division

mathematics

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June 25, 2026

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In mathematics, division is an arithmetic operation that is the inverse of multiplication. It is used to determine how many times one number (the divisor) is contained within another number (the dividend). The result of this operation is called the quotient. Division can be represented by the symbol ÷ or a slash /. For example, 10 divided by 2 equals 5 (10 ÷ 2 = 5). This operation is fundamental to many areas of mathematics and is used in calculations, problem-solving, and understanding relationships between quantities.12

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- $A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”$
  arithmetic
  Theory of divisors
  …drastically, however, as soon as division is introduced. Performing division (its symbol ÷, read “divided by”) leads to results, called quotients or fractions, which surprisingly include numbers of a new kind—namely, rationals—that are not integers. These, though arising from the combination of integers, patently constitute a distinct extension of the…
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  …drastically, however, as soon as division is introduced. Performing division (its symbol ÷, read “divided by”) leads to results, called quotients or fractions, which surprisingly include numbers of a new kind—namely, rationals—that are not integers. These, though arising from the combination of integers, patently constitute a distinct extension of the…
  Read More
- mathematics
  Numerical calculation
  …to perform than multiplication and division, which, as Napier observed, require a “tedious expenditure of time” and are subject to “slippery errors.” By the law of exponents, aⁿa^m = a^{n + m}; that is, in the multiplication of numbers, the exponents are related additively. By correlating the geometric sequence of…
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  …to perform than multiplication and division, which, as Napier observed, require a “tedious expenditure of time” and are subject to “slippery errors.” By the law of exponents, aⁿa^m = a^{n + m}; that is, in the multiplication of numbers, the exponents are related additively. By correlating the geometric sequence of…
  Read More

East Asian mathematics
Arithmetic of fractions
Division is a central operation in The Nine Chapters. Fractions are defined as a part of the result of a division, the remainder of the dividend being taken as the numerator and the divisor as the denominator. Thus, dividing 17 by 5, one obtains a…
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Division is a central operation in The Nine Chapters. Fractions are defined as a part of the result of a division, the remainder of the dividend being taken as the numerator and the divisor as the denominator. Thus, dividing 17 by 5, one obtains a…
Read More
mathematics
The numeral system and arithmetic operations
To divide 308 by 28, the Egyptians applied the same procedure in reverse. Using the same table as in the multiplication problem, one can see that 8 produces the largest multiple of 28 that is less then 308 (for the entry at 16 is already 448),…
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To divide 308 by 28, the Egyptians applied the same procedure in reverse. Using the same table as in the multiplication problem, one can see that 8 produces the largest multiple of 28 that is less then 308 (for the entry at 16 is already 448),…
Read More