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Home >> Educational Materials >> Mathematics## Divisibility rule

A divisibility rule is a shorthand way of discovering whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, and they are all different, we present rules only for decimal numbers.## Subtraction

Subtraction is the arithmetic operation for finding the difference between two numbers. The special names of the numbers in a subtraction expression are, minuend - subtrahend = difference. The expression 7 - 4 = 3 can be spoken as "seven minus four equals three," "seven take away four leaves three," or "four from seven leaves three." If the minuend is less than the subtrahend, the difference will be a negative number. For example, 17 - 25 = ( -8 ). We can say this as, "Seventeen minus twenty-fi## MULTIPLICATION

"Multiply" redirects here. For other uses, see Multiplication (disambiguation). 3 × 4 = 12, so twelve dots can be arranged in three rows of four (or four columns of three). Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division). Multiplication is defined for whole numbers in terms of repeated addition; for example, 4 multiplied by 3 (often said as "4 time## Calculus - Differentiating Special Functions

Differentiating Special Functions In this tutorial, we review the differentiation of trigonometric, logarithmic, and exponential functions. Trigonometric Functions The derivatives of the basic trigonometric functions are given here for reference. f(x) f ¢ (x) sin(x) cos(x) cos(x) -sin(x) tan(x) sec 2 (x) sec(x) sec(x)tan(x) csc(x) -csc(x)cot(x) cot(x) -csc 2 (x) The derivatives of sin(x) and cos(x) can be derived using the limit definition of the derivative . For sin(x), d dx [sin(x)] = lim D x## Equivalence relation

In mathematics, an equivalence relation is, loosely, a relation that specifies how to partition a set such that every element of the set is in exactly one of the blocks in the partition, and the union of all the blocks equals the original set. Two elements of the set are considered equivalent (with respect to the equivalence relation) if and only if they are elements of the same block. Notation Although various notations are used throughout the literature to denote that two elements a and b of## Decision theory

Decision theory in philosophy, mathematics and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality , and the resulting optimal decision. It is very closely related to the field of game theory. Normative and descriptive decision theory Most of decision theory is normative or prescriptive , i.e. , it is concerned with identifying the best decision to take, assuming an ideal decision maker who is fully informed, able to## Brahmagupta interpolation formula

In trigonometry, the Brahmagupta interpolation formula is a special case of the Newton-Stirling interpolation formula to the second-order, which Brahmagupta used in 665 to interpolate new values of the sine function from other values already tabulated. The formula gives an estimate for the value of a function f at a value a + xh of its argument (with h > 0 and -1 = x = 1) when its value is already known at a - h, a and a + h . The formula for the estimate is: where ? is the first-order forward-## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x , denoted by 1 / x or x -1 , is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of x is also called the reciprocal of x . The multiplicative inverse of a fraction a / b is b / a . For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth ( 1 / 5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The## Arithmetical operations

Addition (addends, sum). Subtraction (minuend, subtrahend, difference). Multiplication (multiplicand, multiplier, product, factors). Division (dividend, divisor, quotient, dividing integers, fraction, divisible numbers, remainder, division without remainder, division with remainder). Raising to a power (power, base of a power, index or exponent of a power, value of a power). Extraction of a root (root, radicand, index or degree of a root, value of a root, square root, cube root). Mutually inver## CONSERVATIVE VECTOR FIELD

In vector calculus a conservative vector field is a vector field which is the gradient of a scalar potential. There are two closely related concepts: path independence and irrotational vector fields. Every conservative vector field has zero curl (and is thus irrotational), and every conservative vector field has the path independence property. In fact, these three properties are equivalent in many 'real-world' applications. Definition A vector field is said to be conservative if there e## Venn diagram

A Venn diagram of sets A, B, and C Venn diagrams (or set diagrams ) are illustrations used in the branch of mathematics known as set theory. Invented in 1881 by John Venn, they show all of the possible mathematical or logical relationships between sets (groups of things). They normally consist of overlapping circles. For instance, in a two-set Venn diagram, one circle may represent the group of all wooden objects, while another circle may represent the set of all tables. The overlapping area (## Calculus-Parametric Equations

Parametric Equations Think of a curve being traced out over time, sometimes doubling back on itself or crossing itself. Such a curve cannot be described by a function y = f(x). Instead, we will describe our position along the curve at time t by x = x(t) y = y(t) . Then x and y are related to each other through their dependence on the parameter t. Example Suppose we trace out a curve according to x = t 2 - 4t y = 3t . t x y 0 0 0 1 -3 3 2 -4 6 3 -3 9 4 0 12 where t ³ 0. Drag the point along the## Topology

A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. Topology (Greek topos , "place," and logos , "study") is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with metric properties such as distances between points. Instead, topology involves the study of properties that describe how a space is as## MULTIPLICATION

Multiplication is an arithmetic operation for finding the product of two numbers. Multiplication is the third operation in maths after addition which is the first, subtraction which is the second and then there is multiplication. With natural numbers, it tells you the number of tiles in a rectangle where one of the two numbers equals the number of tiles on one side and the other number equals the number of tiles on the neighbouring side. With real numbers, it tells you the area of a rectangle w## MULTISET

In mathematics, a multiset (or bag ) is a generalization of a set. While each member of a set has only one membership, a member of a multiset can have more than one membership (meaning that there may be multiple instances of a member in a multiset, not that a single member instance may appear simultaneously in several multisets). The term "multiset" was coined by Nicolaas Govert de Bruijn in the 1970s. [ 1 ] The use of multisets in mathematics predates the name "multiset" by nearly 90 years. Ri## Calculus - Antiderivatives

Antiderivatives Let f(x) be continuous on [a,b]. If G(x) is continuous on [a,b] and G ¢ (x) = f(x) for all x Î (a,b), then G is called an antiderivative of f. We can construct antiderivatives by integrating. The function F(x) = ó õ x a f(t) dt is an antiderivative for f since it can be shown that F(x) constructed in this way is continuous on [a,b] and F ¢ (x) = f(x) for all x Î (a,b). Properties Let F(x) be any antiderivative for f(x). For any constant C, F(x)+C is an antiderivative for f(x). p## Paradox

A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth ( cf. kōan, Catuskoti ). Typically, the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The word paradox is often used interchangeably w## RATIONAL NUMBER

In mathematics, a rational number is any number that can be expressed as the quotient a / b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold , Unicode U+211a ℚ ), which stands for quotient. The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of## Arithmetic Series

Arithmetic Series Consider the sequence of numbers below and, without doing any calculations, guess what the average is: 0 1 2 3 4 5 6. If you guessed 3, you are absolutely right. To test this out, just add the numbers to get 21 and divide by the number of terms, which is 7. We could generalize this result to find the sum of consecutive numbers from 0 to n, which is an arithmetic series S n . See if you can write the formula for arithmetic series by writing a formula for the average and then mu## Additive inverse

In mathematics, the additive inverse , or opposite , of a number n is the number that, when added to n , yields zero. The additive inverse of F is denoted - F . For example, the additive inverse of 7 is -7, because 7 + (-7) = 0, and the additive inverse of -0.3 is 0.3, because -0.3 + 0.3 = 0. In other words, the additive inverse of a number is the number's negative. For example, the additive inverse of 8 is -8, the additive inverse of 10002 is -10002 and the additive inverse of x² is -x². T$.ajax({
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