Archive for the ‘Arithmetic’ Category
Tuesday, December 29th, 2009
Overview of the Trichotomy Property
Description
A detailed tutorial on the trichotomy property. Step by step tutorial including several examples of the trichotomy property for reference.
Overview
The trichotomy property is one of the ordering properties of natural numbers. It tells us what order you need to put the natural numbers in – in other words, it tells you the placement of each element of the set of natural numbers. The trichotomy property states that is there are two natural numbers m and n, that m must be either less than n, equal to n, or greater than n. The smaller number is to be placed first, with the larger number after it. If the numbers are equal, then only one number needs to be included as part of the set.
Tags: arithmetic, element, equal, greater, inequality, larger, less, natural, number, order, placement, property, set, smaller, than, trichotomy
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Friday, November 20th, 2009
How to Identify a Perfect Square
Description
A detailed tutorial on how to identify a perfect square. Step by step tutorial including several examples of how to identify perfect squares for reference.
Overview
A perfect square is a number that is the square of a non-negative integer – in other words, a positive whole number. The way you can identify a perfect square is that when you take the square root, you should not end up with a fraction or decimal – you should get the non-negative integer. There are many perfect squares, but most of them are large numbers, so many people do not know more than the squares of the numbers one through twelve.
Tags: arithmetic, basic, decimal, fraction, identify, integer, inverse, negative, non-negative, number, perfect, positive, root, square, squareroot, whol
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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
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Thursday, November 19th, 2009
Overview of the Additive Identity
Description
A detailed tutorial on how to solve equations using the additive inverse. Step by step tutorial including several examples of how to solve equations with the additive inverse for reference.
Overview
The additive inverse is the inverse of the additive identity – which should be very easy to guess. However, the problem is not guessing the definition of the additive inverse – the problem is knowing what the inverse of the additive identity is. The additive identity states that any number plus zero equals itself. The additive inverse states that any positive number minus its true value or any negative number plus its true value is equal to zero – in other words, that two inverses together equal zero. You solve equations by using the additive inverse.
Tags: add, additive, arithmetic, basic, divide, equations, identity, inverse, itself, multiply, nothing, plus, property, same, subtract, zero
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Thursday, November 19th, 2009
Overview of the Additive Identity
Description
A detailed tutorial on the additive identity. Step by step tutorial including several examples of the additive identity for reference.
Overview
The additive identity is very similar to the zero properties of multiplication and addition. However, the additive property is only used with addition – which should be easy to tell from the name of this identity. The additive identity states that any number plus zero, or with zero added to it, is equal to itself. The additive property is one of the properties that all teachers expect you to already know, so it is important to learn it.
Tags: add, additive, arithmetic, basic, divide, identity, itself, multiply, nothing, plus, property, same, subtract, zero
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Thursday, November 19th, 2009
Overview of Negative Square Roots
Description
A detailed tutorial on negative square roots. Step by step tutorial including several examples of negative square roots for reference.
Overview
Negative square roots are just like negative numbers. Just like positive and negative numbers have the same true value, only on opposite sides of the number line, negative square roots and positive square roots also have that same property. However, they should not be confused with the square root of a negative number. The square root of a negative number is known as an imaginary number, and is not used in basic algebra. The negative square root is expressed by the square root of a number, with a negative sign in front of the square root symbol, and the square root of a negative number is expressed as a negative number with a square root symbol placed over it.
Tags: absolute, algebra, arithmetic, imaginary, line, negative, number, positive, root, square, squareroot, symbol, true, value
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Friday, November 13th, 2009
An Overview of Composite Numbers
Description
A detailed tutorial on what composite numbers are. Step by step tutorial including several examples of composite numbers and their definition for reference.
Overview
A composite number is the opposite of a prime number. Some people say they are any number that is not prime, but that is not exactly accurate – negative numbers are not prime (even negative prime numbers), and a composite number is not a negative number, it is a positive number. A composite number is any positive integer that has more divisors than itself and one – which are the only two numbers a prime number can be divided by.
Tags: accurate, arithmetic, composite, examples, integer, negative, number, opposite, positive, prime, real
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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
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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
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Thursday, November 12th, 2009
How to Find the Reciprocal of a Number
Description
A detailed tutorial on how to find the reciprocal of a number. Step by step tutorial including several examples of reciprocals for reference.
Overview
A reciprocal is a way of saying the opposite of a number, although it is not a true opposite. A true opposite of a negative number would be a positive number, and a true opposite of a positive number would be a negative number – that is why there are such things as opposite reciprocals. A more accurate name for a recirpocal would be the reverse of a number. In a fraction, the reciprocal of a number is when the numerator and the denominator are flipped. This also works for whole numbers, because you can think of the number as a numerator with denominator one.
Tags: accurate, arithmetic, denominator, flipped, fraction, integer, negative, number, numerator, opposite, positive, real, reciprocal, reverse, whole
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