Archive for the ‘Arithmetic’ Category
Thursday, November 12th, 2009
How to Find the Next Term in an Arithmetic Sequence
Description
A detailed tutorial on finding the next term of an arithmetic sequence. Step by step tutorial including several examples of arithmetic sequences for reference.
Overview
Arithmetic sequences are sequences of numbers that are written in a particular pattern. Most problems including an arithmetic sequence don’t include all the terms in the sequence, and you have to find the next one in the sequence. In order to do this, you must find the pattern. The pattern can be anything – the same number could be added, subtracted, mutliplied, or divided from each previous number of the sequence. The previous number could be added to the number after it to come up with the next number. Each number in the sequence could be divisible by the same number. All numbers could be perfect or prime. There are an endless number of patterns, all you have to do is look and then follow that pattern to come up with the next term or terms in the sequence.
Tags: add, arithmetic, divide, mutliply, next, number, pattern, perfect, previous, prime, sequence, subtract, term
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Thursday, November 12th, 2009
Zero Pairs Explained
Description
A detailed tutorial on zero pairs. Step by step tutorial including several examples of how to solve equations using zero pairs for reference.
Overview
Zero pairs are a method of adding and subtracting integers, and simplifying expressions with addition and subtraction in them. A zero pair is any pair of numbers that when added or subtracted, equal zero. Based on this definition, the only numbers that can form a zero pair, besides two zeros, are a negative number n and a positive number n. When in equations, zero pairs can be cancelled out, therefore simplifying the expression. This is very useful when more complicated equations are given.
Tags: adding, arithmetic, cancelled, difference, equation, expression, integer, negative, number, pair, positive, simplification, simply, subtracting, sum, zero
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Thursday, November 12th, 2009
Definition of Skew Lines
Description
A detailed tutorial on skew lines. Step by step tutorial including several examples and a visual example of skew lines and what they are for reference.
Overview
Skew lines are two lines that do not intersect and are not parallel. In general, these lines have nothing in common. Think of dropping two sticks on the ground from high up. Provided they do not intersect each other (cross or touch each other in any way), those sticks are now a perfect example of skew lines. Typically, these lines are also not found in the same plane. Skew lines can only exist in three or more dimensions.
Tags: arithmetic, common, cross, different, dimension, Geometry, intersect, line, lines, nothing, parallel, plane, skew, three, touch
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Thursday, November 12th, 2009
An Overview of Magic Squares
Description
A detailed tutorial of magic squares. Step by step tutorial including several examples of magic squares for reference.
Overview
Magic squares are a fun mathematical trick and puzzle. It is an arrangement such as 3×3, 4×4, or any other nxn pattern of numbers. Typically a magic square will contain any of the integers between 1 and n^2. Magic squares are set up so that all rows and columns, and both diagonals, add up to the same constant. It does not matter what constant it is, as long as all rows, columns, and diagonals add up to the same one.
Tags: arithmetic, column, constant, diagonal, integer, magic, n!, normal, number, perfect, real, row, square, sum, word
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Thursday, November 12th, 2009
How to Estimate Values
Description
A detailed tutorial on how to estimate values. Step by step tutorial including several examples of estimating values for reference. Knowledge of estimation is required throughout your mathematical education.
Overview
Estimation is when someone makes an educated guess about something. In mathematics, that something is often the true value of a number. It is usually best to find the exact answer, instead of using estimation, but if there is no way to find an exact answer, then estimation can come in very useful. There are several techniques that make estimation a little easier; most of them are simply common knowledge that you just need to look for. Many people accurately give the nickname “guesstimation” to estimation.
Tags: answer, arithmetic, common, educated, estimate, estimation, exact, guess, guesstimate, guesstimation, knowledge, number, techniques, true, value
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Thursday, November 12th, 2009
How to Identify Perfect Numbers
Description
A detailed tutorial on how to identify perfect numbers. Step by step tutorial including several examples of perfect numbers for reference.
Overview
A perfect number is a number that is the sum of all it’s divisors (excluding the number itself, which is also a proper divisor). The way that you identify a perfect number is to find all of its divisors. Once you have them all, add them together. If they equal the number, then it is a perfect number. If they don’t, then it is not a perfect number.
Tags: add, addition, arithmetic, division, divisor, excluding, identify, integer, natural, number, perfect, proper, real, sum
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Tuesday, November 10th, 2009
The Numerator and Denominator of a Fraction
Description
A detailed tutorial on the numerator and denominator of a fraction. Step by step tutorial including several examples of numerators and denominators for reference.
Overview
Fractions are well known in the world of mathematics. But when first starting out, you may ask yourself why the fraction appears like it does – split into two parts. You will see a fraction either written horizontal or vertical. In a horizontal fraction, the numerator is the number to the left, and the denominator is the number to the right. In the more common and proper vertical fraction, the numerator is on the top and the denominator is on the bottom. This works when there are whole equations in either the numerator and denominator as well, not just for simpler numbers. The numerator and the denominator should never be split, but algebra tricks can sometimes help to simplify them.
Tags: algebra, arithmetic, bar, denominator, equations, fraction, horizontal, number, numerator, parts, simplify, split, tricks, two, vertical
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Tuesday, November 10th, 2009
An Overview of Pi
Description
A detailed tutorial on what pi is. Step by step tutorial including several examples of what pi is for reference.
Overview
Pi is a special number in mathematics. It is the ratio of a circle’s circumference to its diameter. No matter what size circle you use, your answer will always be pi, showing that all circles are proportional to one another. Pi is denoted by the Greek letter pi, which looks a little bit like an “n”. The numerical value of pi is 3.1415926535… but is typically shortened to the simple 3.14. Pi is very important in math and is used in all equations dealing with circles.
Tags: 3.14, arithmetic, circle, circumference, denoted, diameter, equations, Greek, letter, pi, propertional, radius, ration, size, value
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Friday, November 6th, 2009
Overview of Symmetry
Description
A detailed tutorial on symmetry and symmetric images. Step by step tutorial including several examples of symmetry for reference.
Overview
Symmetry is a very basic concept in geometry. It is similar to invariance. It is when something is equal to itself through both of its sides. If you compare the two sides of something and they match, then the object is said to be symmetric. When testing an image for symmetry, the easiest test is to draw an imaginary line down the middle. Then pretend to fold the image over. If the two sides are perfect matches of each other, then the image is symmetric.
Tags: arithmetic, center, equal, fold, Geometry, imaginary, invariance, line, match, middle, same, symmetric, symmetrical, symmetry
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Friday, November 6th, 2009
Introduction to Invariants
Description
A detailed tutorial on invariants and the property of invariance. Step by step tutorial including several examples of invariants for reference.
Overview
Invariants are any function or number that displays the property of invariance. Invariance is when a function or number can go through several transformations without changing, or without going outside of its set parameters. The set parameters differ depending on the function or number. Some examples of invariant functions and numbers are the absolute value of a complex number, the degree of a polynomial, and certain parts of a square matrix
Tags: absolute, arithmetic, complex, degree, determinant, eigenvalue, eigenvector, function, invariance, invariant, matrix, number, parameters, polynomial, square, trace, transformations, value
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