write any three rules of vedic math with 5 examples of each
Answers
1| Nikhilam Sutra ⇒
It's the Method of the Multiplication used in the Vedic maths. By Using this Method, a lot of calculations can be done easily. There are some of the Requirements for using this method.
By this methods, only those numbers can be multiplied, who are closer to the powers of 10, i.e., they are either less than the power of 10 or greater than the power of 10, or lying between both sides of the Power.
Examples of Calculations by the Nikhilam Sutra Methods are ⇒
i) 99 × 98
Steps of the Multiplication by ''Nikhilam Sutra'' ⇒
a) ∵ both the assumed numbers are closer to the power of 10 (i.e. 100 or 10²), thus, this method can be easily 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) Thus, 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) lastly, We will combine them to get the Final Result.
∴ 9702
In the same manner, Using 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
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2| Antyaordasake'pi⇒
It is the method of the Calculation in which the sum of the last two digits of the multiplier must be 10.
Examples of the Calculations by this Methods are ⇒
i) 34 × 36
Steps of Calculations ⇒
a) In this, 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) Then, Multiply the second digit of the first number with the second digit of the second number. 4 × 6 = 24.
d) Lastly, combine both of them to get the Final answer = 1224.
In the same manner, 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
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3| Navamguna Sutra ⇒
It is the method of the Calculations of the Vedic Maths which can only applied 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. :-)