Division 2 Movie
Destiny Olatunji
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. For example, if 21 apples are divided between 4 people, everyone receives 5 apples again, and 1 apple remains.
This is the usual way of specifying division in most computer programming languages, since it can easily be typed as a simple sequence of ASCII characters. (It is also the only notation used for quotient objects in abstract algebra.) Some mathematical software, such as MATLAB and GNU Octave, allows the operands to be written in the reverse order by using the backslash as the division operator:
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 division sign (, also known as obelus though the term has additional meanings), common in arithmetic, in this manner:
More systematically and more efficiently, two integers can be divided with pencil and paper with the method of short division, if the divisor is small, or long division, if the divisor is larger. If the dividend has a fractional part (expressed as a decimal fraction), one can continue the procedure past the ones place as far as desired. If the divisor has a fractional part, one can restate the problem by moving the decimal to the right in both numbers until the divisor has no fraction, which can make the problem easier to solve (e.g., 10/2.5 = 100/25 = 4).
Division can be calculated 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.
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 associated with the faster methods in computer arithmetic.
Integers are not closed under division. 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 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.
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.
"Division" in the sense of "cancellation" can be done in any magma by an element with the cancellation property. Examples include matrix algebras, quaternion algebras, and quasigroups. In an integral domain, where not every element need have an inverse, division by a cancellative element a can still be performed on elements of the form ab or ca by left or right cancellation, respectively. If a ring is finite and every nonzero element is cancellative, then by an application of the pigeonhole principle, every nonzero element of the ring is invertible, and division by any nonzero element is possible. To learn about when algebras (in the technical sense) have a division operation, refer to the page on division algebras. In particular Bott periodicity can be used to show that any real normed division algebra must be isomorphic to either the real numbers R, the complex numbers C, the quaternions H, or the octonions O.
Division of any number by zero in most mathematical systems is undefined, because zero multiplied by any finite number always results in a product of zero.[15] Entry of such an expression into most calculators produces an error message. However, in certain higher level mathematics division by zero is possible by the zero ring and algebras such as wheels.[16] In these algebras, the meaning of division is different from traditional definitions.
The North Carolina Division of Water Infrastructure provides financial assistance for projects that improve water quality. Programs within the division fund many types of projects, including sewer collection and treatment systems, drinking water distribution systems, water treatment plants, stormwater management systems, and stream restoration.
The Fall 2024 Funding Round begins on July 30. Applications are submitted online and are due by 5 p.m. on Monday, Sept. 30. Application training runs July 30 through Aug. 9. A virtual option is offered during the Raleigh training session on Aug. 9. That session will be recorded and posted on this website.
The Division of Social Services (DSS) provides guidance and technical assistance to agencies that provide direct services that address issues of poverty, family violence and exploitation. DSS promotes self-reliance and self-sufficiency and works to prevent abuse, neglect, dependency and exploitation of vulnerable individuals, children and their families. DSS works to accomplish this through the following Family Centered Principles of Partnership:
In North Carolina, the single administrative agency is the NC Department of Health and Human Services (DHHS). This umbrella agency includes separate divisions. Some of the other DHHS divisions with the greatest impact on local offices include:
Division of Health Benefits (NC Medicaid)
Division of Child Development and Early Education
Division of Health Services Regulation
Division of Aging
Child Protective Services: If you suspect a child is being abused or neglected, please contact your local county Department of Social Services.
Leadership: Assistant Secretary for County Operations: Susan Osborne
The Department of Health and Human Services has released the Specialized Foster Care Plan Policy Paper which describes key design features related to foster care eligibility and enrollment, benefits, care management and quality, among other areas.
4a15465005