Vedic Maths - One More than the one before

There is a simple way of squaring numbers that end in 5.
75^2 (75 squared) . We multiply 7(the number before the 5) by the next number up which is 8 = 56. This is the first part of the answer. Then we simply multiply 5 X 5 which is the second part of the answer, which is 25. So the final result is 5625.
Imagine you can do this in your head.
65 ^2 = 6 X 7 = 4225
Try this one for yourself :-
25 ^ 2 =

Vedic Maths - Ratios

To Simplify ratios we divide each one by its highest common factor.
So 24:6 is equal to 4:1 as 6 X4 = 24. So every ratio which is not a simplest ratio can be simplified to a simplest ratio.
Sometimes we have to increase a ratio to get whole numbers:-
1.5/2.5 = 3/5.
Splitting into a ratio.
If we want to split £20.00 into the ratio 3:1, we get 15:5. We first add the ratios to get 4, then divide 20/4 = 5. Then we multiply out to get 15:5.

Vedic Maths - Highest Common Factor

When numbers are close together, the HCF will also be a factor of the sum and of the difference of the numbers.
So 411 and 417. The sum is 828 and the diffence is 6. 2 is not a common factor but 3 is
411 / 3 = 147 417/3 = 139. This is useful if the numbers are close together.
This is the Sutra By addition and by subtration.
Try this one for yourself:-
56,58

Prime and Composite Numbers

Prime Numbers have only 1 and themselves as factors, examples are 7,11, 13. Numbers that are not prime are composite numbers and can be expressed as a product of prime numbers. e.g 6 = 2 X 3
Prouct tree for 12
12 < 6
2
6 < 2
3 So the numbers at the tips of the branches are all prime so 12 = 2 X 3 X 2
Lets try another one 60 < 4 < 2
2

15 < 5
3
So 60 = 2 * 2 * 3 * 5.
Highest Common Factor
Suppose we have two numbers 70 and 99
Express each as prime factors we have 70 = 2 X 5X 7 and 99 = 3X3 X 11
We see there are no common factors except 1, so these numbers are relatively prime, they are prime in relation to one another.
Now Consider 18 and 30
18 can be written as 2 X 3 X 3 and 30 = 2 X 3 X 5
The common factors are 2 and 3 and 6. The highest common factor is 6. So to get the HCF(Highest Common Factor) we express each number as a product of prime factors and then multiplying togethers all the factors which the prime factors have in common. Another way of saying this is find the largest number that divides into both. 6 is the largest number that divides inot 18 and 30.

Multiplication on the flag

Multiplication is also done from left to right. So 237 X 2 is done. 4,6,14 = 474.
236 X 7 = 14,21,42 = 1652. Try this for yourself 73 X 7.

Vedic Maths - On the flag

Vedic Maths is done from left to right, because that is the way we write and the way we call out the answer. So adding 45 + 38 we do 4+3 = 7, then 8 + 5 = 13. Since 13 is a two figure number we carry this over to the left, and we get 83 as the answer.
Similarly 84 + 58 = 13,12 = 142. Try this yourself, 5 6 + 96. All these examples are taken from the Cosmic Calculator Book 1.

Using Bar Numbers

Say we have 444 - 286. This can be written as 2 bar 4 bar 2. So 2 bar 42 can be written as 158(all from 9 last from 10 rule). This allows you to do subtractions with having carry numbers.
Try 6767 - 1908 = 5 bar 2 6 bar 1= 4859. Try these yourself 804 - 388.

Vedic Maths Bar Numbers

This is 10 -1 or 9. Bar Numbers are very useful for subtractions. Think of them as negative numbers so 10 and -1 = 9.
So 7 bar 2 is 68. To create a bar number we substract from 10. 9 bar 1 is 89 as 89 is close to 90 bar 1. If a number has a bar number in it split the nuimber after the bar.
7 bar 3 1= 7 bar 3/ 1= 671.
We can combine bar number resolution with the sutra, All from 9 and last from 10. So 5 bar 33 means 33 subtracted from 100 = 467.
Try this yourself 7 bar 14.

All from 9 last from 10 - First extension

If you want to this subtraction:-
600 - 77. Do the following first,By one less then the one before applied to the 6, this gives 5. Then apply the sutra all from 9 and last from 10 to give 524.
So 5,000 - 123 = 4877.
This is very good to check your change:- You buy something for £3.46 with £20.00 what is your change.Answer £16.54.
Try this yourself:-
8000 - 3222. Remember we are taking more then 3,000 away so 4 will be left in the thousand coulmn. The answer is 4778.

Vedic Maths - All from 9 and Last from 10

This is a very easy method for subtracting numbers from 100,1000's etc
So 1,000 - 876 is done by all from 9 and last by 10. So 8 from 9 is 1,7 from 9 is 2, and 6 from 10 is 4. So the answer is 124.
If your doing 1,000 - 36. Write 36 as 036,and then apply the rule:-964.
Try these yourself 10,000 -3,883,100-64,98

Digit Sums

The Digit sums are found by adding the digits in a number and then adding again if necessary. O and 9 are equivalent in this system.
37 = 10 = 1
461 = 11 = 2

Try these yourself:-
796
6437

Some tricks you can use are cast out 9s as adding 9s to a number does not change its digit sum. You can also forget numbers that add up to 9.
So 5317 (531) add to 9 so the digit sum is 7

Vedic Maths

Vedic Maths is based on simple Indian Sutras. I will explain each sutra and give examples as to how to apply them.
By One more than the One before(Ekadhikena Purvena)
Starting from 1 all whole numbers can be generated by using By One More than the One before i.e 2, 3 etc

Some nice quotes

"Algebra is generous she often gives more than is asked of her" D'Alembert(1717-83) French Mathematcian.
"Bees ... by virtue of a certain geometrical forethought.. know that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material"
Pappus of Alexandria(c 300AD) Greek Mathematician

Vedic Maths

This is the fastest way to learn maths:-
http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp