Vedic Maths Techniques for Faster Multiplication and Division
Mental math seems to be a hurdle for many students, teachers and competitive exam takers. School-learned traditional algorithms (the long multiplication and long division procedures) are universal, reliable, and easy to follow but can be time-consuming and prone to human error when time is limited.
There is an alternative toolkit – Vedic Maths techniques for faster multiplication and division. This system was developed from the old Indian mathematical literature, codified by Swami Bharati Krishna Tirtha between 1911 and 1918, and is based on pattern recognition, base numbers (or numbers within a base number), and mental flexibility.
Vedic Maths calculation methods can help you manipulate numbers, and work in harmony with how your brain thinks.Vedic Maths calculation methods enable you to manage numbers in a way that is visual and linear, working in harmony with how your brain thinks. This easy to use guide teaches you the essential Vedic Maths multiplication tricks and Vedic Maths division tricks with illustrative examples, structural breakdowns and tips for when to use them.
Why Vedic Maths in Multiplication and Division?
Here are some of the practical advantages of vedic maths techniques of calculation:
- Many of the techniques involve doing calculations in the head, so mental calculating becomes easier.
- Less steps in calculations for some number combinations, decreasing the probability of small arithmetic mistakes.
- As more and more problems are encountered, the pattern recognition ability gets better, and you begin to see shortcuts in problems you weren't familiar with.
- Repeatedly using the same logic in different contexts helps develop calculation fluency.
- It is good to have more than one approach to a problem in the timed practice and timed exams.
However, these techniques cannot be used in place of the understanding of standard mathematics. The Vedic Maths tricks are based on the concepts of place value, distributive property, etc. and are not just some shortcuts, but are being reinforced on the basis of understanding these concepts. But if a student just memorises steps without understanding their purpose, he or she will have a problem when the question is not the same kind as before.
How Vedic Maths Makes Multiplication Easier
Most Vedic Maths multiplication Tricks are based on few ideas:
- Recognise sequences of numbers or number pairs that have a predictable pattern.
- Using base 10, 100, or 1,000, because numbers near these are convenient to use.
- Decomposing numbers (e.g., 47 can be thought of as 50 − 3).
- Complementary numbers (numbers that make 10 when added to a number, and that make 100 when added to 100).
- Selecting the appropriate method for the numbers being used; not all of the tricks are appropriate for all of the numbers.
This is more important than one might think. One of the keys to being faster with Vedic Maths is being able to quickly decide which of the Vedic Maths techniques is applicable, and which is not. If you try to use the "near-base" technique on numbers that aren't close to a convenient base, then you will be slower, not quicker.
Vedic Maths Multiplication Techniques
1. Multiplying Numbers Near 10, 100, or 1,000 (Nikhilam Sutra)
This fast multiplication technique is ideal when both numbers are close to a common base like 100 or 1,000.
- Both numbers are near the base 100.
- Find how far each number is from 100 (its deficiency): 97 → −3, 96 → −4
- Cross-subtract: 97 − 4 = 93 (or 96 − 3 = 93 — either works)
- Multiply the deficiencies: (−3) × (−4) = 12
- Combine: 93 followed by 12 → 9312
For comparison, the conventional method would have you multiply 97 by 6, then by 90, and add the results — more steps, more room for a slip. The base method turns this into two small multiplications and an addition.
Multiplying Numbers Using Complements
A complement is simply the gap between a number and a round base. This idea underlies several Vedic Maths multiplication tricks, especially when one number is slightly below a base.
- 998 is close to 1,000, with a deficiency of 2.
- Multiply 88 by the deficiency: 88 × 2 = 176
- Subtract this from 88 × 1,000 conceptually: 88,000 − 176 = 87,824
This technique is most useful when one of the numbers is very close to a clean base like 100, 1,000, or 10,000 — the closer the number, the smaller the adjustment, and the faster the calculation.
