The following tutorials are based on examples and exercises given in the book 'Fun with figures' by Kenneth Williams, which is a fun introduction to some of the applications of the sutras for children.
Click here to visit the bookstore, for more details
of the original book this work is based on
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 8
Tutorial 9
Tutorial 10
Tutorial 11
Tutorial 12
Use the formula ALL FROM 9 AND THE LAST FROM 10 to perform instant subtractions.
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.
So 1000 - 83 becomes 1000 - 083 = 917
Return to Index
Using VERTICALLY AND CROSSWISE you do not need to the multiplication tables beyond 5 X 5.
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.
Here's how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100.
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.
The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3),
and 12 is just 3 x 4.
107 + 6 = 113 and 7 x 6 = 42
Again, just for mental arithmetic
Return to Index
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.
Subtracting is just as easy: multiply crosswise as before, but the subtract:
Return to Index
A quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE.
75^{2} 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
Method for multiplying numbers where the first figures are the same and the last figures add up to 10.
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:
We put 09 since we need two figures as in all the other examples.
Return to Index
An elegant way of multiplying numbers using a simple pattern.
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.
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.
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.
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.
Any two numbers, no matter how big, can be
multiplied in one line by this method.
Return to Index
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.
Notice that the outer figures in 286 are the 26
being multiplied.
And the middle figure is just 2 and 6 added up.
This involves a carry figure because 7 + 7 = 14
we get 77 x 11 = 7_{1}47 = 847.
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.
Return to Index
Method for diving by 9.
The first figure of 23 is 2, and this is the answer.
The remainder is just 2 and 3 added up!
The first figure 4 is the answer
and 4 + 3 = 7 is the remainder - could it be easier?
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.
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
Return to Index
Finding the digit sum of a number.
Any number of any size can always be reduced to a single figure by adding its digits.
The digit sum of 413 is 8 because 4+1+3=8.
For 20511 the digit sum is 9.
Return to Index
Adding from left to right.
For 76 + 86 we get 15_{1}2
So we carry the 1 to the 15 to get 162 as the answer.
Return to Index
Using digit sums to check answers.
Return to Index
Multiplying left to right.
Return to Index
Bigger divisions.
Divide the 36 at the beginning of 369 by the first figure of 72: 36÷7=5 remainder 1.
This gives: 36_{1}9 ÷ 72 = 5
The remainder, 1, is placed as shown and makes 19 with the 9 following
it.
From this 19 we subtract 2×5 (the answer figure multiplied
by last figure of 72):
19-10=9, the remainder.
To sum up: for 369 ÷ 72:
36 ÷ 7 = 5 remainder 1 gives 36_{1}9 ÷ 72 = 5
and 19-2×5=9 the remainder, so 36_{1}9 ÷ 72 = 5 rem 9
Similarly squares, squares roots are easily tackled (in one line) by the Vedic method. We can also solve equations and geometrical and trigonometrical problems. The Vedic system covers all areas of mathematics.
It is not possible to show all variations of the methods here: all
the techniques shown can be extended in various ways.
Return to Index
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.
Copyright © 2011 Inspiration Books and its licensors. All rights reserved. 2011