Finger systems --- Signing --- Days in a month --- Chisenbop --- Multiplication --- Up to 100,000
Here is a simple way to multiply by nine using your fingers.
|Hold both your hands up with palms facing you. Number the fingers from left to right as one to ten.|
|Now hold down the finger of the number you want to multiply by nine. In this example, we are going to multiply by eight, so the eighth finger is held down.|
|The fingers to the left as the tens and the fingers to the right are units. In this example, there are seven fingers to the left (marked blue) and two to the right (marked red) which makes 72.|
Here is a way to multiply by six, seven, eight or nine using your fingers. It doesn't cover multiplying by one to five only 6x6 to 9x9. It is not as simple as the previous method, and to tell the truth, it might just be easier learning your times tables, but it does work. It is said to be widely used in medieval Europe
|Hold your hands with palms facing you and fingers towards each other. Number the fingers on each hand from bottom to top as six to nine. (The thumb could be ten, but it's easy to multiply by ten, so don't bother!)|
|Now touch the two fingers of the numbers that you want to multiply. You may need to twist your hand slightly to do this. This example is multiplying eight by seven, so the finger number 8 touches the finger number 7 on the other hand.|
|Now for the calculation. First you add the fingers below and including the touching ones. These are the tens. Here there are five of them, three on one hand and two on the other (marked blue), so that makes 5x10 = 50.|
|Then you multiply the fingers on the left hand above the touching ones with the fingers on the right hand above the touching ones. These are the units. Here there are two fingers on the left (marked red), and three fingers on the right (marked green), so that makes 2x3 = 6. Add this to the 50 you've already got, and that makes 56.|
I have separated the tens and units in this technique, but if you try to multiply 6x6, you find that the tens figure is 2x10=20, and the units figure is 4x4=16. Added together, this makes 36, which is correct. Perhaps we can think of the 16 as being a 'carry'.
This technique looks a bit like magic, so here is a proof that it does work. If you don't know algebra, then you won't understand this, so just ignore it. You don't need it to use the technique.
We are trying to multiply two numbers. Let us call them a and b. We touch together two fingers. On the left hand, there are 10-a fingers above the touching ones, and 10-b fingers on the right hand. We multiply these together to get the units:
(10 - a) (10 - b) = 100 -10a - 10b + ab
On the left hand, there are a-5 fingers below and including the touching ones, and b-5 fingers on the right hand. These are added and multiplied by ten:
10 x ((a - 5) + (b - 5)) = 10 x (a + b - 10) = 10a + 10b - 100
Add these both together:
100 -10a - 10b + ab + 10a + 10b - 100 = ab
So the answer is ab or a times b which is what we wanted.
This is not a finger system as it uses paper. You might be able to adapt the technique using 4 hands!
The example below multiplies 21 by 23.
1. Draw two lines (to represent 20) and one line (to represent 1). This is 21.
2. Draw 1 line (to represent 10) and three lines (to represent 3). This is 13.
3. Where the lines cross, count the intersections and work out the sum. So 20 x 10 is 200, and 20 x 3 is 60, and 1 x 10 is 10, and 1 x 3 is 3.
Add them all up, and the answer is 273.
This looks more impressive than it actually is. Write out the 'long multiplication' sum and you will see the same figures mentioned.
It will also be a clumsy method for digits above 6, as you will have a lot of counting, plus you will still need to know what sums like 6x7 are! Or count the intersections, which would become TEDIOUS!
© Jo Edkins 2007 - Return to Numbers index