Vedic Maths Tricks for Addition and Subtraction | Vedic Maths tricks for fast calculation

Vedic Maths techniques are the best techniques through which we can perform fast calculation. Vedic mathematics was an ancient method of solving mathematics problems. Later, Shankaracharya Swami Bharati Krishna Tirtha discovered Vedic mathematics. He is called the Father of Vedic mathematics
Addition Tricks! Get better at calculations
Some special number pairs that add to 10
Example
1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 + 5 = 10
Merely on seeing such pairs, the sum is understood mentally.
Benchmarks
To add one-digit number to another digit number, the technique involves having a basic number for easy calculation. To have multiples of 10 as benchmarks is safe and easy.
Example
23 + 8. Take 20 as a benchmark. Then 23 + 8 = 20 + 3 + 8 = 20 +11 = 31.
126 + 8. Benchmark 130.
126 + 4 + 4 = 130 + 4 = 134.
Breaking apart by place value
Decimal place value system for every number is used.
Example
14 + 77
= 10 + 4 + 70 + 7 = 10 + 70 + 4 + 7 = 80 + 11 = 91
42 + 66 = (40 + 2) + (60 + 6) = (40 + 60) + (2 + 6) = 100 + 8 = 108.
Nature of additions
1. Additions are Commutative
In sums for additions, the numbers can be rearranged or interchanged.
The result will be the same, even after the rearrangements.
Example
8 + 3 = 3 + 8 = 11
6 + 41 = 41 + 6 = 47
22 + 63 = 63 + 22 = 85
Generalizing, a + b = b + a
Multiplication of numbers in a sum is also commutative.
(operations in subtraction and division are not commutative.
Example
6 - 3 ≠ 3 - 6 and 6 ÷ 3 = 2 ≠ 3 ÷ 6 = 12
2. Addition is Associative
This is another law of addition.
As per this law, problems of additions with a greater number of additions, the items can be added in any order. The answer will not change.
Subtraction Tricks! Get better at calculations
Subtraction is the opposite of the addition process. By going through the following examples, substitution can be learnt.
Subtraction is made easy and simple mathematical operation by Vedic mathematics.
1. Subtracting 1
10 - 1 =9
100 - 1 = 99
When subtracting 1 from zero, the answer contains only 9s.
2. Subtraction from power of 10
In this technique, we take the nearest power of 10 for the numbers involved and subtract the numbers from the base.
Another rule called Nikhilam rule helps us. Nikhilam is one of the 16 main Sutras of Vedic mathematics.
Nikhilam rule says, “All from 9 and the last from 10”.
Example
10000-8675
99910 - 8675 =1325 Answer.
In this, we subtract each digit of the number simply from 9 for all digits except for the last digit, which is subtracted from 10.
If the number has a smaller number of digits, add leading zeros to have more digits.
Example
100000-875 = 999910-00875
= 999910 - 00875
= 99125 Answer.
Example
Subtrahend is less than minuend.
3625 - 1789
Subtract the subtrahend from the highest next power of 10 by Nikhilam rule.
99910 - 1789 = 8211
Add the result to the minuend, i.e., 3625 + 8211 = 11836.
Deleting the first digit, 1, the answer is 1836.
4529 - 2380
In this, 2380, the last digit from the left is zero. Here ‘8’ is to be subtracted from 10, keeping the zero as the last digit from left.
Then,
99100 - 23 80 = 7620 + 4529
= 12149
Deleting the left first digit, the answer is 2149.
45827 - 398 (subtrahend is of less digits than minuend)
i.e., 45827 - 00398
i.e., 999910 - 00398 = 99602 ---------(1)
Add (1) with 45827
99602 + 45827 = 145429
Deleting 1, the answer is 45429.
Minuend less than subtrahend
351 - 497
Apply NIKHILAM rule to Minuend
9910 - 351 = 649
Add subtrahend
649 + 497 = 1146
Deleting 1, first digit at left, the answer is -146.
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