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Multiplication Made EasyFinger notationFrom the earliest times people counted on their fingers and often still do. In ancient civilizations systems were developed so that numbers could be represented by positions of the fingers in a manner similar to that currently used by deaf mutes. The left hand usually represented the lower numbers and those above 100 were calculated on the right. In his tenth satire Juvenal, the Roman writer, says: "Happy is he indeed who has postponed the hour of his death so long, and finally numbers his years upon his right hand." Multiplication times tables take time to learn and before paper and pen were common a finger based system was developed to aid rapid calculation Multiplication using fingersFrom finger notation there developed a system of finger computation. Examples: To multiply 7 by 8 Subtract 5 from 7 and raise two fingers on one hand; subtract 5 from 8 and raise three fingers on the other. Add the 2 and 3 to give the tens column =5 and multiply the remaining fingers (3 by 2) to give the units =6 and the answer is: 56. Multiply 6 by 6 Raise one finger on each hand and add 1+ 1 = 2 multiply the remaining fingers 4x4= 16 add 2 to the ten column of 16 =36 Multiply 6 by 7 Raise one finger on one hand and two on the other and add 1+ 2 = 3 multiply the remaining fingers 4x3= 12 add 3 to the ten column of 12 =42 Multiply 8 by 9 Raise three fingers on one hand and four on the other and add 3+ 4 = 7 multiply the remaining fingers 2x1= 2 add 7 to the ten column of 2 =72 This formula explains the calculation: (10-a)(10-b) = 10(5-a+5-b)+ab In a similar manner we can find the product of numbers from 10 to 14 Example: To Multiply 14 by 13 Multiply 11 by 15 Multiply 12 by 13 This formula explains the calculation: (10+a)(10+b) = (100+10(a+b)+ab This method of multiplication was commonly used in the middle ages and made it unnecessary to learn the times tables beyond 5 by 5. It was particularly useful at international fairs and such events where people did not speak the language, and was in use in undeveloped countries until comparatively modern times. Nowadays, all you need is a calculator to do your multiplication even if you have forgotten your times tables, but the trusty finger is still very much in use.
Thirteenth Century Finger Symbolism
Johannes Aventinus Finger Symbolism 1522 Learn multiplication Times Tables with Toptables
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