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About

Manual arithmetic requires specific spatial organization. Errors often stem from misalignment of columns or incorrect carry-over notation rather than simple calculation mistakes. This tool generates the exact vertical layout used in standard educational curricula for long division and long multiplication.

It breaks down the process digit-by-digit. For division, it visualizes the quotient, the product of the divisor and the current digit, the subtraction step, and the carry-down process. For multiplication, it displays partial products and the final summation. This is useful for verifying homework or generating examples for worksheets.

math education long division multiplication step-by-step

Formulas

The algorithm relies on positional notation. For a number N represented by digits d:

N = ni=0 di × 10i

In long division of A ÷ B, we find integers Q (Quotient) and R (Remainder) such that:

A = B × Q + R

Reference Data

OperationTermsSymbolDescription
AdditionAddend + Addend+Summation of values.
SubtractionMinuend − SubtrahendDifference between values.
MultiplicationMultiplicand × Multiplier×Scaling one number by another.
DivisionDividend ÷ Divisor÷Splitting into equal parts.
RemainderrmodLeftover value in integer division.

Frequently Asked Questions

Each partial product corresponds to a specific place value. Multiplying by the tens digit effectively multiplies by 10, requiring a shift or a placeholder zero in the ones column to maintain correct magnitude.
Currently, the visualizer focuses on integer operations to maintain a clean grid structure used in primary education. Decimals complicate the visual alignment logic significantly.
Division by zero is undefined. The tool will return an error state as no quotient exists.