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Home >> Educational Materials >> Mathematics## 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## Primary mathematics:Subtracting numbers

Subtracting numbers and adding numbers should be taught together, the process of teaching subtraction is the same as teaching addition. You should not teach children negative numbers at a young age as there is no way to physically show them a negative number. As with addition it is important for children to remember the simple combinations of single digit numbers. Moving to 2 digit addition (having learnt place values), start with simple problems: 45 -32 === first 5-2=3 second 40-30=10 45 -32 =## Derivative

In calculus, a branch of mathematics, the derivative is a measurement of how a function changes when the values of its inputs change. Loosely speaking, a derivative can be thought of as how much a quantity is changing at some given point. For example, the derivative of the position or distance of a car at some point in time is the instantaneous velocity, or instantaneous speed (respectively), at which that car is traveling (conversely the integral of the velocity is the car's position). A c## DECIMAL

The decimal numeral system (also called base ten or occasionally denary ) has ten as its base . It is the numerical base most widely used by modern civilizations. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] . Decimal notation often refers to the base-10 positional notation such as the Hindu-Arabic numeral system , however it can also be used more generally to refer to non-positional systems such as Roman or Chinese numerals which are still based on powers of ten. Decimal notation Decimal notation is the writ## Theory of computation

The theory of computation is the branch of computer science that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into two major branches: computability theory and complexity theory, but both branches deal with formal models of computation. In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several model## Laplacian vector field

In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v , then it is described by the following differential equations: Since the curl of v is zero, it follows that v can be expressed as the gradient of a scalar potential (see irrotational field) f : . Then, since the divergence of v is also zero, it follows from equation (1) that which is equivalent to . Therefore, the potential of a Laplacian field satisfies La## COMPOUND INTEREST

Compound interest Main article: Compound interest Compound interest is very similar to simple interest; however, with time, the difference becomes considerably larger. This difference is because unpaid interest is added to the balance due. Put another way, the borrower is charged interest on previous interest. Assuming that no part of the principal or subsequent interest has been paid, the debt is calculated by the following formulas: where I comp is the compound interest, B 0 the initial balan## DIVISION

In mathematics division is an operation which is the opposite of multiplication. If c times b equals a , written: where b is not zero, then a divided by b equals c , written: For instance, since . In the above expression, a is called the dividend, b the divisor and c the quotient. Division by zero ...is not defined. Notation Division is most often shown by placing the dividend over the divisor with a horizontal line, also called a vinculum, between them. For example, a divided by b is written T## Boolean algebra

Boolean algebra (or Boolean logic ) is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers , but with the numeric operations of multiplication xy , addition x + y , and negation - x replaced by the respective logical operations of conjunction x ? y , disjunction x ? y , and complement ¬ x . The Boolean operations are these and all other operations that can be built from these, such as x ?( y ? z ). These turn out to coincide with## COUNTING

Counting is the action of finding the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elemen## SIMPLE INTEREST

Simple interest Simple interest is calculated only on the principal amount, or on that portion of the principal amount which remains unpaid. The amount of simple interest is calculated according to the following formula: where r is the period interest rate (I/m), B 0 the initial balance and m the number of time periods elapsed. To calculate the period interest rate r , one divides the interest rate I by the number of periods m . For example, imagine that a credit card holder has an outstanding## Ellipse

In geometry, an ellipse (from Greek ἔ??e???? elleipsis , a "falling short") is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is perpendicular to the axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. Ellipses are closed curves and are the bounded case of the conic sections, the curves## 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## Decimal separator

The decimal separator or decimal point or decimal comma is a symbol used to mark the boundary between the integral and the fractional parts of a decimal number in a positional numeral system. Different symbols have been and are used for the decimal separator. The choice of symbol for the decimal separator affects the choice of symbol for the thousands separator used in digit grouping. Consequently the latter is treated in this article as well. The decimal separator is mathematically a radix poi## Calculus-Special Trigonometric Integrals

Special Trigonometric Integrals In the study of Fourier Series, you will find that every continuous function f on an interval [-L,L] can be expressed on that interval as an infinite series of sines and cosines. For example, if the interval is [- p , p ], f(x) = A 0 + ¥ å k = 1 [A k cos(kx) + B k sin(kx)] where the constants are given by integrals involving f. The theory of Fourier series relies on the fact that the functions 1, cos(x), sin(x), cos(2x), sin(2x), ¼ , cos(nx), sin(nx), ¼ form an o## Multiply - accumulate

In computing, especially digital signal processing, multiply-accumulate is a common operation that computes the product of two numbers and adds that product to an accumulator. When done with floating point numbers it might be performed with two roundings (typical in many DSPs) or with a single rounding. When performed with a single rounding, it is called a fused multiply-add (FMA) or fused multiply-accumulate (FMAC). Modern computers may contain a dedicated multiply-accumulate unit, or "MAC-uni## PARITY

In mathematics, the parity of an object states whether it is even or odd. This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2. (The old-fashioned term "evenly divisible" is now almost always shortened to " divisible ".) A formal definition of an odd number is that it is an integer of the form n = 2 k + 1, where k is an integer. An even number has the## Differentiation rules

This is a summary of differentiation rules , that is, rules for computing the derivative of a function in calculus. Elementary rules of differentiation Unless otherwise stated, all functions will be functions from R to R , although more generally, the formulae below make sense wherever they are well defined. Differentiation is linear For any functions f and g and any real numbers a and b . In other words, the derivative of the function h ( x ) = a f ( x ) + b g ( x ) with respect to x is In Lei## 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## Angle excess

Angle excess is the amount by which the sum of the angles of a polygon on a sphere exceeds the sum of the angles of a polygon with the same number of sides in a plane. For instance, a plane triangle has an angle sum of 180°; an octant is a spherical triangle with three right angles, so its angle sum is 270°, and its angle excess is 90°. The angle excess of any polygon on a sphere is proportional to the polygon's area, with the proportionality constant being the reciprocal of the square of t$.ajax({
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