Vedic Maths is based on sixteen sutras or principles. These principles are general in nature and can be applied in many ways. In practice many applications of the sutras may be learned and combined to solve actual problems. These tutorials will give examples of simple applications of the sutras, to give a feel for how the Vedic Maths system works. These tutorials do not attempt to teach the systematic use of the sutras. For more advanced applications and a more complete coverage of the basic uses of the sutras, we recommend you study one books avilable from our book store or try the correspondence course.

N.B. The following tutorials are based on examples and exercises given in the book 'Fun with figures' by Kenneth Williams, which is a fun introduction some of the applications of the sutras for children.

If you are having problems using the tutorials then you could always read the instructions.

Tutorial 1
Tutorial 2
Tutorial 3
Tutorial 4
Tutorial 5
Tutorial 6
Tutorial 7

Tutorial 1

Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.

• For example 1000 - 357 = 643

  We simply take each figure in 357 from 9 and the last figure from 10.
  
  So the answer is 1000 - 357 = 643

  And thats all there is to it!

  This always works for subtractions from numbers consisting of a 1 followed by noughts: 100; 1000; 10,000 etc.
  

• Similarly 10,000 - 1049 = 8951
  
• For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose 83 is 083.

  So 1000 - 83 becomes 1000 - 083 = 917

Try some yourself:

1) 1000 - 777	=
2) 1000 - 283	=
3) 1000 - 505	=
4) 10,000 - 2345	=
5) 10000 - 9876	=
6) 10,000 - 1101	=
7) 100 - 57	=
8) 1000 - 57	=
9) 10,000 - 321	=
10) 10,000 - 38	=
Total Correct	=

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Tutorial 2

Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.

• Suppose you need 8 x 7

  8 is 2 below 10 and 7 is 3 below 10.
  Think of it like this:
  
  The answer is 56.
  The diagram below shows how you get it.
  
  You subtract crosswise 8-3 or 7 - 2 to get 5,
  the first figure of the answer.
  And you multiply vertically: 2 x 3 to get 6,
  the last figure of the answer.

  That's all you do:

  See how far the numbers are below 10, subtract one
  number's deficiency from the other number, and
  multiply the deficiencies together.

• 7 x 6 = 42
  
  Here there is a carry: the 1 in the 12 goes over to make 3 into 4.

Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.

• Suppose you want to multiply 88 by 98.

  Not easy,you might think. But with
  VERTICALLY AND CROSSWISE you can give
  the answer immediately, using the same method
  as above.

  Both 88 and 98 are close to 100.
  88 is 12 below 100 and 98 is 2 below 100.

  You can imagine the sum set out like this:

  

  As before the 86 comes from
  subtracting crosswise: 88 - 2 = 86
  (or 98 - 12 = 86: you can subtract
  either way, you will always get
  the same answer).
  And the 24 in the answer is
  just 12 x 2: you multiply vertically.
  So 88 x 98 = 8624

This is so easy it is just mental arithmetic.

Multiplying numbers just over 100.

• 103 x 104 = 10712

  The answer is in two parts: 107 and 12,
  107 is just 103 + 4 (or 104 + 3),
  and 12 is just 3 x 4.

• Similarly 107 x 106 = 11342

  107 + 6 = 113 and 7 x 6 = 42

Again, just for mental arithmetic

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Tutorial 3

The easy way to add and subtract fractions.

Use VERTICALLY AND CROSSWISE to write the answer straight down!

• 

  Multiply crosswise and add to get the top of the answer:
  2 x 5 = 10 and 1 x 3 = 3. Then 10 + 3 = 13.
  The bottom of the fraction is just 3 x 5 = 15.
  You multiply the bottom number together.

  So:
• 

  Subtracting is just as easy: multiply crosswise as before, but the subtract:

• 

Try a few:

Total Correct =

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Tutorial 4

A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.

• 75² = 5625

  75² means 75 x 75.
  The answer is in two parts: 56 and 25.
  The last part is always 25.
  The first part is the first number, 7, multiplied by the number "one more", which is 8:
  so 7 x 8 = 56
  

• Similarly 85² = 7225 because 8 x 9 = 72.

Try these:

1) 452 =

2) 652 =

3) 952 =

4) 352 =

5) 152 =

Total Correct =

Method for multiplying numbers where the first figures are the same and the last figures add up to 10.

• 32 x 38 = 1216

  Both numbers here start with 3 and the last
  figures (2 and 8) add up to 10.

  So we just multiply 3 by 4 (the next number up)
  to get 12 for the first part of the answer.

  And we multiply the last figures: 2 x 8 = 16 to
  get the last part of the answer.

  Diagrammatically:
  

• And 81 x 89 = 7209

  We put 09 since we need two figures as in all the other examples.

Practise some:

1) 43 x 47 =

2) 24 x 26 =

3) 62 x 68 =

4) 17 x 13 =

5) 59 x 51 =

6) 77 x 73 =

Total Correct =

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Tutorial 5

An elegant way of multiplying numbers using a simple pattern.

• 21 x 23 = 483

  This is normally called long multiplication but
  actually the answer can be written straight down
  using the VERTICALLY AND CROSSWISE
  formula.

