long division

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long division

A student solves a long division problem on a chalkboard.

Definition

Noun: 1. A method of dividing one number by another, typically a larger number by a smaller one, where the calculation is set out and solved step-by-step in a written format. This method breaks down the division process into a series of easier steps (divide, multiply, subtract, bring down), which are written down in a specific layout to show the detailed working.

Usage
  • Long division is used to solve division problems that are too complex for mental math or short division, especially when dividing by numbers with two or more digits.
  • The process is characterized by its structured, written format that clearly displays each step of the calculation, including the quotient, remainder, and intermediate calculations.
Examples
Advanced Usage
  • "To do/work out long division": This phrase describes the action of performing the calculation.
    • Can you do the long division for this problem and show your work?
  • The term can be used attributively (like an adjective) to describe related concepts.
    • She made a common long division error in the subtraction step.
Variants and Related Words
  • Division (n): The general arithmetic operation of splitting a number into equal parts.
  • Short division (n): A quicker, more compact method of division used when dividing by a small number, where the steps are performed mentally and not written out in full.
  • Algorithm (n): A step-by-step procedure for calculations. Long division is a specific arithmetic algorithm.
  • Quotient (n): The result obtained from division.
  • Remainder (n): The amount left over after division when one number does not divide the other exactly.
Synonyms
  • Step-by-step division: A descriptive synonym emphasizing the procedural nature.
  • Written division: A descriptive synonym emphasizing the format.
Related Phrases
  • "Show your work": A common instruction in mathematics that often requires the use of long division to demonstrate the calculation process.
  • "Divide and bring down": A phrase recalling the repeated steps within the long division algorithm.
long division

A student solves a long division problem on a chalkboard.

Noun
  1. the operation of division in which the sequence of steps are indicated in detail