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 Multiplication Using Fingers

 

Multiplication Made Easy with the use of your fingers explained. Can be printed.

    Finger notation

From 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 fingers

From 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
Raise four fingers in one hand and three on the other and add
Multiply the addition by ten = 10(4+3)
And add the 4x3 = 10x7+12
Add this to one hundred: 100+ 70+12=182

Multiply 11 by 15
Raise one finger in one hand and five on the other and add.
Multiply the addition by ten = 10(1+5)
And add the 1x5 = 10x6+5
Add this to one hundred: 100+ 60+5=165

Multiply 12 by 13
Raise two fingers in one hand and three on the other and add.
Multiply the addition by ten = 10(2+3)
And add the 2x3 = 10x5+6
Add this to one hundred: 100+ 50+6=156

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.

Pacioli's Suma: finger notation symbols image
Finger Symbols from Pacioli's Summa Arithmetica, Middle ages Venice 1494
Left side, left hand. Right side, right hand

13th century finger symbolism image

Thirteenth Century Finger Symbolism

Johannes
                Aventinus Finger Symbolism 1522 image

Johannes Aventinus Finger Symbolism 1522


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