Showing every Abacus module we have built so far
Each one generates fresh questions, endlessly
Foundational Bead Moves & Friend Formulas
Usually Levels 0–27 modulesWithout Formula
Direct bead moves on upper and lower decks. No formula needed. Perfect for beginners learning place values.
Small Friend
Drill the 5s complement pairs (+1 = +5 -4, etc.) on every single sum to build sub-second mental reflex.
Big Friend
Drill the 10s complement pairs (+9 = +10 -1, etc.) across multiple columns and digit carries.
Combination
Both Big Friend and Small Friend rules acting together in one sum (e.g. +6 = +10 -5 +1).
Addition
Direct keyboard entry and rapid bead addition drills across 1-digit and 2-digit sets.
Add & Sub
Mixed rapid addition and subtraction rows with alternating friend formulas.
Multiplication
Visual abacus multiplication drills (2-digit × 1-digit) utilizing rod placement and running sums.
Multi-Digit Arithmetic & Decimals
Usually Levels 3–55 modulesLong Multiplication
Multi-digit multiplication (3-digit × 2-digit, 4-digit × 2-digit) with rod shifting logic.
Times Table Grid
Interactive speed-grid practice for tables up to 19×19 to reinforce mental multiplication.
Division Exercises
Abacus quotient and remainder placement exercises for 3-digit ÷ 1-digit and 4-digit ÷ 2-digit.
Decimal Add & Sub
Addition & subtraction with decimal reckoning dots. Aligns place values effortlessly.
Negative Numbers
Practice negative arithmetic and complement conversion when subtraction exceeds the total.
Percentages, Powers, Roots & Flash Audio
Usually Levels 6–1010 modulesPercentages
Calculate commercial percentages and discount splits using fast decimal-fraction conversions.
Decimal Multiply
Multiplication with decimal numbers, keeping track of decimal index places across rods.
Decimal Division
Division with decimals yielding accurate quotients and recurring precision controls.
Squares
Calculate perfect squares of numbers up to 3 digits on the abacus frame.
Square Roots
Extract exact square roots of 4-digit and 6-digit perfect numbers using group subtraction.
Cubes
Calculate perfect cubes of integers with rapid place-holding algorithm.
Cube Roots
Determine exact cube roots instantly by identifying ending patterns and root intervals.
LCM
Find the Lowest Common Multiple using simultaneous factor decomposition drills.
HCF
Find the Highest Common Factor using Euclidean division and factor comparisons.
Audio / VisualLevel 9–10
Voice & Flash MCQ Games
Listen to audio numbers dictated in real time, read flashed beads, and sum numbers under competition timers.
Vedic Multiplication & Base Methods
Instant Mental Sutras10 modulesNumbers Ending in 5
Multiply the leading part by its next consecutive number, then append 25 (e.g. 75² = 7×8 | 25 = 5625).
Nikhilam — Below 100
Cross-subtract the deficits for the left half, multiply the deficits for the right half (e.g. 96 × 94).
Nikhilam — Above 100
Cross-add the surpluses for the left half, multiply surpluses for the right half (e.g. 104 × 107 = 11128).
Urdhva-Tiryagbhyam
Criss-cross multiplication: multiply vertically at ends and crosswise in middle, carrying as you go.
Multiply by 11
Keep outer digits and insert the sum of each neighbouring pair between them with carry adjustments.
ComplementsMultiplicationMultiply by 9, 99, 999
Left half is the number minus 1; right half is its 9s/10s complement (Ekanyunena Purvena).
Multiply by 5, 25, 50
×5 = halve then ×10 · ×25 = ×100 then ÷4 · ×50 = ×100 then ÷2. Do it all mentally in seconds.
Special PairMultiplicationSame Tens, Units Sum to 10
Tens digit × (tens + 1), followed by the product of the units as two digits (e.g. 43 × 47 = 2021).
Special PairMultiplicationSame Units, Tens Sum to 10
(Tens product + units digit) for left half, followed by units squared as two digits (e.g. 64 × 44 = 2816).
Doubling and Halving
Halve one factor and double the other repeatedly until one factor becomes an easy single digit.
Vedic Squares & Cubes
Powers & Identities5 modulesSquares Near 50
Add the deviation to 25 for the left half; square the deviation for the right half (e.g. 53² = 2809).
Yavadunam (Any Base)
Apply the deviation a second time for left half; square it for right half (e.g. 108² = 116 | 64 = 11664).
Duplex (Dwandwa Yoga)
Build answers from duplexes: squares for single digits, twice the product for pairs. Works for any size.
Cubes Near a Base
Left: number + 2×deviation · Middle: 3 × deviation² · Right: deviation³. Fast mental 3-step cubing.
Difference of Squares
Calculate a² − b² = (a + b)(a − b) instantly for adjacent or symmetric numbers (e.g. 64 × 56 = 60² - 4²).
Vedic Division & Faster Operations
Usually Level 28 modulesNikhilam Division
For divisors just below a base (8, 9, 88, 97), bring down and add the complement repeatedly.
Paravartya Division
For divisors just above a base (11, 12, 103, 112), transpose by using the negative complement and add down.
Dhwajanka (Flag Division)
Flag all but first digit of divisor. Divide only by first digit, subtract cross products from remainders.
Divide by 5, 25, 125
÷5 = ×2 then ÷10 · ÷25 = ×4 then ÷100 · ÷125 = ×8 then ÷1000. Turn hard divisions into simple multiplications.
Nikhilam Subtraction
"All from 9 and last from 10" subtraction rule for subtracting any number from powers of 10.
Left-to-Right Addition
Add the highest place values first and adjust as you go to read out answers naturally left-to-right.
Vinculum (Bar) Numbers
Replace digits above 5 with negative bar digits to completely eliminate messy carryovers.
Complement Addition
Round addends to the nearest ten or hundred, add smoothly, then subtract back the excess difference.
Vedic Roots, Divisibility & Checks
Usually Levels 4 & 58 modulesCube Root of Perfect Cube
Group in threes. The last digit comes from the unique cube ending; the first digit comes from the left group.
Square Root of Perfect Square
Pair digits from right. The ending fixes the last digit candidates; the left pair fixes the first digit.
Duplex Square Root
Iterative duplex subtraction yields exact square roots of non-perfect numbers to any decimal precision.
Digital Root Check (Cast 9s)
Sum digits repeatedly (casting out 9s) to verify massive sums and products in under 3 seconds.
Osculation Divisibility
Use the Ekadhika multiplier to instantly test divisibility by prime numbers 7, 13, 19, 29 and beyond.
Recurring Decimals by Ekadhikena
For fractions like 1/19, use multiplier 2 to build the full 18-digit recurring cycle directly right to left.
Percentage Flip
x% of y equals y% of x. Transform hard calculations like 16% of 50 into simple 50% of 16 (= 8).
Crosswise Fraction Addition
Cross-multiply for the numerator, multiply denominators for the denominator (a/b + c/d = (ad+bc)/bd).