"Once the mind of a student develops an understanding of mental mathematics, he/she begins to think systematically and more creatively. In this article, we discussed some of the most basic Vedic maths tricks for beginners under different categories, with relevant examples and explanations."
Vedic Maths is a collection of techniques/sutras to solve mathematical problem sets in a fast and easy way. These tricks introduce wonderful applications of Arithmetical computation, theory of numbers, mathematical and algebraic operations, higher-level mathematics, calculus, and coordinate geometry, etc.
It is very important to make children learn some of the Vedic maths tricks and concepts at an early stage to build a strong foundation for the child. It is one of the most refined and efficient mathematical systems possible.
Vedic maths was discovered in the mid-1900s and has certain specific principles to perform various calculations in mathematics. But the question that arises is that is mathematics only about performing calculations?
However fascinating it might be to calculate faster using Vedic mathematics tricks, it fails to make a student understand the concepts, applications, and real-life scenarios of those particular problems.
What are the benefits of Vedic Maths?
These are the benefits of Vedic Maths:
It helps a person to solve mathematical problems many times faster
It helps in making intelligent decisions to both simple and complex problems
It reduces the burden of memorizing difficult concepts
It increases the concentration of a child and his determination to learn and develop his/her skills
It helps in reducing silly mistakes which are often created by kids
The addition is one of the most basic operations of Vedic mathematics. It states that,
Find out the number which is closest to the 10s multiple because it is easier to add those numbers.
7, 8, 9 close to 10
21, 22, 23 close to 20
67, 68, 69, are close to 70
97, 98, 99, are close to 100 ....... and so on.
Add the numbers which are the multiples of 10s
Add/Subtract the deficiency of numbers.
Let’s understand with the help of an example.
Suppose, we have to add 27 and 98.
So, Vedic maths tells us to add 30 and 100 which is 130 and then subtract (3+2) i.e. the deficiency from 130. So the result will be 125.
Similarly, if we have to add 66 and 576.
So, Vedic maths tells us to add 70 and 580 which is 650 and then subtract (4+4) i.e. the deficiency from 650. So the result will be 642.
There is yet another trick to perform addition using Vedic maths which states to add hundreds with hundreds, tens with tens and ones with ones, and so on.
For example, Suppose we have the following question, 220 + 364 + 44 + 18 = ?
Vedic maths tells us to break the numbers as per their place values. So, we will break the addition into:
200 + 300 = 500
20 + 60 +40 +10 = 130
4 + 4 +8 = 16
Repeat the process:
500 + 100 = 600
30 + 10 = 40
And at the units place we have 6.
Now perform, 600 + 40 + 6 = 646
Vedic maths tricks for Subtraction
For subtraction using Vedic maths, we follow the rules given below,
If the subtrahend is less than minuend, we subtract the numbers directly.
If any digit in minuend is less than the corresponding digit in subtrahend, we use the concept of complements.
Let us have a look at a few examples to understand these techniques.
1) When subtrahend is less than minuend: If we have to subtract 47 from 98, then, we can directly subtract the digits in subtrahend from the corresponding digits in minuend.
98 - 47 = 51
2) When any digit in minuend is less than the corresponding digit in subtrahend: 896 - 239
In this case for the places where the digit in subtrahend is greater we use the complement symbol while subtracting as shown below,
896 - 239 = 66\(\bar3\)
The complement of 3 = \(\bar3\) = 10 - 3 = 7
While replacing the value of \(\bar3\), we subtract 1 from the digit in the next place. Here, 1 will be subtracted from 6.
Therefore, 896 - 239 = 657.
Vedic maths tricks for squares
For the numbers ending with 5:
Step 1: Perform 5 × 5 = 25
Step 2: Add 1 to the previous number and the result with the previous number.
For example, in the case of the square of 85, Add 1 to 8 = 9 and multiply 9 with 8 = 72
Step 3: The result from step two will become the initial numbers of the final answer and the result of step one is the ending two numbers of the final answer. So the final answer will be 7225.
