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For example, a divided by b is written. A way to express division all on one line is to write the dividend or numerator , then a slash , then the divisor or denominator , like this:.
This is the usual way to specify division in most computer programming languages since it can easily be typed as a simple sequence of ASCII characters.
A typographical variation halfway between these two forms uses a solidus fraction slash but elevates the dividend, and lowers the divisor:.
Any of these forms can be used to display a fraction. A fraction is a division expression where both dividend and divisor are integers typically called the numerator and denominator , and there is no implication that the division must be evaluated further.
A second way to show division is to use the obelus or division sign , common in arithmetic, in this manner:. This form is infrequent except in elementary arithmetic.
The obelus is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator.
In some non- English -speaking countries colon is used to denote division. However, in English usage the colon is restricted to expressing the related concept of ratios.
The history of this notation is not entirely clear because it evolved over time. Division is often introduced through the notion of "sharing out" a set of objects, for example a pile of lollies, into a number of equal portions.
Distributing the objects several at a time in each round of sharing to each portion leads to the idea of " chunking ", i.
More systematic and more efficient but also more formalised and more rule-based, and more removed from an overall holistic picture of what division is achieving , a person who knows the multiplication tables can divide two integers using pencil and paper using the method of short division , if the divisor is simple.
Long division is used for larger integer divisors. If the dividend has a fractional part expressed as a decimal fraction , one can continue the algorithm past the ones place as far as desired.
If the divisor has a fractional part, we can restate the problem by moving the decimal to the right in both numbers until the divisor has no fraction.
A person can calculate division with an abacus by repeatedly placing the dividend on the abacus, and then subtracting the divisor the offset of each digit in the result, counting the number of divisions possible at each offset.
A person can calculate division with a slide rule by aligning the divisor on the C scale with the dividend on the D scale. The quotient can be found on the D scale where it is aligned with the left index on the C scale.
The user is responsible, however, for mentally keeping track of the decimal point. Modern computers compute division by methods that are faster than long division.
For division with remainder , see Division algorithm. In modular arithmetic modulo a prime number and for real numbers , nonzero numbers have a multiplicative inverse.
In these cases, a division by x may be computed as the product by the multiplicative inverse of x. This approach is often the most efficient one.
The Euclidean division is the mathematical formulation of the outcome of the usual process of division of integers. Division of integers is not closed.
Apart from division by zero being undefined, the quotient is not an integer unless the dividend is an integer multiple of the divisor.
For example, 26 cannot be divided by 11 to give an integer. Such a case uses one of five approaches:. Dividing integers in a computer program requires special care.
Some programming languages , such as C , treat integer division as in case 5 above, so the answer is an integer. Other languages, such as MATLAB and every computer algebra system return a rational number as the answer, as in case 3 above.
These languages also provide functions to get the results of the other cases, either directly or from the result of case 3. Definitions vary regarding integer division when the dividend or the divisor is negative: Divisibility rules can sometimes be used to quickly determine whether one integer divides exactly into another.
The result of dividing two rational numbers is another rational number when the divisor is not 0. All four quantities are integers, and only p may be 0.
This definition ensures that division is the inverse operation of multiplication. Division of two real numbers results in another real number when the divisor is not 0.
Dividing two complex numbers results in another complex number when the divisor is not 0, which is found using the conjugate of the denominator:.
All four quantities p , q , r , s are real numbers, and r and s may not both be 0. Again all four quantities p , q , r , s are real numbers, and r may not be 0.
One can define the division operation for polynomials in one variable over a field. Then, as in the case of integers, one has a remainder.
See Euclidean division of polynomials , and, for hand-written computation, polynomial long division or synthetic division. Mathematics The operation of determining how many times one quantity is contained in another; the inverse of multiplication.
The proportional distribution of a quantity or entity: Something, such as a boundary or partition, that serves to divide or keep separate. One of the parts, sections, or groups into which something is divided.
An area of government or corporate activity organized as an administrative or functional unit. A territorial section marked off for political or governmental purposes.
An administrative and tactical military unit that is smaller than a corps but is self-contained and equipped for prolonged combat activity.
A group of several ships of similar type forming a tactical unit under a single command in the US Navy. A former unit of the US Air Force that was larger than a wing and smaller than an air force.
Botany The taxonomic category ranking just below kingdom, consisting of one or more related classes, and corresponding approximately to a phylum in zoological classification.
The physical separation and regrouping of members of a parliament according to their stand on an issue put to vote. A type of propagation characteristic of plants that spread by means of newly formed parts such as bulbs, suckers, or rhizomes.
Parliamentary Procedure a formal vote in Parliament or a similar legislative body. General Sporting Terms in sports a section, category, or class organized according to age, weight, skill, etc.
Mathematics a mathematical operation, the inverse of multiplication, in which the quotient of two numbers or quantities is calculated.
Biology biology in traditional classification systems a major category of the plant kingdom that contains one or more related classes. Horticulture horticulture any type of propagation in plants in which a new plant grows from a separated part of the original.
Logic 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.
Classical Music esp in 17th-century English music the art of breaking up a melody into quick phrases, esp over a ground bass. The act, process, or operation of dividing one number or quantity by another; the process of finding out how many times one number or quantity is contained in the other.
A group of plants ranking above a class and below a kingdom, corresponding to a phylum in other kingdoms. See Table at taxonomy. A number of naval vessels of similar type grouped together for operational and administrative command, or a tactical unit of a naval aircraft squadron, consisting of two or more sections.
An air division is an air combat organization normally consisting of two or more wings with appropriate service units.
The combat wings of an air division will normally contain similar type units. An organizational part of a headquarters that handles military matters of a particular nature, such as personnel, intelligence, plans, and training, or supply and evacuation.
A method of propagating a herbaceous plant vegetatively by lifting the crown and cutting it into small sections each with roots and shoots. A useful technique for reinvigorating an old herbaceous plant using the same method.
Switch to new thesaurus. Special Forces , U. Cyanophyta , division Cyanophyta - prokaryotic organisms sometimes considered a class or phylum or subkingdom; coextensive with the Cyanophyceae: Chrysophyta , division Chrysophyta - mostly freshwater eukaryotic algae having the chlorophyll masked by brown or yellow pigment; yellow-green and golden-brown algae and diatoms: Xanthophyceae, Chrysophyceae, Bacillariophyceae; some classification systems superseded or subsumed by Heterokontophyta.
Chlorophyta , division Chlorophyta - large division of chiefly freshwater eukaryotic algae that possess chlorophyll a and b, store food as starch, and cellulose cell walls; classes Chlorophyceae, Ulvophyceae, and Charophyceae; obviously ancestral to land plants.
Cynodontia , division Cynodontia - a division of the order Therapsida from the Triassic period comprising small carnivorous tetrapod reptiles often with mammal-like teeth.
Dicynodontia , division Dicynodontia - a division of Therapsida.