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The Abacus

The Abacus. What is it?. The History. Abacus is a Latin word meaning “sand tray” Pebbles replaced the sand Salamis tablet used as early as 300 B.C. by Babylonians Updated by Greeks - using marble & Romans – using bronze Abax –table or tablet Romans added add’l grooves

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The Abacus

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  1. The Abacus What is it?

  2. The History • Abacus is a Latin word meaning “sand tray” • Pebbles replaced the sand • Salamis tablet used as early as 300 B.C. by Babylonians • Updated by Greeks - using marble & Romans – using bronze • Abax –table or tablet • Romans added add’l grooves • Corresponded with Roman numerals

  3. The History • Portable devices created • Created by Romans • Could fit in shirt pocket • Used by merchants • Introduced to China in early Christian era • Chinese abacus, suan pan, born in 11th century

  4. The History • The use of the Suan Pan spread to Korea and Japan in the 15th century • Called the Soroban • Changed over time with the final (1850) taking away one bead from both the top and bottom

  5. Today • Abaci are still in use today • The blind are able to make calculations by feel • Merchants and bankers still depend on their abacus for day-to-day business • Asia • Middle East • Africa

  6. How To Use: Place Value • Place Value • Each column represents a place value • Starting at the farthest right is the 1’s, then 10’s, 100’s, so on. • So 236 is represented like: • Now you try… • 9 • 12 • 372 • 5,065 http://www.mandarintools.com/abacus.html

  7. How To Use: Simple + / - • Simple Addition & Subtraction • Always work from LEFT to RIGHT • Example: 237 + 152 • Example: 187 - 125 = 389 • Now You Try! • 1 + 3 = • 12 + 31 = • 123 + 321 = • 9 – 6 = • 43 – 12 = • 263 – 142 = = 62

  8. Complementary Numbers In the case of 5: 4 & 1 3 & 2 In the case of 10: 9 & 1 8 & 2 7 & 3 6 & 4 5 & 5 Examples: 4 + 8 = 12 The complementary number for 8 with respect to 10 is 2. Therefore, subtract 2 from 4 and carry 1 to tens How To Use: Complements

  9. How To Use: + / - with Complements • Adding • Subtract the complement • Examples: • 4+7 = • 2+9 = • 3+8 = • Subtracting • Add the complement • Examples: • 10-7 = • 15-8 = • 17-9 =

  10. Speed: Combining Finger Movements • Using thumb & index finger – pinch beads together (1 “heaven” bead and 3 “earth beads” to create 8) • Using thumb & index finger – push beads simultaneously (3 “earth” beads from ones place and 1 “earth” bead to tens place to add 7) • Examinations – 10th level (easiest)  1st level (most difficult) • Speed ~ What do you think is faster? http://www.youtube.com/watch?v=yj7XbnYrIk0

  11. Crazy but True… • http://www.youtube.com/watch?v=Px_hvzYS3_Y

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