Transcript Abacus - Awtrey Middle School

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
• Corresponded with Roman numerals
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
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
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
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
How To Use: Simple + / Simple Addition & Subtraction
Always work from LEFT to RIGHT
Example: 237 + 152 = 389
Now You Try!
•1+3=
• 12 + 31 =
Example: 187 - 125 = 62
• 123 + 321 =
•9–6=
• 43 – 12 =
• 263 – 142 =
How To Use: Complements
 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: + / - with Complements
 Adding
Subtract the complement
Examples:
 4+7 =
 2+9 =
 3+8 =
 Subtracting
Add the complement
Examples:
 10-7 =
 15-8 =
 17-9 =
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
Crazy but True…
http://www.youtube.com/watch?v=Px_hvz
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