  We first put, or imagine, 23 below 21:

  

  There are 3 steps:

  a) Multiply vertically on the left: 2 x 2 = 4.
      This gives the first figure of the answer.
  b) Multiply crosswise and add: 2 x 3 + 1 x 2 = 8
      This gives the middle figure.
  c) Multiply vertically on the right: 1 x 3 = 3
      This gives the last figure of the answer.

And thats all there is to it.

• Similarly 61 x 31 = 1891
  

  

• 6 x 3 = 18; 6 x 1 + 1 x 3 = 9; 1 x 1 = 1

Try these, just write down the answer:

1) 14     21 x	2) 22     31 x	3) 21     31 x	4) 21     22 x	5) 32     21 x
Total Correct =

Multiply any 2-figure numbers together by mere mental arithmetic!

If you want 21 stamps at 26 pence each you can
easily find the total price in your head.

There were no carries in the method given above.
However, there only involve one small extra step.

• 21 x 26 = 546

The method is the same as above
except that we get a 2-figure number, 14, in the
middle step, so the 1 is carried over to the left
(4 becomes 5).

So 21 stamps cost £5.46.

Practise a few:

1) 21     47 x	2) 23     43 x	3) 32     53 x	4) 42     32 x	5) 71     72 x
Total Correct =

• 33 x 44 = 1452

  There may be more than one carry in a sum:

  

  Vertically on the left we get 12.
  Crosswise gives us 24, so we carry 2 to the left
  and mentally get 144.

  Then vertically on the right we get 12 and the 1
  here is carried over to the 144 to make 1452.

6) 32     56 x	7) 32     54 x	8) 31     72 x	9) 44     53 x	10) 54       64 x
Total Correct =

Any two numbers, no matter how big, can be
multiplied in one line by this method.

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Tutorial 6

Multiplying a number by 11.

To multiply any 2-figure number by 11 we just put
the total of the two figures between the 2 figures.

• 26 x 11 = 286

  Notice that the outer figures in 286 are the 26
  being multiplied.

  And the middle figure is just 2 and 6 added up.

• So 72 x 11 = 792

Multiply by 11:

1) 43 =

2) 81 =

3) 15 =

4) 44 =

5) 11 =

Total Correct =

• 77 x 11 = 847

  This involves a carry figure because 7 + 7 = 14
  we get 77 x 11 = 7₁47 = 847.

Multiply by 11:

1) 88 =

2) 84 =

3) 48 =

4) 73 =

5) 56 =

Total Correct =

• 234 x 11 = 2574

  We put the 2 and the 4 at the ends.
  We add the first pair 2 + 3 = 5.
  and we add the last pair: 3 + 4 = 7.

Multiply by 11:

1) 151 =

2) 527 =

3) 333 =

4) 714 =

5) 909 =

Total Correct =

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Tutorial 7

Method for diving by 9.

• 23 / 9 = 2 remainder 5

  The first figure of 23 is 2, and this is the answer.
  The remainder is just 2 and 3 added up!

• 43 / 9 = 4 remainder 7

  The first figure 4 is the answer
  and 4 + 3 = 7 is the remainder - could it be easier?

Divide by 9:

1) 61 = remainder

2) 33 = remainder

3) 44 = remainder

4) 53 = remainder

5) 80 = remainder

Total Correct =

• 134 / 9 = 14 remainder 8

  The answer consists of 1,4 and 8.
  1 is just the first figure of 134.
  4 is the total of the first two figures 1+ 3 = 4,
  and 8 is the total of all three figures 1+ 3 + 4 = 8.

Divide by 9:

6) 232 = remainder

7) 151 = remainder

8) 303 = remainder

9) 212 = remainder

10) 2121 = remainder

Total Correct =

• 842 / 9 = 8₁2 remainder 14 = 92 remainder 14

  Actually a remainder of 9 or more is not usually
  permitted because we are trying to find how
  many 9's there are in 842.

  Since the remainder, 14 has one more 9 with 5
  left over the final answer will be 93 remainder 5

Divide these by 9:

1) 771 = remainder

2) 942 = remainder

3) 565 = remainder

4) 555 = remainder

5) 777 = remainder

6) 2382 = remainder

7) 7070 = remainder

Total Correct =

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Instructions
for using the tutorials

Each tutorial has test sections comprising of several questions each. Next to each question is a box (field) into which you can enter the answer to the question. Select the first question in each test with the mouse to start a test. Enter the answer for the question using the numeric keys on the keyboard. To move to the answer field of the next question in the test, press the 'TAB' key. Moving to the next question, will cause the answer you entered to be checked, the following will be displayed depending on how you answered the question :-

Correct
Wrong
Answer has more than one part (such as fractions and those answers with remainders). Answering remaining parts of the question, will determine whether you answered the question correctly or not.

Some browsers will update the answer on 'RETURN' being pressed, others do not. Any problems stick to the 'TAB' key. Pressing 'SHIFT TAB' will move the cursor back to the answer field for the previous question.
The button will clear all answers from the test and set the count of correct answers back to zero.

N.B. JavaScript is used to obtain the interactive nature of these tutorials. If you cannot get this to work then try the text/picture based version of this tutorial.

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