Posts Tagged ‘multiplication’
Tuesday, December 29th, 2009
How to Use the Product Rule in Algebra
Description
A detailed tutorial on the algebraic product rule. Step by step tutorial including several examples of the algebraic product rule for reference.
Overview
There are many product rules in the world of math. This tutorial focuses on a product rule that is used in algebra and statistics. The product rule states that if two independent tasks T1 and T2 are to be performed, then T1 can be performed m ways and T2 can be performed n ways. Therefore, the number of ways the tasks can be performed together is m * n ways. Remember that this is only the number of possible ways to do something, not how much time it takes to do something. Also, the same method is used no matter how many different tasks you are given.
Tags: algebra, combination, multiplication, multiply, number, permutation, product, rule, statistics, task
Posted in Algebra | No Comments »
Tuesday, December 29th, 2009
How to Construct a Cayley Table
Description
A detailed tutorial on how to construct a Cayley table. Step by step tutorial including several examples of how to construct a Cayley table for reference.
Overview
A Cayley table is a table that expresses the structure of a finite set. A Cayley table is set up by having the elements of the set across the first row, and numbers going in a numerical order of n + 1 starting at 1 down the first column. Sometimes the table is simply different ways the elements can be ordered. Other times is is a true table, where an operation is performed between two numbers in the space where they cross each other. However, a true Cayley table must be constructed using an identity skeleton. Once an identity skeleton for the finite set has been decided on, the Cayley table can be filled out using the identity skeleton. Since there is more than one possible identity skeleton for a finite set, you may have to go through a trial and error process until you find the right one.
Tags: addition, Cayley, chart, column, cross, discrete math, division, elements, error, finite, graph, identity, multiplication, operation, order, process, row, set, skeleton, subtraction, table, trial
Posted in Discrete Math | No Comments »
Friday, December 18th, 2009
Your Guide to Lattice Multiplication
Description
A detailed tutorial on lattice multiplication. Step by step tutorial including several examples of lattice multiplication for reference.
Overview
Lattice multiplication is a method that is used to multiply large numbers. It uses the multiplication of smaller numbers to figure out the product of two larger numbers. Because of this, basic knowledge of times tables is required. Lattice multiplication is compromised of boxes with diagonal lines through them. Draw the diagonal line in each box from the top right corner to the bottom left corner. The top left is for your tens place (the first digit in a two digit number) and the bottom right is for your ones place (the second digit in a two digit number). The number of boxes you have depends on the number you are multiplying – for example, if you are multiplying two one-digit numbers, there is one box. If you are multiplying two 2-digit numbers, there are four boxes. The first number is across the top, and the second down the side. Where each single digit number instersects, multiply them together using the box technique. Then, using the same pattern you drew the diagonals with, mutliply the diagonals. If you have two 2-digit numbers, there will be four diagonals. Multiply together the diagonals to come up with four numbers, and the pattern you use to put them together is going from the top down and then to the right.
Tags: algebra, box, combine, diagonal, digit, double, larger, lattice, multiplication, multiply, single, small, tables, times
Posted in Algebra | No Comments »
Thursday, November 19th, 2009
How to Find the Common Ratio of a Geometric Series
Description
A detailed tutorial on how to find the common ratio of a geometric series. Step by step tutorial including several examples of the common ratio for reference.
Overview
The common ratio is part of a geometric series, used commonly in calculus. The common ratio is the ratio of each term to the next – in other words, the common ratio is the pattern that the series or sequence follows. This is possible because in a geometric series, terms are only being multiplied by one number to get the next number, and it is always the same number. If a series is not geometric, it will not have a common ratio.
Tags: Calculus, common, geometric, multiplication, multiply, number, pattern, ratio, sequence, series, term
Posted in Calculus | No Comments »
Thursday, November 19th, 2009
Overview of Computation Methods
Description
A detailed tutorial on the four basic computation methods. Step by step tutorial including several examples of the four basic computation methods for reference.
Overview
Computation methods are the way you solve expressions and equations. The four basic ones are addition, subtraction, multiplication, and division. Addition and subtraction are inverses of each other, and multiplication and division are inverses of each other. All of them are extensions of counting and can easily be solved without too much effort.
Tags: add, addition, arithmetic, basic, computate, computation, counting, divide, division, method, multiplication, multiply, subtract, subtraction
Posted in Arithmetic | No Comments »
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
Posted in Algebra | No Comments »
Friday, November 13th, 2009
An Overview of Area Models
Description
A detailed tutorial on how to use area models. Step by step tutorial including several examples of how to use area models for reference.
Overview
An area model is used to help mutliply and divide integers. It is called an area model because of the way it is set up – it looks like you are solving for area when the model is used correctly. These models are typically composed of many small one by one squares, although different sizes can be used in order to make mulitplication and division earlier. Area models are used to provide a visual representation of the multiplication and division algorithms.
Tags: algorithms, area, arithmetic, division, integers, manipulatives, model, multiplication, rectangle, representation, square, visual
Posted in Arithmetic | No Comments »
Friday, November 6th, 2009
Identity Matrix Explained
Description
A detailed tutorial on the identity matrix. Step by step tutorial including several examples of the identity matrix and how to solve it for reference.
Overview
An indentity matrix is a matrix that is said to be of size n. It is considered to be the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. The identity matrix is denoted as the variable I. The identity matrix has some extremely important properties of its own, especially multiplication properties. It is a unique type of matrix that is found rarely, but is used very often in several different branches of math.
Tags: -1, 0, algebra, diagonal, i, identity, linear, main, matrices, matrix, multiplication, one, properties, square, uniquem, variable, zero
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Definition of an Operand
Description
A detailed tutorial on the definition of an operand. Step by step tutorial including several examples of an operand for reference.
Overview
An operand can be any number. However, a number is only called an operand when there is some kind of operation being performed on it. There are simple operands and complex operands. A simple operand is what people call an operand – just one number. A complex operand is an operand that consists of an operation inside it, and therefore has at least 2 operands inside the first operand.
Tags: addition, arithmetic, complex, division, exponents, multiplication, number, operand, operation, order, parenthesis, simple, subtraction
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Introduction to Linear Transformations
Description
A detailed tutorial on linear transformations. Step by step tutorial including several examples of linear transformations for reference.
Overview
A linear transformation takes place between two vector spaces. For two vector spaces V and W, there is a map T such that T(v_1 + v_2) = T(v_1) + T(v_2) for any vectors v_1 and v_2 in V, and T(a v) = a T(v) for any scalar a. Examples of linear transformation are often obtained through matrix multiplication. Linear transformations can also be injective or surjective
Tags: algebra, injective, linear, map, matrix, multiplication, scalar, space, surjective, transformation, vector
Posted in Algebra | No Comments »
