Introduction to Vedic mathematics: what it is and where it came from, the sixteen sutras in plain English, the four techniques worth learning first with worked examples, what Vedic maths is good for (speed, confidence, mental arithmetic) and what it is not (a replacement for school maths), the right age, and how to start

Vedic mathematics has a devoted following, a sceptical one, and a lot of confusion in between, mostly about what it is. This page is an introduction for a student or parent who has heard of it and wants to know what it actually contains, what it is good for, what it is not, and how to start. Short version: sixteen memorable rules for fast calculation, four of which are worth any child's time once the times tables are secure, and none of which replaces school maths.

What it is, and where it came from

Vedic mathematics is the name of a book published in 1965, after the death of its author, Bharati Krishna Tirtha, a scholar and monk who was also a capable mathematician. In it he set out sixteen short rules, called sutras, with thirteen sub-rules, which he presented as being derived from the Vedas, the ancient Sanskrit texts. Historians of mathematics have looked and not found them there; the honest description is that the sutras are patterns of ordinary arithmetic and algebra that he noticed, organised and named in a memorable way. That does not make them less useful. It means the name is a brand, not a provenance.

What the system is good at is calculation: multiplying, squaring, some division, some algebra, by methods that are faster than the written school method for particular kinds of number. What it is not is a complete mathematics; there is no geometry, no proof, no statistics, and the techniques work beautifully for 97 × 96 and not at all for most of what a Grade 9 exam asks.

The sixteen sutras, in plain English

Of these, numbers 1, 2, 3 and 10 do nearly all the everyday work, and they are the four to learn first.

The four techniques to learn first

1. Multiplying by 11. Write the number, and between its digits put their sums. 52 × 11: 5, then 5 + 2 = 7, then 2, giving 572. 68 × 11: 6, 6 + 8 = 14, 8; carry the 1 into the 6, giving 748. Two minutes to learn, used for life.

2. Squaring a number ending in 5 (sutra 1). Take the digit before the 5, multiply it by one more than itself, and write 25 after the result. 35²: 3 × 4 = 12, so 1225. 85²: 8 × 9 = 72, so 7225. 115²: 11 × 12 = 132, so 13225.

3. All from nine and the last from ten (sutra 2): multiplying numbers near 100. Write each number's distance below 100. 97 × 96: 97 is 3 below, 96 is 4 below. Subtract crosswise: 97 − 4 = 93 (or 96 − 3, the same). Multiply the distances: 3 × 4 = 12. Answer: 9312. For 98 × 89: distances 2 and 11; 98 − 11 = 87; 2 × 11 = 22; answer 8722. The same works above 100 with the distances added: 103 × 104: 103 + 4 = 107; 3 × 4 = 12; answer 10712.

4. Vertically and crosswise (sutra 3): any two-digit multiplication. For 23 × 41: multiply the right digits vertically (3 × 1 = 3), then crosswise and add (2 × 1 + 3 × 4 = 2 + 12 = 14), then the left digits vertically (2 × 4 = 8). Write from the right with carries: 3; 14 gives 4 carry 1; 8 + 1 = 9. Answer: 943. It takes a week of practice to become automatic and then it is faster than the written method for every two-digit product.

Why each works is worth showing a child, because the "why" is what makes it mathematics rather than a trick: technique 3 is the algebra (100 − a)(100 − b) = 100(100 − a − b) + ab, and technique 4 is simply the expansion of (10a + b)(10c + d) done in a tidy order. A child who sees this learns some algebra by accident. More techniques, with the age for each and the practice that makes them stick, are in Vedic maths tricks for kids.

What Vedic maths is good for

• Speed in mental arithmetic, which is useful in itself and frees attention in exams for the actual question.
• Confidence. A child who can square 65 in their head stops believing they are bad at maths. This is the largest benefit and the reason to do it.
• Number sense. The techniques work because of patterns, and a child who learns why 97 × 96 works has learned something about place value and algebra.
• Competition maths. Olympiad and Kangaroo papers reward fast, flexible calculation.

What it is not

• Not a replacement for school maths. The techniques cover particular cases; the school method covers every case and is what exams mark. A child taught Vedic methods instead of school methods will be fast at the cases the tricks cover and lost at the rest.
• Not for a child whose basics are shaky. Every technique assumes the times tables to 12 and secure place value. Taught earlier, the tricks become a substitute for understanding.
• Not ancient, and not mystical. It is good arithmetic with a memorable name.
• Not a whole curriculum. No geometry, no data, no proof, little of the reasoning that later maths is made of.

Which of abacus, Vedic maths and ordinary school maths a particular child needs, and when, is in abacus, Vedic maths or school maths.

Vedic maths and the Trachtenberg system

The two are often confused. The Trachtenberg system, devised in the 1940s, gives one rule for multiplying any number by each digit from 2 to 12 and a general method for larger numbers; it is a routine, learned as a routine, and easy to drill. Vedic maths has more special-case techniques and more insight into why they work. For a child, the most useful things in either are the Vedic "vertically and crosswise" and near-base methods and the Trachtenberg rules for 11 and 12. The same multiplications done both ways, and which a 9-year-old should learn first, are in Trachtenberg method vs Vedic maths.

The right age, and how to start

About 9 or 10, once the times tables and place value are secure; earlier for a child who already has them, later for one who does not. Ten minutes a day for a fortnight:

• Days 1 to 3: multiplying by 11, until it is instant.
• Days 4 to 6: squares of numbers ending in 5.
• Days 7 to 10: numbers near 100, below and above.
• Days 11 to 14: vertically and crosswise for two-digit numbers, ten a day, checked against the written method.

Then one technique a week, always alongside school maths and never instead of it, and always with the question "why does this work?" asked at least once.

Where to get help

A 1-on-1 online maths class with a tutor who holds a master's in mathematics: the school's own curriculum first, and the four Vedic techniques taught alongside it once the basics are secure, with the "why" shown each time. For Grade 3 to 8, CBSE Class 3 to 8, KS2 and the competition track (Kangaroo, AMC 8). The free 30-minute first class is a real lesson on whatever the child is doing in school this week.

Questions parents ask

See how we teach this, 1-on-1 online →