Posts Tagged ‘equation’
Friday, December 18th, 2009
Finding the Canonical Form of an Object
Description
A detailed tutorial of finding the canonical form of an object. Step by step tutorial including several examples of finding the canonical form of an object for reference.
Overview
Canonical form is also referred to as normal form or standard form. The canonical form of an object is a standard way of presenting that object. The process of finding a canonical form of something is referred to as canonization. Sometimes the word canonicalization is used instead. Canonical forms of objects are closly linked to differential forms of equations and numbers, and equivalence relations.
Tags: canonical, canonicalization, canonization, differential, discrete math, equation, equivalence, finding, form, normal, number, object, presenting, process, relations, standard
Posted in Discrete Math | No Comments »
Thursday, December 10th, 2009
Overview of Two-Way Counting
Description
A detailed tutorial on two-way counting. Step by step tutorial including several examples of two-way counting for reference.
Overview
Two-way counting is when any expression for a given quantity are determined using two different counting approaches. Many people believe that a quadratic equation is the perfect example of two-way counting, because you find the quantity in more than one way. However, this is incorrect. Two-way counting is actually a backwards method – you have the quantity already, you just need to figure out how you could get it. This is used often in combinations and permutations, where you often already know what quantity you need to have, you just have to figure out how to get there.
Tags: binomial, combination, counting, equation, example, expression, method, permutation, quadratic, quantity, statistics, two, two-way, way
Posted in Statistics | No Comments »
Friday, November 20th, 2009
How to Pick Variables
Description
A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.
Overview
Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.
Tags: a, algebra, b, c, choose, equation, expression, lowercase, m, mathematical, n!, number, operation, slope, symbol, unknown, uppercase, value, variable, variables, x, y, z
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Overview of Half-Circles
Description
A detailed tutorial on equations of a half-circle. Step by step tutorial including several examples and an explanation of half-circles for reference.
Overview
A half-circle is truely half of a circle. If you take a circle and cut it in half, you will get a half circle. Because of this, the equations of the half-circle are very similar to the equations of a full circle – simply divide the equation by two. The only ones that you cannot find that way are the radius, diameter, and circumference. The radius and diameter do not change on a half-circle. There is no circumference on the half-circle, but if you need the circumference for another formula you can use the circumference of the whole circle of that half-circle.
Tags: area, basic, circle, circumference, coordinates, cut, diameter, divide, equation, Geometry, half, half-circle, pi, radius, shape, split, two, whole
Posted in Geometry | No Comments »
Friday, November 13th, 2009
How to Check Your Work
Description
A detailed tutorial on how to check your work. Step by step tutorial including several examples of how to check your work for reference.
Overview
Checking your work is the process of inserting the value you solved for back into the original problem, to confirm that you came up with the correct solution. This process is quite commonly used with word problems, which nearly always have you solving for an unknown variable that would be a very important part of the original equation.
Tags: arithmetic, check, equation, guesstimation, original, problem, process, solution, unknown, value, variable, word, work
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Draw Best-Fitting Lines
Description
A detailed tutorial on how to draw best-fitting lines. Step by step tutorial including several examples on how to draw best-fitting lines for reference.
Overview
Best-fitting lines are lines that are drawn on a graph or on scatter plots. However, a best-fitting line is different than a normal line found on a graph. A normal graph simply requires you to connect the dots. A best fitting line focuses not on what dots to connect, but how to connect them. The line will curve or go in different directions, not just straight to the other line, depending on the relationship of the two dots to each other. Best-fitting lines typically require more information than simply the graph, you must explore the equation and each point to find the true relationships, and from that you can find the best-fitting line.
Tags: algebra, best, best-fitting, connect, coordinate, curve, direction, dots, equation, fitting, graph, line, plot, points, relationship, scatter, straight
Posted in Algebra | No Comments »
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
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Solve Negative Exponents
Description
A detailed tutorial on how to solve negative exponents. Step by step tutorial including several examples of solving negative exponents for reference.
Overview
An exponent is a number representing how many times you multiply the base – the number the exponent is on – by itself. Which is why negative exponents are so confusing – how can you multiply something by itself a negative number of times? The easiest way to think of a negative exponent, is that if you take away the negative sign and put the base and exponent under the number 1 (like as a fraction), you are saying the same thing! A negative exponent simply needs to be moved to the denominator (or the numerator, if it is in the denominator) to make it a positive exponent. This can be tricky when there are other numbers or expressions found in the same fraction, but not impossible.
Tags: algebra, base, denominator, equation, exponents, expression, fraction, multiply, negative, numerator, positive, power
Posted in Algebra | No Comments »
Tuesday, November 10th, 2009
How to Find the Degrees of Polynomials
Description
A detailed tutorial on degrees of polynomials. Step by step tutorial including several examples of degrees of polynomials for reference.
Overview
The degree of a polynomial is the highest power found in it. For example, in your normal quadratic equation, the degree is two, because the highest power – the highest number found in an exponent – is a two. In other polynomials, the degree may be something different. No matter what order the variables and their powers are placed in, the degree is always the highest one. For example. the degree of x^2 + x + 7 is exactly the same as x + 7 + x^2.
Tags: algebra, coefficient, degree, equation, exponent, highest, polynomial, power, quadratic, variable
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
How to Avoid the Freshman Dream
Description
A detailed tutorial on avoiding the freshman dream. Step by step tutorial including several examples of the freshman dream for reference.
Overview
The freshman dream is a mistake commonly made in algebra that was named for the probability that only freshman would make this mistake. In reality, this mistake can be made by anyone, regardless of your academic standing. The freshman dream is employed when you are given a squared binomial. If your equation looks like (x + n)^2, people using the freshman dream will write this as x^2 + n^2. However, this is wrong! Your equation should look like (x + n)(x + n) in the first step, and from there it is obvious to see that you would need to use FOIL to solve for it.
Tags: algebra, avoid, binomial, dream, equation, FOIL, formula, freshman, mistake, multiply, quadratic, square
Posted in Algebra | No Comments »
