Maths Logics

Subtracting 2 Digit Numbers - Vedic Maths Tips and Tricks
Example 1:
Step 1:
Let us consider subtraction of two 2digit numbers 36 from 62 .
Step 2:
Now, split the values 62 and 36 as follows
6 / 2
3 / 6
Step 3:
Now, perform simple subtraction between the numbers written splitted
6 / 2
- 3 / 6
--------
3 / (-4)
Step 4:
As we get negative result, we are in need to add 10 with the second digit and subtract 1 with the first digit obtained after subraction.
3 / (-4)
(3-1) / (10-4)
------------
2 / 6
Step 5:
Final answer attained is 26.

Multiply Two Numbers using Vedic Maths Base Method
Rules:
Rule 1. Subtract both the numbers from the base value.
Rule 2. Cross section the multiplier and multiplicand value and add it with the reduced result. You should get same value on both the sides.
Rule 3. Multiply the reduced values. If the obtained value is greater than the base value, carry the remainder.
Rule 4. Subtract the remainder value from the difference value and find complement for the reduced result. If you get the carry value again, subtract the one from the difference value.
Rule 5. Join the obtained value to get the final result.
Multiplication of Numbers Above and Below Base 100
Example 1 : 92 X 111

Here base value is 100
Rule 1 : 92 – 100 = - 8 ; 111 – 100 = 11,
Rule 2 : 92 + 11 = 103 ; 111 – 8 = 103
Rule 3 : 8 x 11 = 88
Rule 4 : 103 - 1 = 102 Complement of 88 is 12 (100 - 88 = 12)
Rule 5 : Join the values, , 92 X 111 = 10212.
Multiplication of Numbers Above and Below Base 1000
Example II : 985 X 1099

Here base value is 1000
Rule 1 : 985 – 1000 = -15 ; 1099 – 1000 = 99,
Rule 2 : 985 + 99 = 1084 ; 1099 - 15 = 1084
Rule 3 : 15 x 99 = 1485. 15 x 99 = 1485. Here the obtained value is greater than one. Carry the remainder 1.
Rule 4 : 1084 - 1 = 1083. Now again subtract the one from the difference value because we have the carry value one. So the result wil be 1082. Complement of 1485 is 515.(2000 – 1485 = 515)
Rule 5 : Append the resultant values, 985 X 1099 = 1082515
Thus, the vedic maths base method multiplication can be used for faster multiplication.

Multiplication of Numbers Below the Base Number

Rules:
Rule 1. Reduce numbers from the base values.
Rule 2. Cross section the multiplier and multiplicand and add it to the reduced values. You will get same difference on both the sides.
Rule 3. Multiply the reduced values. If the resultant value is less than the base value add zero before it. If the resultant value is greater than the base value carry the remainder 1.
Rule 4. Add the carry value with the difference value.
Rule 5. Append both the values to get the final result.
Example I : 89 X 98
Rule 1 : Here base value is 100. So, 89 - 100 = -11 and 98 - 100 = -2
Rule 2 : 89 – 2 = 87 ; 98 -11 = 87
Rule 3 : -2 x -11 = 22
Rule 4 : No carry values
Rule 5 : Append the result is, 89 x 98 = 8722
Example II : 928 X 986
Rule 1 : Here base value is 1000. So, 928 - 1000 = -72 and 986 - 1000 = -14
Rule 2 : 928 - 14 = 986 - 72 = 914
Rule 3 : 14 x 72 = 1008. Here the obtained value is greater than the base value. So carry the one. i.e., 008 (carry 1)
Rule 4 : 914 + 1 = 915
Rule 5 : Append the obtained values, 928 x 986 = 915008

Thus, the vedic maths multiplication for numbers below the base numbers can be done easier.

Multiply Two Numbers Above Base Number - Vedic Maths
Multiplication of Numbers Above the Base Number
Rules:
Rule 1. Reduce the base values from the multiplier and multiplicand.
Rule 2. Cross section the multiplier and multiplicand and add to the reduced values. You will get same difference on both the sides.
Rule 3. Multiply the reduced numbers.
Rule 4. If the resultant value is less than the base value assign zero before the resultant value to equal the base value digits. If the resultant value is greater than the base value carry the one.
Rule 5. If you get carry values, add it to the difference values.
Rule 6. Join both the values to get the final result.
Example I : 106 X 108
Here base value is 100
Rule 1 : , 106 - 100 = 6 and 108 - 100 = 8
Rule 2 : 106 + 8 = 114 ; 108 + 6 = 114
Rule 3 : 6 x 8 = 48
Rule 4 : Here the obtained value is less than the base value. So there is no carry value.
Rule 5 : Join both the values (106 x 108 = 11448)

Multiply with Base of 100 | Vedic Multiplication Tips and Tricks:

