Last updated on July 14th, 2024 at 05:56 pm
Subtraction is the process of calculating the difference between two numbers. We calculate the difference by taking away a number from the other.
Subtraction is an arithmetic operation that is signified by the minus sign, −. For example, the difference between 8 and 5 is 3, that is 8 – 5 = 3.
Generally students find it difficult when they have to subtract big numbers or a number from 100, 1000 or 10000. They need to borrow from the first digit which makes them confused.
In vedic maths there is no more borrowing or carrying numbers to others. Just by using simple tricks anyone can subtract any number from any one. It need just a few seconds to answer
There are two types of combinations in substitution:
Match combination subtraction
5 6 8 7
-2 -4 -6 -3
___ ___ ___ ___
3 2 2 4
Mismatch combination subtraction
5 7 4 6
-7 -8 -6 -9
___ ___ ___ ___
-2 -1 -2 -3
Doing match combinations is easy.
Example 1:
2 6 8 9
-1 4 5 4
_________
1 2 3 5
Example 2:
6 8 9 7
-1 2 4 3
______________
5 6 5 4
Subtracting mismatched numbers is a bit difficult especially when numbers are big, you have to carry numbers to next. E.g. 856 – 672 here middle numbers 5 and 7 are mismatched so you have to carry one to next. This carry problem creates confusion.
Here’s how you can do it easily by applying vedic math tricks without carrying.
Step 1: Always start from left
Step 2: Before writing the exact value first see the next number adjacent to that, if that is a matched number then write the exact result but if it is mismatched then write one lesser than exact one.
Here you can see that the number adjacent to 8 and 6 is 5 and 7 that are mismatched. So instead of writing the exact value of 8 – 6 = 4 you write 3(one less than 4) . But here the next numbers after 5 and 7 are matched, that is 6 and 2, so you write the exact values 5 and 7.
➡️ start from left
8 5 6
-6 7 2
_________
1 8 4
↖️
(Write 1 instead of 2)
Example 1:
(Mismatched)
⬇️
6 5 3
-2 6 1
_________
3 9 2
↖️
(One lesser)
Example 2:
(Tens and ones are mismatched)
⬇️ ⬇️
6 5 3
-3 6 4
___________
2 8 9
⬆️ ↖️
⬆️ (One less)
(One less)
Example 3:
6 5 8 3
-3 7 9 2
______________
2 7 9 1
⬆️ ↖️
⬆️ (write one less than 8)
(Write one less than 3)
Example 4: 87258 – 35461
(Mismatched)
⬇️ ⬇️
8 7 2 5 8
-3 5 4 6 1
____________________
5 1 7 9 7
⬆️ ↖️
↖️ (write one less because adjacent numbers are mismatched)
Example 5: 5346 – 2347
(Mismatched)
⬇️
5 3 4 6
-2 3 4 7
_______________
3 0 0 9
2 9 9 9 – Answer
⬆️ ⬆️ ⬆️
(Write one less than 3 because the next adjacent numbers 6 and 7 are mismatched. Here 0 has no value)
Example 6: 832575 – 332577
8 3 2 5 7 5
-3 3 2 5 7 7
________________
4 9 9 9 9 9 (apply same method)
So, just remember these systems and you can subtract any big number in 2 to 5 seconds. The only thing required is practice.
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Special Subtraction
Very easy method by applying Nikhilam Navatascaramam Dasatah which means – All from 9 the last from 10.
This sutra is generally used in subtraction from base numbers like 10,100,1000,10000 and so on.
Example 1: 1000 – 678
1 0 0 0
-6 7 8
___________
3 2 2 – Answer but how?
1 0 0 0
9 9 10 (Don’t write these numbers but just calculate in mind)
6 7 8
_____________
3 2 2
(Subtract All from 9 last from 10)
Example 2: 1000 – 43
Put one 0 before 43 to make it three digit numbers, that will become 043.
1 0 0 0
-4 3
__________
9 5 7 – Answer. But how?
Solution – vedic maths:
1 0 0 0
9 9 10 – All from 9 last from 10
0 4 3
_________
9 5 7
Example 3: 10000 – 27.3257
1 0 0 0 0
-2 7. 3 2 5 7
____________________
9 9 7 2. 6 7 4 3- Answer but how?
Solution:
1 0 0 0 0. 0 0 0 0
9 9 9 9 9 9 9 10- (Apply same formula)
0 0 2 7. 3 2 5 7
_________________________
9 9 7 3 . 6 7 4 3
Example 4: 10000 – .567
1 0 0 0 0. 0 0 0
9 9 9 9. 9 9 10
0 0 0 0. 5 6 7
___________________
9 9 9 9. 4 3 3
Example 5: 2000 – 67
2 0 0 0
9 9 10
0 6 7
____________
1 9 3 3
⬆️
(The 2 is reduced to 1)
Example 6: 60000 – 87
6 0 0 0 0
⬇️ 9 9 9 10
⬇️ 0 0 8 7
_________________
5 9 9 1 3
⬆️
(The 6 is reduced to 5. Because you are subtracting 87 from 1000 not 6000, so 5000 left that’s why we write 5)
Example 7: 40000 – 3.678
4 0 0 0 0. 0 0 0
9 9 9 9. 9 9 10
0 0 0 3. 6 7 8
_______________________
3 9 9 9 6. 3 2 2
So again these kinds of so-called looking hard subtraction you can solve it easily without any delay and mistake.
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Frequently Asked Questions
Final Words
From the above article you must have learned very effective techniques of subtracting numbers. But applying these techniques need lot of practice, so that you can do any subtraction fast within 2 to 5 seconds.