Using fingers to calculate products is not a new method. In his book “Number Words and Number Symbols”, Karl Menninger mentions that Leonardo of Pisa, the originator of the Fibonacci sequence, once wrote how multiplication using fingers needs to be applied regularly so the mind is more coordinated with adding and multiplying various numbers. Around 1543, Robert Recorde explained this method of multiplication in his book "Grounde of Artes". In Florian Cajori’s "A History of Mathematical Notations," specific instructions are given regarding this method. It is considered the origin of using X in multiplication.
Substitute numbers with fingers in a certain way. Suppose a closed fist represents five and any finger, when raised on that hand, adds one to the original value. So, a closed fist that has two fingers sticking out stands for five plus two, which is seven. To multiply two numbers between five and 10, represent one number on each hand and count "10" for each raised finger. Sometimes, children mark their fingers with numbers: thumbs as six, index fingers as seven, middle fingers eight, ring fingers nine and little fingers 10. When multiplying two numbers, raise the fingers one by one, starting with the thumb, until the appropriate number is displayed. This helps children keep track of the numbers.
Next, count the number of folded fingers on each hand and multiply those two numbers together. This gives you the "unit" of the answer. Add the unit to the result of the first operation to get the answer to the problem.
Sometimes, the unit measures up to a number greater than 10. In that case, 10 must be carried and added to the tens of the actual product. For example, if you multiply six with seven, there will be three tens, which equals 30, with three and four fingers remaining closed on either fist. The unit would be three times four, which is 12, or one ten and two units. You can either add 12 to 30 right away, or add one ten to 30 and two units to that. Either way, the result will be 42.
To multiply eight by nine, raise three fingers on your right hand and four on the left and add three to four to get seven. Count 10 seven times to get 70. Multiply the remaining fingers on left hand with those of right hand to get the "unit." (2 x 1= 2). Add the "unit" to the original result: 70 + 2 = 72.
For multiplying numbers greater than 10, subtract 10 from each of the numbers. Let the fingers on your two hands represent these remainders. Multiply the sum of the number of fingers raised with 10. To this product, add the product of the number of fingers raised in each hand (or the number of fingers raised in right hand multiplied by number of fingers raised in the right hand). To this, add 100.
For example, to multiply 14 by 13, raise four fingers on the right hand and three on the left and add four to three to get seven. Multiply this by 10, obtaining 70. To that, add the 4 x 3 = (10 x 7) + 12. Now, add this to 100: 100+ 70+12=182.