What are the three rules of vedic maths with 5 examples of each?
Answers
1| 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
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Using this method, those numbers can only be multiplied in which one of the multiplier is 9, 99, 999..... or so on.
Examples of the Calculations using this methods are ⇒
i) 11 × 99
Steps of Calculations ⇒
a) Firstly we will Subtracts the non - nine number (such as 9, 99, 999,.....so on) with 1. The, 11 - 1 = 10. After that, we will subtracts the 9 (or 99 or 999) with the resulting number. 99 - 10 = 89.
b) Then, 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
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3| 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
Hope it helps.
Answer:
(1) Nikhilam Sutra
examples :
(i) 94 * 96 ( Both the no. are closer to 10 ( power base 100))
94 is 6 less than 100 and 96 is 4 less than 100
so (-6)*(-4) = 24
94 - 4 = 90 OR 96 - 6 = 90
90 / 24 = 9024 Answer
(ii) 88 * 86 ( Both the no. are closer to 10 ( power base 100))
88 is 12 less than 100 and 86 is 14 less than 100
so (-12)*(-14) = 168 ( Since base is 100, we need to have only 2 digits so carry forward one )
88 -14 = 74 OR 86 -12 = 74
74 + 1( CARRY) /68 = 7568 Answer
(iii) 35 * 98 ( Both the no. are closer to 10 ( power base 100))
35 is 65 less than 100 and 98 is 2 less than 100
so (-65)*(-2) = 130 ( Since base is 100, we need to have only 2 digits so carry forward one )
98 -65 = 33 OR 35 -2 = 33
33 + 1( CARRY) /30 = 3430 Answer
(iv) 991 * 971 (Both the no. are closer to 1000
991 is 9 less than 1000 and 971 is 29 less than 1000
so (-29)*(-9) = 261 ( Since base is 1000, we need to have only 3 digits)
991 -29 = 962 OR 971 -9 = 962
962/261 = 962261 Answer
(v) 1011 * 1009 (Both the no. are closer to 1000
1011 is 11 more than 1000 and 1009 is 9 more than 1000
so (11)*( 9) = 99 ( Since base is 1000, we need to have only 3 digits )
1011 + 9 = 1020 OR 1009 + 11 = 1020
1020/099= 1020099 Answer
(2) Gyarasguna Sutra :
At first, write non 11 number twice
Add "0" to one of the numbers
Add both the numbers.
examples :
(i) 33 * 11 = 33 + 33
=330+ 33
=363 Answer
(ii) 48 * 11 = 48 + 48
=480+ 48
=528 Answer
(iii) 65 * 11 = 65 + 65
=650+ 65
=715 Answer
(iv) 29 * 11 = 29 + 29
=290 + 29
=319 Answer
(v) 98 * 11 = 98 + 98
=980+ 98
=1078 Answer
(3) Ekanunena Purneva Sutra :
examples:
(i) 11 * 99
11 - 1 = 10
99 - 10 = 89
So, 11 * 99 = 1089 Answer
(ii) 12 * 99
12 - 1 = 11
99 - 11 =88
So, 12 * 99 = 1188 Answer
(iii)13 * 99
13 - 1 = 12
99 - 12 =87
So, 13 * 99 = 1287 Answer
(iv) 14 * 99
14 - 1 = 13
99 - 13 =86
So, 14 * 99 = 1386 Answer
(v) 15 * 99
15 - 1 = 14
99 - 14 =85
So, 15 * 99 = 1485 Answer
Step-by-step explanation:
Nikhilam Sutra
In this method, Numbers can be multiplied which are close to the power of 10.
Gyarasguna Sutra
In this method, numbers can be easily multiplied by 11. “Gyarasguna word split into three words . Gyara mean 11, guna mean Multiplication and Sutra mean method.
write non 11 number twice
Add “0” to one of the number
Add both the numbers.
Ekanunena Purneva Sutra
In this method, numbers can be multiplied in which one of the number is multiplied by 9, 99, 999 …….
First, subtract 1 from 11, then subtract the resulting number from 99 or 999.
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