Arithmetic & Fractions
Addition: Traditional Method
Column addition with carries
Multi-digit column addition shown as a pencil-and-paper grid with carry row.
Compute →Binary
decimal ↔ binary (base 2)
Convert between decimal and binary representations of integers.
Convert →Exponent
y = b^n
Power and root of any base to an integer or fractional exponent.
Calculate →Factorial
n! = n · (n−1) · … · 2 · 1
Factorial of a non-negative integer.
Calculate →Final Grade
F = (target − weighted) / weight_final
Grade needed on the final exam to reach a target course grade.
Calculate →Fraction: Addition
a/b + c/d = (ad + bc) / bd
Add fractions with like or unlike denominators — step-by-step.
Compute →Fraction: Division
(a/b) ÷ (c/d) = ad / bc
Divide fractions by multiplying by the reciprocal — step-by-step.
Compute →Fraction: Multiplication
(a/b) × (c/d) = ac / bd
Multiply two or more fractions and simplify the result.
Compute →Fraction: Simplify
a/b ÷ GCF = simplest form
Reduce a fraction to lowest terms using the greatest common factor.
Simplify →Fraction: Subtraction
a/b − c/d = (ad − bc) / bd
Subtract fractions with like or unlike denominators — step-by-step.
Compute →Fraction to Decimal
a / b → decimal
Convert a fraction to its decimal equivalent — terminating or repeating.
Convert →GCF (Greatest Common Factor)
GCF(a, b) via Euclidean algorithm
Greatest common factor of two or more integers via the Euclidean algorithm.
Calculate →Hex
decimal ↔ hex (base 16)
Convert between decimal and hexadecimal representations of integers.
Convert →LCM (Least Common Multiple)
LCM(a, b) = a · b / GCF(a, b)
Least common multiple of two or more integers.
Calculate →Division: Long Method
Long division grid
Traditional long-division algorithm rendered as a pencil-and-paper grid with quotient and remainder.
Compute →Modulo
a mod n = remainder
Remainder of integer division — the modulo operation.
Calculate →Multiplication: Grid Method
Box/area method
Multiplication by the grid (area) method — split factors by place value and sum.
Compute →Multiplication: Lattice Method
Lattice method
Multiplication by the lattice (gelosia) method — diagonal sum of partial products.
Compute →Number Sequence
aₙ = a₁ + (n−1)d (arithmetic)
Arithmetic and geometric sequence terms and sums.
Calculate →Percentage
% = part / whole · 100
Percent of a number, percent increase/decrease, and reverse percent.
Calculate →Prime Factorization
n = p₁^a · p₂^b · …
Prime factorization of a positive integer.
Factor →Roman Numerals Converter
I, V, X, L, C, D, M
Convert between Arabic numerals and Roman numerals.
Convert →Root
ⁿ√x = y
Square root, cube root, and nth root of any positive number.
Calculate →Subtraction: Traditional Method
Column subtraction with regroup
Multi-digit column subtraction shown as a pencil-and-paper grid with regroup row.
Compute →Arithmetic and fraction calculators with full step-by-step work shown — pencil-and-paper grid renders for long division, grid multiplication, and lattice multiplication so the algorithm itself is visible.
Includes the full fraction operations suite (add, subtract, multiply, divide, simplify, fraction-to-decimal), GCF, LCM, exponents, roots, factorials, prime factorization, modulo, percentages, binary and hex converters, and Roman numerals.
When to use these calculators
These tools are designed for students learning the algorithm — not just the answer. Each calc shows the full step-by-step work as a math grid (long division, multiplication-grid, lattice multiplication) or substituted arithmetic, with a Copy result button that captures the complete derivation.
Use long division and grid/lattice multiplication for elementary-school homework verification, fraction operations for middle school, and exponent/factorial/prime-factorization for algebra and number theory.
Frequently Asked Questions
- Do these calculators show the work?
- Yes — every arithmetic calculator displays the algorithm step-by-step. Long division renders the classic long-division grid (divisor, dividend, partial quotients, remainders). Grid and lattice multiplication render the box/array and lattice methods. Fraction operations show numerator and denominator at each step.
- What's the difference between grid multiplication and lattice multiplication?
- Grid (box) method splits each factor by place value into a rectangle, multiplies the cells, and sums. Lattice method writes products in a diagonal lattice and sums along diagonals. Both are visual alternatives to traditional column multiplication for two-and-three-digit numbers.
- Can I copy the work to paste into homework?
- Yes — every calculator's Copy result button copies the full step-by-step derivation as plain text (or ASCII grid for the visual-grid calcs like long division), so you can paste into a notebook or LMS submission.