencement number in the dividend (3) by the divisor (2), and put it in the get-go blank column in the reply section. 2 goes into iii once, and then record a ane there.
- To do this, push ane bead from the bottom portion up in the first column of the answer section.
- If you lot like, you lot tin can skip a column (get out information technology blank) betwixt the dividend and the columns y'all want to use for the answer section. This can help you distinguish between the dividend and the work you do every bit you calculate.
3
Decide the remainder. Next, you need to multiply the quotient in the first reply department column (1) by the dividend in cavalcade one (2) to determine the residuum. This product (2) needs to be subtracted from the first column of the dividend. The dividend should now read fourteen.
- To make the dividend read 14, push two of the bottom portion beads currently pushed up to the middle bar at the fifth column dorsum down to their starting position. Only one bead in the lower portion of the fifth column should remain pushed up to the center bar.
iv
Repeat the procedure. Record the next digit of the quotient in the adjacent blank column of the reply section, subtracting the production from the dividend (here, eliminating it). Your board should now read 2, followed by bare columns, and then 1, 7, showing your divisor and the quotient, 17.
- Two beads from the lesser portion of the left well-nigh column will exist pushed upwardly to the center bar.
- This will be followed by several blank columns.
- One bead from the bottom portion of the first reply section column volition exist pushed to the eye bar.
- In the next answer section column, ii chaplet from the lesser portion will be pushed up to the heart bar, and the bead from the pinnacle portion will be pushed down to information technology.
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Question

Is it good for children to employ an abacus?

This reply was written by one of our trained team of researchers who validated it for accurateness and comprehensiveness.

wikiHow Staff Editor

Staff Answer

Yes, an abacus is a great tool for teaching children bones math. The different senses involved in using an abacus, similar sight and touch, can also help reinforce the lessons.
Question

Where was the abacus invented?

This answer was written by ane of our trained team of researchers who validated information technology for accuracy and comprehensiveness.

wikiHow Staff Editor

Staff Answer

The type of abacus about ordinarily used today was invented in China around the 2nd century B.C. However, abacus-like devices are first attested from ancient Mesopotamia around 2700 B.C.!
Question

My abacus has five chaplet on the lesser and two on the pinnacle. Why?

Your abacus is a Chinese abacus. It has more calculative power than a Japanese Soroban abacus. Notwithstanding, the essentials are effectively the same, so these instructions should still work.
Question

My abacus has 5 chaplet in the bottom rows. Was information technology built incorrectly? It says "made in People's Republic of China".

As with the terminal reply to this question, your abacus is a Chinese abacus (called suan pan). It has five beads in the lesser row and ii in the upper. This page shows instructions for the Japanese abacus (chosen soroban).
Question

Tin I make one with x columns or does it have to be 9?

The number of columns tin be whatever you lot want it to be. The important office is the number of beads per column.
Question

Which of the abacus is easier to do mentally?

Pehaps the Soroban ane because it has less beads than a Suan Pan, and also it'due south the almost familiar one.
Question

Is in that location a maximum number of columns an abacus can take?

No. Columns stand for digits in a number. An abacus with one column tin represent 0-9. Two columns tin represent 0-99. Three can represent 0-999, and so on. The "maximum" number of columns would simply be however many y'all can have while still having an abacus that'due south small enough to be applied.
Question

How tin can I represent a non-whole number on an abacus?

When yous assign each column a place value, you don't have to put 1 on the right, and then ten, etc. You could put the decimal point anywhere, so the columns could be 10, 1, .1, .01, etc. You tin can determine what each point stands for.
Question

My abacus has 17 columns, is information technology even so the aforementioned?

Yes, an abacus with more columns does not change the construction and methods shown here. The 17 columns mean 17 digits maximum tin can be calculated.
Question

How do I borrow numbers?

Let'due south say you are going to add 24 and 37. Firstly you are to add the ones get-go, then 4+7=11. Put down the ones digit which is ane then put the other i above the tens digit which ways you lot put 1 above 2 or 3 (depends to the number). Then add the tens digit which is ii+3=five then at the aforementioned time, add 1 to the sum, so v+1=6. The answer is 61.Here'due south the analogy: ane 37 +24 ----- 61

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Article Summary Ten

To use an abacus to add, beginning orient it by pushing 1 or 2 beads to the height of each row and 4 chaplet to the bottom of each row, which will set it back to zip. Afterward you've oriented information technology, assign each a column a place value. For example, the furthest column on the correct should be the ones place, similar 1-nine, and the second farthest column on the correct should be the tens place, like x-99. If you're working with decimals, make sure to make the furthest column the tenths place. When you're ready to start calculation, push button upwardly the designated chaplet in each column to represent your first number. For example, if you're adding 1,234 and 5,678, push up iv chaplet in the ones column, three in the tens column, 2 in the hundreds column, and 1 in the thousands place to represent one,234. Then simply lower the beads, starting in the thousands place, to add to the 2d number, 5,678. To acquire how to do other functions on an abacus, like multiplying and dividing, read on!

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