Mental arithmetic methods

What each fast-calculation method is, how it works and how it helps

Mental arithmetic is a set of methods that teach a child to calculate quickly in their head, without a calculator. Here the soroban (abacus), Vedic mathematics and Trachtenberg techniques are explained in simple language. Each method has its benefit, a worked example and an exercise — start learning for free.

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Abacus (Soroban) — the foundation of mental arithmetic

The abacus, called soroban in Japanese, is a counting frame used for thousands of years and today it is the main tool of mental arithmetic. Each column stands for a place value (ones, tens, hundreds), and by sliding the beads you can represent any number.

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Friend of 10

The most important soroban rule! Know the friends of 10, and adding or subtracting any number becomes easy!

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Big Friends

Adding numbers that go past 10! On the soroban, this means "carrying" — sliding a bead to the left!

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Big Brother

The Big Brother method — adding through 5! Add 5, then subtract the extra. The secret of the 5-bead!

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Bridge to 10

The "through 10" technique! First reach 10, then add the rest. A clever method!

×11 Magic

A magical way to multiply any number by 11! Place digits side by side and add neighbors — done!

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×9 Technique

The secret method for multiplying by 9! Subtract 1 from the digit, then fill to 9. Fast and accurate!

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×12 Technique

The fast way to multiply by 12! Double the digit and add its neighbor. Simple!

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Vedic Math (100)

An ancient Indian method for multiplying numbers near 100! A 3000-year-old technique that still works!

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Vedic Math (1000)

Multiply large numbers near 1000 using the Vedic method! 3-digit numbers — no problem!

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Urdhva-Tiryagbhyam — vertical and crosswise multiplication

Urdhva-Tiryagbhyam is the universal multiplication method of Vedic mathematics: any two numbers can be multiplied quickly in a single line using vertical and crosswise products.

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Squaring a number — the fast way

Learn to square numbers quickly with special tricks — no paper or calculator, all in your head.

Division

Division exercises! Learn to split numbers into equal parts!

Frequently asked questions

It is a method that teaches a child to calculate quickly in their head — without paper or a calculator — by relying on a mental image of the soroban (abacus).
Soroban techniques (Friends of 10, Big Brother and more), Vedic mathematics (Nikhilam), Trachtenberg fast multiplication (×11, ×9, ×12), squaring and division.
Soroban basics are recommended from age 5-7, while fast multiplication and Vedic techniques usually start around age 9-10.
Yes, on MentalMath all mental-arithmetic lessons and exercises are free and require no registration.
The basics take a few weeks, and the mental calculation skill develops over a few months with regular practice of 10-15 minutes a day.