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.

Noun

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