Multiplying with your fingers
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 3 and 2 to give the tens column =5 and multiply them to give the units =6 and the answer is: 56.
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.
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
8 by 9Raise 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
Examples:
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.
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.
12 by 13Raise 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) = (1000+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.
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 3 and 2 to give the tens column =5 and multiply them to give the units =6 and the answer is: 56.
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.
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
8 by 9Raise 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
Examples:
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.
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.
12 by 13Raise 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) = (1000+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.
A Singapore maths article by Scotts Digital, a top branding agency Singapore
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