Finger Representation 2

In Chapter 5.5, we saw how numbers up to 9 can be represented using fingers. We will now deal with representations of numbers greater than 9, using fingers.

A representation does not need to reflect reality. It has to be interpreted with "rules" which are related to it. For example, in all public places certain arrows are used to indicate the idea of Up or Down. While it may be familiar to most, it may confuse persons who may have never encountered the idea previously.

The basic principle is to use the place value concept. We represent the numbers as bundles in one hand and sticks in the other. Hence 3 in the left palm & 4 in the right palm can represent 34. With this idea numbers up to 99 can be represented with 2 palms.

But this requires representing a number up to 9 with fingers of just one palm. Let us first see how to do this.

There are basically 2 techniques which we can call, for want of a better word, as "Segment" & "Modulo 5" representations.

Segment Representation - Using the segments of the fingers

1. If we observe our fingers, we can see that each of them is divided into 3 segments by lines. For convenience let us call them segment lines. Our thumb is designed so that it can touch each of these 12 segment lines.

2. If we take the right palm, the thumb can start with touching the middle segment line on the ring finger. Then it can move in a downward and then clockwise direction touching 10 segment lines. The sequence can be written down as

3. 1 (Ring - middle), 2 (Ring - bottom), 3 (Little - bottom), 4 (Little - middle), 5 (Little - top), 6 (Ring - top), 7 (Middle - top), 8 (Index - top), 9 (Index - middle) & 10 (Index - bottom)

4. This was a technique used by ancient Hindus to count up to 100 using just their fingers! 108 is a sacred number for Hindus and many mantras were chanted 108 times.

Modulo 5 Representation - Using finger positions

1. Counting from 1 starts from the thumb and as the other fingers are extended sequentially to represent 1 to 5. Hence 3 is represented by the thumb, index and middle fingers. The open palm with all the fingers extended represents 5.

2. To proceed further, the fingers close into a fist which also represents 5. Hence both a closed fist & an open palm represent 5.

3. 6 is represented by the closed fist with the little finger extended. 7 is represented by the closed fist with little and ring fingers extended and so on.

4. An easier way to remember would be that to represent numbers from 1 to 5, we start with the thumb and to represent numbers from 6 to 9 we start with the closed fist and the small finger.

5. Though this method sounds complicated in written form, it can be understood with a little practice.

6. This method can be called "5 Modulo Representation" since it represents numbers more than 5 with numbers which are obtained after subtracting 5. The 5 is hidden and its presence implied by the position of the fingers used.

With these methods, we can represent numbers up to 999 with the fingers of our palms.

Addition & Multiplication

The Modulo 5 method also makes the addition of 2 one-digit numbers (each more than 5) & multiplication facts of 6X6 up to 9X9 very visual with fingers. We will study these later in chapters 12.9 & 12.10.