Multiply with Base of 100
Rules:
Rule 1: Add multiplicand with a value (Multiplier-100), then multiply by 100.
Rule 2: x = (multiplicand-100), y = (multiplier-100).
Rule 3: Multiply x and y.
Rule 4: Add rule 1 result with the rule 3 result. Its a final result.
Example: 105 X 107
Rule 1 : (105 + 7) X 100 = 112 X 100 = 11200
Rule 2 : x = 105 - 100 = 5, y = 107 - 100 = 7
Rule 3 : 5 X 7 = 35
Rule 4 : = 11200 + 35 = 11235
105 X 107 = 11235

Get it right, with vedic mathematics tricks : Tips and Tricks
http://indiatoday.intoday.in/education/story/get-it-right-with-vedic-mathematics-tricks/1/417135.html

Get it right, with vedic mathematics tricks : Tips and Tricks Vedic math's is an ancient system of Mathematics which was followed by the Vedas which was later rediscovered by Jagadguru Shankaracharya Bharti Krishna Tirthaji Maharaja

The Remainders by the Last Digit (Shesanyankena Charamena) is used to express a fraction as a decimal to all its decimal places.It is similar to Ekadhikina Purvena .
Example 1:
a) Express 1/7 as a decimal
1. Add 'zero' to the numerator which makes 1 as 10
2. If the numerator is less than the denominator, add another 'zero' , else proceed as follows ...
3. Divide : (10)/7 = 1 remainder 3
4. Adding zero to the remainder (since it is less than the denominator), we divide as (30)/7= 4 remainder 2
5. We continue taking the remainder the following the steps from the start as follows :
(20) /7 = 2 remainder 6
(60) /7 = 8 remainder 4
(40) /7 = 5 remainder 5
(50) /7 = 7 remainder 1
6. Now note that the remainder is '1' which is same as the numerator '1'.This means we would get the repetition of the answers again and again.So we will stop here.
7. Using the numbers(remainders) 3,2,6,4,5,1 got above , we multiply them with the denominator '7',
7 x 3 = 2 1
7 x 2 = 1 4
7 x 6 = 4 2
7 x 4 = 2 8
7 x 5 = 3 5
7 x 1 = 7
8. Now we take the red shaded numbers from the above steps as sequence ,142857 (which would be our final result)
Therefore, Result (1/7) = 0.142857142857

ONE LESS THAN PREVIOUS-

One less than the previous or One less than the before :As the name indicates this sutra involves subtracting one from the given number to get our final result.This sutra is highly helpful in case of multiplication by 9,99,999....to any other number and in solving fractions of certain numbers like (1/7),(1/13),(1/17)..etc.

PART 1: For solving Multiplications

Example 1:

6 * 9 = ?

Step 1 : Minus one from the number on L.H.S digit above
Step 2 : Minus the answer(result) got from step 1 from R.H.S digit (i.e 5 from number 9)

6-1 = 5
9-5 = 4
Combine them LHS,RHS ,to get 54

Therefore,The Result for 6 * 9 = 54

EXAMPLE 2:
Now lets try the same again with 999

899 * 999 =?

Step 1: 899-1 = 898
Step 2: 999-898 = 101

Combining the above, 898101

Therefore,The Result :899 * 999 = 898101

GRID METHOD or Sum of the Products

Example : 1
15 x 17 =?

For this method rewrite 15 as (10 + 5) and 17 as (10 + 7) and then fill in the grid as shown

Finally add all the numbers inside the grid for the final answer ( 100 + 50 + 70 + 35) = 255

Therefore 15 x 17 = 255

VERTICALLY AND CROSSWISE(Urdhva-Tiryagbyham)

(b) For numbers above 100

Example 1: 102 * 105

102 - 2
105 - 5 ........> gives 100
---------------
(105+2) / 5 * 2 ...here we have to add the opposite numbers
107/10

Therefore,102 * 105 =10710

Example 2: 111 * 108

111 - 11
108 - 8.......> gives 100
-------------
(111+8) / 11 * 8
119 /88
Therefore , 111 * 108 = 11988

VERTICALLY AND CROSSWISE(Urdhva-Tiryagbyham)

VERTICALLY AND CROSSWISE for multiplying numbers close to 100
Now let us see another simple form of vertically and crosswise method for numbers close to 100.This method will amuse you with its simplicity.

(a) For numbers below 100

Example 1 : 82 * 94
The above numbers are close to 100
82 is 18 below 100 and 94 is 6 below 100.

So,
82 +18
\/
/\
94 + 6
----------------

(82-6) or (94-18) / (6 * 18) ,now by multipying the right side and subracting the left side
76 / 108 ....76+1 / 08 ,by carrying over '1' since it is a two digit number

Therefore ,82 * 94 =7708

Example 2: 88 * 95

88 +12
95 + 5 ------> gives 100
-------------
(88-5)/(12 * 5)
83 / 60

Therefore, 88 * 95 =8360