Question

Write any five rule of vedic math with 5 examples of each

Answer 1

The Five Rules of the Vedic Math with 5 examples of each are ⇒ 

1| Nikhilam Sutra ⇒

This is the Method of the Multiplication and one of the application in Vedic Maths. Using this Method, a lot of calculations can be done within a minutes. There are some of the Requirements for using this method.

Only those numbers can be multiplied, who are closer to the power of 10, i.e., either less than the power of 10 or greater than the power of 10, or lying between both sides of the Power.

Examples of Nikhilam Sutra Methods are ⇒

i)  99 × 98

Steps of the Multiplication by ''Nikhilam Sutra'' ⇒

 a) Since, both the numbers are closer to the power of 10 (i.e. 100 or 10²), thus, this method can be applied in this Multiplication.

b) 100 - 1 = 99 & 100 -2 - 98. 99 is 1 less than the 100 and 98 is 2 less than the 100. Now, Since, they are less than the 100, thus, there difference will be written in the negative form and will be multiplied.
∴ (-1) × (-2) = 02

c) Now, First number is subtracted with the difference of the other and second number is subtracted with the difference of first number.
∴ 99 - 2 = 97 & 98 - 1 = 97

d) At last, We will combine them to get the Final Result.
∴ 9702

Similarly, Applying this Method in more examples.

ii) 96 × 97
100 - 96 = 4 | 100 - 97 = 3
 96 - 3 & 97 - 4|(-4) × (-3) = 12
 93|12
 9312

iii)  99 × 99
100 - 99 = 1 & 100 - 9 = 1| (-1) × (-1) = 01
 99 - 1 = 98 & 99 -1 = 98 | 01
 9801

iv) 98 × 98
100 - 2 = 98 & 100 - 2 = 98| -2 × -2 = 04
  98 - 2 = 96 & 98 - 2 - 96|04
 9604

v) 95 × 99
100 - 5 = 95 & 100 - 1 = 99| (-5) × (-1) = 05
95 - 01 = 94 & 99 - 5 = 94| 05
9405
  

2| Gyarasguna Sutra ⇒

In this Method of Multiplication, One number can be easily multiplied with 11.  Gyarasguna is the Sanskrit word which is made up of three words namely, Gyaras, guna and Sutra.  Gyaras means 11 and guna means Multiplication and Sutra means Methods.


Examples of the Multiplication be Gyarasguna Sutra are ⇒

i) 44 × 11 

Steps of the Calculations ⇒
a) Write the non -11 numbers two times. 

b) Add the Zero in one of the Number.

c) Add both the number now. 
440 + 44 = 484 

Similarly, solving the Others examples by this methods.

ii) 33 × 11                                                                                                           
330 + 33 = 363

iii) 95 × 11 = 950 + 95 = 1045

iv) 99 × 11 = 990 + 99 = 1089

v) 67 × 11 = 670 + 67
= 737

3| Ekanunena Purneva Sutra ⇒

In this method, only those numbers can be multiplied in which one of the multiplier is 9, 99, 999..... or so on.

Examples of the Calculations using the Ekanunena Purneva Sutra are ⇒

i) 11 × 99

Steps of Calculations ⇒

a) First Subtracts the non - nine number (such as 9, 99, 999,.....so on) with 1. 11 - 1 = 10 then subtracts the 9 (or 99 or 999) with the resulting number. 99 - 10 = 89.

b) After this, Combine both of them, 1089. Hence, the Multiplication is 1089. 
Similarly, Applying the same method in further calculations.

ii) 12 × 99
12 - 1 = 11 | 99 - 11 = 88
 11|88
 1188

iii) 5 × 9
 5 - 1 = 4|9 - 4 = 5
 4|5
 45

iv) 9 × 9
9 - 1 = 8| 9 - 8 = 1
8|1
81

v) 88 × 99
88 -1 = 87|99 - 87 = 12
87|12
8712

4| Antyaordasake'pi⇒

In this method of the Calculation, the sum of the last two digits of the multiplier must be 10. If this Requirement is not filled then the Calculations be this method cannot be possible.

Examples of the Calculations by this Methods are ⇒

i) 34 × 36

Steps of Calculations ⇒

a) Since, the sum of the last two digits is 10, thus this 'Sutra' can be applied.

b) Add 1 in the First digit of the second number and multiply it with the first digit of the first number. 3 × (3 + 1) = 3 × 4 = 12.

c) After this Multiply the second digit of the first number with the second digit of the second number. 4 × 6 = 24.

d) At last, combine both of them to get the Exact Multiplication. 1224.

Similarly, Applying this Method in further calculations.

ii) 42 × 48
4 × 5|2 × 8
20|16
2016

iii) 54 × 56
5 × 6| 4 × 6
30|24
3024

iv) 98 × 92
9 × 10|8 × 2
90|16
9016

v) 28 × 22
2 × 3| 8 × 2
6|16
616

5| Navamguna Sutra ⇒

This method of the Calculations of the Vedic Maths can be applied only in those numbers which have one multiplier as 9, 99, or 999. It is one of the application of the Vedic Maths.


Examples of the Calculations by this Methods are ⇒

i) 42 × 9
Steps of the Calculations ⇒

a) First write the 9 (or 99 or 999, etc.) as 10 - 1.
b) Then multiply it with other number.
42 (10 - 1) = 420 - 42 = 378

Similarly, Applying this methods in further examples.

ii) 52 × 99
52 (100 - 1) = 5200 - 52
= 5148

iii) 67 × 999
67 (1000 - 1) = 67000 - 67
= 66933

iv) 44 × 99
44(100 - 1) = 4400 - 44
= 4356

v) 5789 × 999999
 = 5789 (10000000 - 1) = 57890000000 - 5789
= 57889994211



Hope it helps. 

Answer 2

1.   Navamguna Sutra :

In this method of calculation, the “Vedic Maths” can be applied on those number which has the multipliers as 9, 99, 999….

  $\Rightarrow 52 \times 99 = 52 \times (100 - 1)$

            = 5200 - 52 = 5148

2.   Ekanunena Purneva Sutra:

In this method, we can only multiply with this number like 9, 99, 999, 9999….

  $\Rightarrow 88 \times 99$

            88 - 1 = 87

            99 - 87 = 12

            $88 \times 99 = 87 | 12 = 8712$

3.   Antyaordasake'pi:

In this method of calculation, the sum of the last two numbers of the two multiple should be of multipliers of 10.

  $\Rightarrow 98 \times 92 =9 \times 10 | 8 \times 2$

           $= 90 | 16 = 9016$