Multiplication with Fingers

Considering the importance teachers give to memorising multiplication tables and the heartburn it creates in lower primary students, we are devoting this chapter to explain how we can easily get multiplication tables of 6 to 9 on our fingers

Why only 6 to 9?

Table of 1, 2 & 3 are learnt through skip counting.

Table of 4 can be seen as doubling the table of 2!

Table of 5 can be remembered if we visualise a clock face!

The Method

This method uses the “Modulo 5” representation we studied in Chapter 7.3 and is useful when both the numbers which are to be multiplied are between (& including) 6 & 9. We assume that multiplication facts till 5 are easy to learn. The next chapter gives the reason why this method works.

To multiply 7 & 8, represent one number in each hand. Some fingers are extended in each hand. The rest of the fingers in each hand are touched together at the top of the thumb. Both the palms (facing you) are brought together. The extended fingers are added and they represent the “tens” part of the product. The number of fingers touching the thumb (& including it) in each hand are identified. Their product represented the “units” part of the product. The product can be found by combining them together. Though it sounds complicated, an example will make it easy to understand.

Let us take 7 X 8. (Insert pictures for every stage)

1. 7 on the left hand – 2 fingers extended & 3 touching the left thumb

2. 8 on the right hand – 3 fingers extended & 2 touching the right thumb

3. Keep both the hands together with the palms facing towards you.

4. Add the extended fingers: 2 + 3 = 5 and take it as ‘5’ tens I.e 50

5. Multiply the numbers represented by the touching fingers. 3 X 2 = 6

6. The answer is 50 + 6 = 56

7. The multiplication will require remembering multiplication facts only up to 4 X4 which is easy.

As mentioned earlier, it is a good principle to allow students to explore different ways of doing a given problem, before showing them the standard method. These different methods will deepen their understanding of the operation

Table of 9 on fingers

There is an even more easy way to get 9 tables.

1. Keep all the ten fingers extended

2. For 1X9, fold the (finger no 1) thumb on the left hand. 9 fingers will be extended. Hence the 1 X 9 = 9

3. For 2X9, fold the (finger no 2) index finger on the left hand. 1 finger & 8 fingers would be extended on either side of the folded finger. Read this as 18. Hence 2 X 9 = 18

4. For 3 X 9, fold the (finger no 3) middle finger on the left hand. 2 fingers & 7 fingers would be extended on either side of the folded finger. Read this as 27. Hence 3 X 9 = 27

5. By extending the logic, we can get the 9 tables up to 9X9=81.

This exercise also reveals a nice pattern about the 9 table. The sum of every product of 9, when added together is also 9.

This pattern works for the product of 9 & any other number. If we keep on adding the numbers in the product (and repeat the process) ultimately the total would be 9! Let us see an example.

43,567 X 9 = 392,108. The sum of the digits is 18. The sum of 1 & 8 is 9. Hence, we can also say without actually dividing that 9 is a factor of 393,108.