Abacus

introduction
history
calculations

1. ABACUS By - NARESH Kumar v

2. CONTENTS INTRODUCTION AND HISTORY WHAT IS ABACUS ? STRUCTURE AND CONCEPT CALCULATION USING ABACUS ADVANTAGE AND DISADVANTAGE OF ABACUS CONCLUSION

3. INTRODUCTION Abacus is a Latin word that has its origins in the greek word “ Abax ” or “ Abakon ” which means “table” or “tablet The earliest counting device was the human hand and its fingers, capable of counting up to 10 things; Toes were also used to count in tropical cultures The Abacus is one of many types of counting devices which are used to count large no.

4. HISTORY OF ABACUS In earlier period Merchants who traded goods needed to way to keep count of they bought and sold. Various portable counting devices were invented to keep tallies. The Abacus is one of them When Hindu Arabic number system came into use abaci were adopted to use place value counting The evolution of counting devices can be divided into 3 Ages Ancient times, Middle ages, and Modern ages

5. ANCIENT TIMES The Oldest surviving counting board is the salamis tablet, used by Babylolians circa 300 B.C., Discovered in 1846 on the islands of salamis

6. MIDDLE AGE The Apics, the coin board and the line board or from the period c. 5 C.E., to c. 1400C.E., The “exchequer” derives is named from the chequered table which was used in England from c. 1100 for calculating expenditure and receipts.

7. MODERN TIMES The saun-pan, the soroban and the schoty are the period C 1200 to the present The Abacus called saun-pan in Chinese as it appears today was first chronicled circa 1200 C.E., in China Japanese the Abacus is called soroban The Russian Abacus is called schoty and was invented in 17 Century and is still in use today

8. WHAT IS ABACUS ? It is a wooden/plastic framed tool with beads used to inculcate place value concept It is used for addition, subtraction, multiplication and division It is a calculator used by manually sliding bids along rods The Abacus is still in use today by shopkeepers in Asia and China towns in northamerica The Abacus is still thought in ancient schools and few schools in the west Blind children are thought to use abacus for calculation.

9. STRUCTURE OF ABACUS A modern abacus is made of wood or plastic. It consists of a rectangular frame about the size of a shoe-box. Within the frame are at least nine vertical rods strung with moveable beads. A horizontal crossbar is placed perpendicular to the rods separates the abacus into two unequal parts . The beads above the crossbar are known as heaven beads, and those below the crossbar are called earth beads . Rectangular frame Vertical rod’s Haven beads Crossbar Earth beads PART’s OF ABACUS

10. CONCEPT OF ABACUS The numerical value of each bead depends on its location in the abacus. Each heaven bead has a value of five times than that of an earth bead below it. Each rod represents columns of written numbers. Beads on the vertical rod farthest to the right have their values multiplied by one. On this rod, each earth bead is one and each heaven bead is five. Beads on the second rod from the right, have their value multiplied by 10. On this rod, each earth bead represents 10 and each heaven bead stands for 50. Beads on the third rod from the right have their value multiplied by 100, so that each earth bead represents 100 and each heaven bead stands for 500, and so on. 5 50 500 1 10 100 10 × 10 ×

11. CALCULATION USING ABACUS ADDITION Lets add 1234 and 5678. Enter 1234 on the abacus by pushing up four beads in the ones place, three in the tens place, two in the hundreds place, and one in the thousands place. Start adding from the left . The first numbers you'll add are the 1 and the 5 from the thousands place, in this case moving the single bead from the top row of that column down to add the 5, and leaving the lower bead up for a total of 6. Likewise , to add 6 in the hundreds place, move the top bead in the hundreds place down and one bead from the bottom row up to get a total of 8 . Complete an exchange. Since adding the two numbers in the tens place will result in 10, you'll carry over a 1 to the hundred place, making it a 9 in that column. Next, put all the beads down in the tens place, leaving it zero . In the ones column, you'll do 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 . Count your beads to get the answer. You're left with a 6 in the thousands column, a 9 in the hundreds, a 1 in the tens, and a 2 in the ones: 1,234 + 5,678 = 6,912.

12. CALCULATION USING ABACUS Subtracting Subtract by doing the addition process in reverse. Borrow digits from the previous column instead of carrying them over. Say you're subtracting 867 from 932. After entering 932 into the abacus, start subtracting column by column starting on your left. Eight from nine is one, so you'll leave a single bead up in the hundreds place. In the tens place, you can't subtract 6 from 3, so you'll borrow the 1 in the hundreds place (leaving it zero ) and subtract 6 from 13, making it 7 in the tens place (the upper bead up and two lower beads). Do the same thing in the ones place, "borrowing" a bead from the tens place (making it 6) to subtract 7 from 12 instead of 2. There should be a 5 in the ones column: 932 - 867 = 65 .

13. ADVANTAGES OF ABACUS Using Abacus can help you improve comprehension in math. Using Abacus can help you Building up better and faster calculation skills. Using Abacus can help you improve problem solving skills Using Abacus can help you improve memory Using Abacus can help you improve confidence in maths

14. DISADVANTAGES OF ABACUS It takes a lot of room in your back pack it is hard to carry It takes long time to calculate using abacus It is hard to learn abacus We cannot calculate decimal sums using abacus Abacus is not use for complex Equations

15. CONCLUSION We Conclude that Abacus is Oldest calculator in the world which was widely used of trading before Hindu Arabic number system came into use. THE END