1. All sums up to 10

2. Addition of all single digit numbers.

9 + 8 = 17 etc.

3. All compositions of 10.

**Additioin Tricks! Get better at calculations**

**Some special number pairs that add to 10**

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.

- 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.

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.

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.

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.

(1 + 8) + 5 = 1 + (8 + 5) = 14

4 + (21 + 6) = (4 + 21) + 6 = 31

General rule:

a + (b + c) = (a + b) + c

**3. Partitioning and Reasoning **

When 1 is added to any positive number,

If the last digit is not 9, the last digit of the number is raised to the next higher number.

6897 + 1 = 6898

If all the digits are nines, except the first digit, replace them with zeros and raise the first digit to the next higher number.

6999 + 1 = 7000.

**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”.

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.

100000-875 = 999910-00875

= 999910 - 00875

= 99125 Answer.

- 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.

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.

**Summary**

This blog talks about the addition and subtraction tricks for fast calculation. Apart from getting quick at calculations, vedic maths helps develop a child's mind and improves his/her cognitive ability. Some features of vedic maths are:

- Vedic Mathematics gives the answers in mathematical problems of addition, subtraction and multiplication etc in one step.
- Vedic Mathematics is outdated.
- Yet, it is easy and simple.
- Problems can be solved quickly in Vedic Mathematics.
- Hence it is helpful in competitive examinations of CBSE, ECSE mathematics or JEE problems in less time and with high accuracy.
- No need arises for any calculation when Vedic Mathematics is used for mathematical problems.

**About Cuemath**

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**FAQs**

**How do you add using Vedic Maths?**

In Vedic maths, addition operation is made as follows:

- By associative method
- By commutative method
- By using benchmark, and
- By breaking apart based on place value.

**How do you subtract using Vedic Maths?**

In Vedic maths, subtracting is done by following techniques:

- Subtracting the number in the question, the operation is started from the nearest power of 10,
- Using the Nikhilam rule, “All from 9 and the last from 10”.

**What is Nikhilam formula?**

- Nikhilam formula is used in the mathematical processes of subtraction and multiplication.
- Nikhilam formula (Sutra) is one of the 16 sutras of Vedic Mathematics.
- Nikhilam's formula states, “All from nine and the last from ten”.
- i.e., Nikhilam is applied to a number, subtract each digit from 9 and the last digit from 10.

**How many formulas are there in Vedic Maths?**

There are 16 formulas in Vedic Maths.