Multiplying Two-Digit Numbers Using Vedic Maths
For general two-digit multiplication where numbers aren't conveniently close to a base, a cross-multiplication pattern (sometimes called "vertically and crosswise") works well.
- Multiply the units digits: 3 × 2 = 6 (write down 6, carry nothing)
- Cross-multiply and add: (2 × 2) + (3 × 4) = 4 + 12 = 16 (write down 6, carry 1)
- Multiply the tens digits and add the carry: (2 × 4) + 1 = 9
- Reading the results together: 9, 6, 6 → 966
Common beginner mistakes with this technique include forgetting to carry over digits between steps, mixing up which digits to cross-multiply, and rushing the addition in the middle step. Slowing down for the first few practice attempts pays off later.
Squaring Numbers Ending in 5
This is one of the simplest Vedic Maths tricks to learn and a good confidence-builder for beginners.
- Take the digit(s) before the 5 — here, that's 6.
- Multiply it by the next whole number: 6 × 7 = 42
- Append 25 to the result: 4225
This works because any number ending in 5 can be written as (10n + 5), and squaring that expression algebraically simplifies to n(n+1) followed by 25 — which is exactly the shortcut above.
Learn Vedic Maths Division Techniques
Vedic maths division techniques are more dependent on the divisor than the multiplication techniques. The strategies that work well for dividing by 9 may not be as effective for dividing by 37. Part of the skill is to choose the right approach.
Using Number Complements to divide.
When dividing by 9 (and other numbers close to a base) there is a shortcut involving carry over, which involves adding digits to each other in steps. The main principle is that, because 9 is one less than 10, it is possible to keep track of remainders and quotient digits by running additions, which is a simpler method to long division's repeated subtraction, but more difficult requires practice to internalise it.
If the sum of the digits is 10 or more, or less than 9, then you know that the number is not exactly divisible by 9, so a good rule of thumb to get a quick estimate of divisibility is to add the digits of each number, as in 1234, (1+2+3+4 = 10, then 1+0 = 1), which tells you that 1234 is not exactly divisible by 9 and is a useful shortcut before doing a full division.
Division by Numbers Close to 10, 100, or 1,000
If the divisor is slightly larger or less than a clean base, the difference may be accounted for to ease the process.
- 98 is close to 100, with a deficiency of 2.
- Begin to divide, using the "deficiency" (2) at each stage.
- The quotient is computed one digit at a time with each digit added a small correction for the deficiency, in much the same way as the near-base multiplication method is computed.
The mechanics are more complex and would benefit from being explained in more than one single example, and that is why divisor shortcuts are typically taught in a series of examples instead of as single tricks; they are more amenable to structured practice than most multiplication methods are.
Using Vedic Maths patterns for dividing numbers.
A simpler and more generally useful technique for dividing mentally is to divide the divisor into simpler factors.
- Calculate 12 in terms of 4 x 3, rather than dividing by 4.
- Divide 144 by 4 first: 144 ÷ 4 = 36
- Then divide the result by 3: 36 ÷ 3 = 12
This pattern is particularly useful if the divisor factors neatly to form two easier divisions.
What Vedic Maths Tricks are used in Multiplication and Division?
Vedic Maths is based on 16 Sutras, which are short aphorism statements that describe each of the calculation methods. While some Sutras relate to multiplication and division, others relate to algebra, operations of calculus or some types of numbers.
Here two Sutras are of particular importance. The near base multiplication technique illustrated above is based on the concept of quickly finding complements to a base, which is the basis of the idea "all from 9 and the last from 10. The two-digit cross-multiplication method takes its cue from the principle of "vertically and crosswise" which is one of the most commonly used Sutras in both multiplication and division problems.
If you don't learn all 16 Sutras and practice all the techniques, but rather learn a Sutra with a certain type of problem it solves, it is normally easier. For a detailed explanation of all 16 Sutras and which ones are used in which problems, refer to our detailed explanation: What are the 16 Sutras of Vedic Maths? A Beginner's Guide.