What is the square of 195?
Step 1: 5 × 5 = 25
Step 2: 19 × 20 = 380
Step 3: Combining the two results, which will give us 38025 which is the final answer.
Steps for Square Roots Math tricks
For performing square roots, we will have to keep some facts in mind:-
Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, 49, 64, 81.
Square of a number cannot end with 2, 3, 7, and 8.
We can say that numbers ending with 2, 3, 7, and 8 cannot have a perfect square root.
The square root of a number ending with 1 (1, 81) ends with either 1 or 9
The square root of a number ending with 4 (4, 64) ends with either 2 or 8
The square root of a number ending with 9 (9, 49) ends with either 3 or 7
The square root of a number ending with 6 (16, 36) ends with either 4 or 6
If the number is of ‘n’ digits then the square root will be ‘n/2’ OR ‘(n+1)/2’ digits.
Let us understand an example of finding a square root of 1764.
The number ends with 4. Since it’s a perfect square, square root will end with 2 or 8.
We need to find 2 perfect squares (In Multiples of 10) between which 1764 exists.
The numbers are 1600 (40) and 2500 (50).
Find to whom 1764 is closer. It is closer to 40. Therefore the square root is nearer to 40. Now from Step 2, possibilities are 42 or 48 out of which 42 is closer to 40.
Hence the square root = 42
Vedic maths tricks for Multiplication
There are a number of techniques to perform various types of multiplication calculations using Vedic maths tricks. Some of the most useful and the easiest ones are mentioned below:-
The trick of 11:
Step 1:- Divide the number into two parts
Step 2:- Add the two parts which will form the middle number
Let us understand this with the help of an example which will clear the doubts.
Let us say that we have to multiply 32 with 11.
Step 1: Divide 32 into 3 and 2
Step 2: The middle will be 3 + 2 = 5
So our answer to 32 × 11 would be 352.
Similarly, 75 × 11 = 7, 7 + 5, 5. Because 7+5 = 12, we will carry 1 to the previous digit and our final answer would be 825.
Multiplying numbers which are close to powers of 10:
It would be easy to directly jump into the example and understand this concept through it. Suppose, we have 2 questions:
Multiply 99 × 97
Multiply 103 × 105
Our approach should be something as shown in the picture.
Step 1: Find by how much the number is more or less than the power of 100 and write it on the right side of the vertical line.
Step 2: Either cross subtract or cross add. This will form the first part of the final answer.
Step 3: Multiply the right side of the vertical line and this shall form the right side of the result.
Similarly, suppose we have to find 996 × 997. Our approach will be as shown in the picture below.
Multiplying 2 digit numbers:
This would again be simple if followed by a step approach through what is displayed in the picture. Suppose, we have to multiply 31 ×12. We have to follow the vertical and crosswise sutra. Our approach would be:-
Step 1: Multiplying vertically the units place.
Step 2: Multiplying in a cross pattern and adding the results. For example, 3 × 2 = 6 and 1 × 1 = 1 and 6 + 1 = 7.
Step 3: Multiplying the tens digit vertically.
Similarly, if we have to find 12 × 34, our approach will be as shown below:
Firstly, multiply 2 × 4 = 8
Then, (3 × 2) + (4 × 1) = 10. The zero remains and 1 is carried to the left.
Finally, (3 × 1) = 3. Add to it the carried number so that it becomes, (3 + 1) = 4.
Our final answer would be 408.
Vedic Maths just showcases a process to do things faster. It does not teach a child the underlying philosophy or the background of the problem set given. Calculating faster is of no use if we fail to understand the meaning or the learning behind the problem set.
These tricks can do wonders only if used properly after imbibing a proper learning experience. Practice makes a man perfect but Learning makes a man capable. Therefore, make Vedic Maths a habit only after understanding its nuances.
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