Mathematics

Multicultural Mathematical Activities - Vedic Mathematics

Vedic Multiplication

The three activity sheets demonstrate methods for multiplication based on the Indian Vedic tradition.

Example 1 demonstrates the basic method that will be used. The problems dealt with in this sheet are simple, especially for students who are confident with their multiplication tables. However, it is worth spending a little time on this, as the approach is developed on the other two examples

Vedic Multiplication - 1

You probably already know your multiplication tables, but we will start by seeing another way to multiply single-digit numbers together. The way we will do it is quite simple, and it means that:

  • You will not need any multiplication tables greater than 5

  • You will be able to use the same method with larger numbers!

Here is an example. We are going to work out 6 ´ 9 .

We start by working out how far each of the numbers is away from 10.

  • 6 is 4 away from 10, and 9 is 1 away from 10.

We set out the working like this:

6

4

9

1

   

  • Notice that we put the numbers from the question in the first column, and their ‘differences from 10’ in the second column.

  • The answer goes in the third row, as shown below; but how do we work it out?

6

4

9

1

5

4

  • First, find the difference between the two numbers in the shaded boxes. The numbers are 6 and 1, so the difference is 5. Put the 5 in the bottom-left box.

  • Now multiply the numbers in the right hand column: 4 ´ 1 = 4. Put this answer in the bottom-right box.

That’s it! Notice that when we found the difference between 6 and 1, we could just as easily have used the other pair of diagonally opposite numbers (9 and 4), since the result will always be the same.

Here are some examples to try: (a) 9 ´ 8 (b) 7 ´ 8 (c) 4 ´ 9 (d) 7 ´ 7

Sometimes there will be a ‘carry’ involved.

7

3

6

4

3

12


Here the ‘1’ in the ‘12’ is carried over to the ‘tens’ column to give the answer 42.

Here are some more examples: (a) 7 ´ 4 (b) 8 ´ 3 (c) 5 ´ 7 (d) 6 ´ 6

Vedic Multiplication - 1 (file size 25KB) - (download)

 

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Example 2 goes on to look at multiplying two numbers ‘a bit less than 100’. The same method as before is used, but can now be applied to rather more meaningful problems!

Vedic Multiplication - 2

Now we are going to see how we can use the multiplication method that we have developed to deal with multiplying numbers close to, but smaller than, 100. Basically we use exactly the same method as before…

Example: multiplying 96 by 89. Set it out as shown below:

96

4

89

11

   


In the right-hand column, put the differences from 100. Now, what goes in the bottom row?

  • Put 85 in the bottom-left box. We can get this from 96 – 11, or 89 – 4.

  • Now put 44 in the bottom-right box. (This is just 4 ´ 11, of course.)

And there’s your answer: 96 ´ 89 = 8544.

Here are some examples to try:

(a) 97 ´ 88 (b) 95 ´ 87 (c) 94 ´ 98 (d) 89 ´ 93 (e) 96 ´ 83

There’s no need to worry about carrying here, unless the number in the bottom-right box is greater than 100. (It won’t be, if the numbers being multiplied are close to 100.)

The method may not work if the numbers are too far from 100, as the numbers you have to multiply in the right-hand boxes may be too big to multiply

Vedic Multiplication - 2 (file size 21KB) - (download)

 

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Example 3 moves on to multiplying two numbers ‘a bit more than 100’. This is first done using the existing method – then a quick method is developed. (Use of the ‘existing’ method here relies upon students being confident with the arithmetic of directed number, and this initial stage can be left out if required.)

Vedic Multiplication - 3

Finally, we are going to adapt the method shown on the two previous sheets to multiply together a pair of numbers a little larger than 100. We’ll first do it a slow way, to get the idea, then do it a really quick way!

Example: multiplying 102 by 108. Set it out as shown below:

102

-2

108

-8

   


In the right-hand column, put the answer to the calculation 100 – n, where n is the number at the left. Since the starting numbers are bigger than 100, the numbers on the right will always be negative. Then carry on as before:

  • Put 110 in the bottom-left box. We can get this from 102 – -8 = 110, or 108 – -2 = 110.

  • Now put 16 in the bottom-right box. (This is -2 ´ -8.)

And the answer is: 102 ´ 108 = 11016.

If this seems a little complicated, here’s a very easy short cut:

  • Think of the numbers you are multiplying as 100 + a, and 100 + b.

  • Put 100 + a + b into the bottom-left box.

  • Put a ´ b into the bottom-right box.

  • Read the answer off; you don’t need to carry, unless there are more than 2 digits in the bottom-right box.

In fact, this is so easy you should be able to do it mentally!

Here are some examples to try:

(a) 103 ´ 108

(b) 107 ´ 111

(c) 106 ´ 109

(d) 104 ´ 105

(e) 112 ´ 104

 

There are more ‘unusual’ methods of multiplication in the activity ‘Multiplication Around the World’.

Vedic Multiplication - 3 (file size 23KB) - (download)

 

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This material can be used in a number of ways. For example, it could be used as the basis for a series of short starter activities, or for a single differentiated lesson. Higher-attaining students could be challenged to explain why certain details of the methods work; for example, why the ‘diagonal differences’ are the same, or how the use of directed numbers in Sheet 3 works.

The sheets have been designed so that they can be used either as student worksheets or as a teacher’s ‘script’.

Vedic multiplication intro. (file size 20KB) - (download)

 

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