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.