Vedic Maths vs Traditional Multiplication and Division
To make sense of the two perspectives, it is best to consider them together and not assume one is necessarily superior:
Vedic Maths Approach
- Pattern-based techniques
- Can minimize the number of steps required in a calculation
- A useful tool for mental arithmetic.
- Needs practice to identify which to use
Traditional Approach
- Uses standard algorithms
- Applies a uniform procedure to most calculations
- Develops a solid basis for written calculation
- Familiar to most learners from school
The sincere fact is, Vedic Maths is better used as an alternate method of calculation and not as a replacement for the core maths. The traditional methods are reliable in all situations; Vedic Maths methods are quicker in certain situations where one can identify the applicable method.
How to Practise Vedic Maths Multiplication and Division
- Use simple numbers, such as two-digit numbers before three or four-digit numbers.
- Don't learn multiple tricks at once; learn one at a time.
- Do the work without a calculator so that you develop number sense, rather than step recall.
- Use another method to check your answers at least until you have learned a new method.
- Once a technique is comfortable with easy numbers, start to make it harder and harder.
- Do not rush, a quick incorrect answer is not going to help.
- Only add timed practice when you're getting the correct answer without the timing.
Common Mistakes that Beginner Make
- Using a method which is not suitable for the numbers in front of them.
- Attempts to go quickly without the steps being internalised (causing careless mistakes).
- Learning a series of steps to perform without grasping the rationale behind them.
- Not paying attention to place value, particularly when combining digits at the end of a calculation.
- Mistakes go undetected as it is not a habit to check answers.
- Using a near-base trick for numbers that are not close to any base.
Is Vedic Maths a way to smartly enhance calculation speed?
Yes — many children do make improvements in their calculation over time with continued practice. However, the increase is not automatic and even. The faster the speed will be the better you can match a technique to a problem and how many repetitions you have done with that technique. Two pupils who practise the same amount can get very different results depending on their experience with basic arithmetical skills and how systematic their practice is.
Speed should never be sacrificed for accuracy. The learner who can multiply rapidly but with a mistake is not learning anything useful.
Know the Vedic Maths Techniques Systematically
The examples, provided in this guide, are just a starting point and Vedic Maths is a structured learning that rewards it more than random exposure to tricks. It is easier to get the guidance in learning which Sutra is for which technique, when and how to apply it, or to build up from the simplest to the most complex examples than to deduce methods from assorted sources.
For a proper development of these skills, from the basic level to the higher level, with systematic practice at each level, Vedic Maths course offered by IIVA is the right choice for you.
Learn these techniques systematically with Vedic maths course at Explore IIVA
FAQ
What is the fastest Vedic Maths multiplication trick?
The near base method of multiplication is generally faster when the number is close to a base such as 100 or 1,000 because it involves making small adjustments instead of multiplying the numbers.
How can I multiply numbers quickly using Vedic Maths?
Use the matching technique instead of a general technique: know whether the numbers are close to a common base, have simple factors or follow a cross-multiplication pattern with a 2-digit number.
What is the Vedic Maths trick for division?
There is no single universal method, it varies by the divisor. There are shortcuts for dividing by numbers that are close to a base, and for numbers that factor nicely.
Can beginners learn Vedic Maths multiplication?
Yes. Methods such as squaring numbers that end in 5 and multiplying numbers close to a base can be learned by the student with a bit of practice.
Which Sutra is used for multiplication?
There are several Sutras depending on the numbers being used, but the most common are 'vertically and crosswise' and the complement-based 'near-base' methods used in multiplication.
Can Vedic Maths improve mental calculation speed?
Yes, with practice — but it will depend on the learner and their ability to match techniques to problems.
Is Vedic Maths faster than traditional multiplication?
Not always. It may be quicker for some number combinations, but the traditional approach works for any kind of problems.
How can I practise Vedic Maths at home?
Use one number, one technique and one technique - and check the others against the standard technique - and build time pressure when you are accurate and consistent.
