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division, in mathematics

division, fundamental operation in arithmetic; the inverse of multiplication. Division may be indicated by the symbol ÷, as in 15 ÷ 3, or simply by a fraction, 15/3. The number that is being divided, e.g. 15, is called the dividend and the number dividing into it, e.g. 3, the divisor. The result of division is called the quotient. If the dividend is an exact (integral) multiple of the divisor, then the division will be exact, the quotient being the factor by which the divisor must be multiplied to yield the dividend (in the above example the quotient 5 multiplied by the divisor 3 equals the dividend 15). If the dividend is not an exact multiple of the divisor there will be a remainder expressed as a fraction with the divisor as the denominator; e.g., 16-3 = 5 1-3, where 1-3 is the remainder. A division in which the divisor b is larger than the dividend a is simply indicated by the fraction a/b, with no actual operation being carried out. In terms of multiplication either of the symbols 1/b or b⁻¹ is called the multiplicative inverse of b with the property that the product of a number and its inverse equals 1, or b · b⁻¹ =1. The division of a by b is equivalent to the multiplication of a by the multiplicative inverse of b, i.e., a ÷ b = a · (1/b) = a · b⁻¹; for example, when a = 25 and b = 5, then 1/b = 1/5 and 25 ÷ 5 = 25 · (1/5) = 5.

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division, in taxonomy

division, in taxonomy: see classification.

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division

1. a part of a government, business, country, etc., that has been made into a unit for administrative, political, or other reasons

2. a formal vote in Parliament or a similar legislative body

3. a mathematical operation, the inverse of multiplication, in which the quotient of two numbers or quantities is calculated. Usually written: a ? b, a/b

4. Biology (in traditional classification systems) a major category of the plant kingdom that contains one or more related classes

5. Horticulture any type of propagation in plants in which a new plant grows from a separated part of the original

6. Logic the fallacy of inferring that the properties of the whole are also true of the parts, as Britain is in debt, so John Smith is in debt

7. (esp in 17th-century English music) the art of breaking up a melody into quick phrases, esp over a ground bass