Posts Tagged ‘algebra’
Tuesday, November 17th, 2009
Overview of the Fundamental Counting Principle
Description
A detailed tutorial on the fundamental counting principle. Step by step tutorial including several examples of the fundamental counting principle for reference.
Overview
The fundamental counting principle is a simple method of finding out how many times something occurs. It is a simplified form of finding permutations and combinations, and is used very often in statistics when permutations and combinations must be found. The fundamental counting principle states that if an event can occur in M ways, and another event can occur in N ways, then the first event followed by the second event can occur M * N ways. Basically, if you have two different options, and a different amount of each option, you can multiply them together to find the total number of ways you can combine these options.
Tags: algebra, amount, combinations, combine, counting, fundamental, multiplication, option, permutate, permutations, principle, statistics
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Tuesday, November 17th, 2009
How to Draw a Boundary Line
Description
A detailed tutorial on how to draw a boundary line. Step by step tutorial including several examples on how to draw a boundary line for reference.
Overview
A boundary line is used when graphing inequalities on a number line or a regular Cartesian graphing system. What the boundary line does is connect the two points in the inequality – in other words, it sets a boundary of what an unknown variable would be on that inequality. The boundary line can either be solid or dashed. The boundary line is only dashed when it is drawn on a regular graph, to express that the line was somewhere else at one point and was then moved. In all other cases, the boundary line is solid.
Tags: algebra, boundary, closed, coordinates, dashed, equal, graph, greater, inequality, interval, less, line, number, open, points, solid, then, to
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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
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Thursday, November 12th, 2009
How to Make a Histogram
Description
A detailed tutorial on how to make a histogram. Step by step tutorial including several examples on how to make a histogram for reference.
Overview
A histogram is similar to a bar chart or bar graph, only it cannot go in either direction – histograms can only have vertical bars. The main difference between them is that bar charts and bar graphs can be used to show the number of items in a category. Histograms are used between two sets of numbers, to show which numbers relate to each other. The numbers themselves each fall under their own category. This is a very common chart to see in the later levels of math, especially statistics, as they reflect statistical data.
Tags: algebra, bar, category, chart, data, difference, graph, histogram, horizontal, number, relationship, set, statistics, vertical
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Thursday, November 12th, 2009
How to Use Algebra Tiles
Description
A detailed tutorial on how to use algebra tiles. Step by step tutorial including several examples of how to use algebra tiles for reference.
Overview
Algebra tiles are a visual expression of polynomials and polynomial equations. Each tile is meant to represent a different polynomial. A large square tile represents the squared variable, a smaller square tile represents a single number, with no variable, and a rectangle represents the single variable. The tiles are red and green. Green represents positive monomials, and red represents negative monomials. Tiles can be combined to create equations, or the same tiles can be combined to express the coefficient. Addition and subtraction can be performed by adding and removing tiles.
Tags: addition, algebra, coefficient, cubed, green, large, negative, polynomial, positive, rectangle, red, small, square, squared, subtraction, tiles, variable
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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
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Tuesday, November 10th, 2009
How to Make Factor Trees
Description
A detailed tutorial on how to make factor trees. Step by step tutorial including several examples on how to make factor trees for reference.
Overview
A factor tree is a type of tree diagram that splits numbers into their factors. It is a very useful method of simplification. First, start with a number and draw two lines from it. Two numbers that when multiplied equal your first number need to go there. A great number to start with is 2, if your number is an even number. you can start with any two numbers you like, provided they fit the guidelines, excluding anything paired with the number one – because then you won’t get anywhere. Then for each of your two numbers, if they are not simplified, you do the same process with them. Keep it up until you are down to simplified, or prime, numbers. You will know you have reached one when the only multiples are one and itself.
Tags: algebra, diagram, even, factor, itself, multiple, number, odd, one, prime, simplification, simplified, simplify, tree, two
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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
How to Make a Circle Graph
Description
A detailed tutorial on how to make circle graphs. Step by step tutorial including several examples of how to make circle graphs for reference.
Overview
Circle graphs, also referred to as pi charts to avoid confusing them with graphs on the coordinate plane, are graphs in the shape of a circle that deal with a specific set of data. Circle graphs deal with percentages of a whole. The title of the circle graph is your whole, and the circle represents the whole. Then the circle is cut off into different percentages, and each is labelled with the proper category and exactly what percent it is meant to represent. Very often each section of the circle will be a different color to avoid confusion.
Tags: algebra, categories, category, chart, circle, color, data, different, graph, label, percent, percentage. title, pi, represent, section, set
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Tuesday, November 10th, 2009
How to Make a Bar Graph
Description
A detailed tutorial on how to make bar graphs. Step by step tutorial including several examples on how to make a bar graph for reference.
Overview
A bar graph, also referred to as a bar chart as to not be confused with graphs on the coordinate plane, is a visual expression of a set of data. Bar graphs deal with the real numbers in specific data sets. Typically they are split up into more than one category. A bar is drawn on each category extending to the number associated with that category. Traditionally, bar graphs need to have a title, an assigned label to each axis, and a certain pattern to continue writing numbers in.
Tags: algebra, axis, bar, categories, category, chart, graph, label, number, pattern, set, title, visual
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