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A detailed tutorial on the four basic computation methods. Step by step tutorial including several examples of the four basic computation methods for reference.

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.

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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.

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.

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A detailed tutorial on the additive identity. Step by step tutorial including several examples of the additive identity for reference.

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.

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A detailed tutorial on equations of a half-circle. Step by step tutorial including several examples and an explanation of half-circles for reference.

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.

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A detailed tutorial on finding the next term of an arithmetic sequence. Step by step tutorial including several examples of arithmetic sequences for reference.

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.

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A detailed tutorial on solving work rate problems. Step by step tutorial including several examples of work rate problems for reference.

A work rate problem is a word problems that asks you to calculate the amount of time it will take to do something with two different rates of work. They first show up in basic algebra courses but work rate problems get more complicated and will continue on even in calculus. It is easier to solve work rate problems if you use a chart. First, you need to find the task rate – the rate at which each person is doing something. You do this by dividing the number of tasks (which should be one) by how many hours it takes them to finish it. Then you choose a variable for time. Your task will take that variable divided by the number of hours. You should come up with 2 (or more) results for task. Add these results together and have them equal the number of people there are total working on the task. Then solve for your time variable. Sometimes it will be difficult to solve for the time variable without using an algebra trick of multiplication to change the numbers a bit.

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A detailed tutorial on the property of reflexive relations. Step by step tutorial including several examples of reflexive relations for reference.

A reflexive relation can be mathematically defined as for all x belonging to A, x R x. In this statement, A is a set, and R is a relation of that set. If the relation is an empty set, then it is not reflexive, unless the set itself happens to be an empty set. When writing a proof for a reflexive relation, you must attempt to prove that (x, x) does not belong to R. If you cannot prove this, then you know that the relation must be reflexive.

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A detailed tutorial of what a semiperimeter is. Step by step tutorial including a visual example of a semiperimeter for reference.

In geometry, a semiperimeter of a polygon (squares, rectangles, triangles, or any closed and none-rounded shape) is simply half a perimeter – like a radius would be for a circle, almost. If you already have the perimeter of the figure, you can easily obtain the semiperimeter by dividing it in half.  The semiperimeter is given its own seperate variable and identity because it is used sometimes in mathematical equations, such as Heron’s formula.

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Description

A detailed tutorial on how to divide decimals. Step by step tutorial including several examples of dividing decimals for reference. It is a requirement to know how to divide decimals for all math classes.

Overview

Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be a little tricky to figure out. The operation we will be talking about is division. With division, you set it up just like any long division problem. Move the decimal over to the right on the divisor so that there is no decimal, and then you must move the decimal point over exactly that many spaces on the dividend. Then solve it just like you would any other division problem, and don’t forget about the decimal point.

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Description

A detailed tutorial on how to solve problems using long division. Step by step tutorial including several examples of long division for reference.

Overview

Long division is the first method students learn to solve division problems. The process looks complicated but long division is much easier than any other method. Long division involves drawing a symbol that looks a lot like a square root symbol, putting the divisor on the outside (to the left) and the dividend on the inside (under the line of the symbol). The divisor should be smaller number than the dividend. Basically, you take each number of the dividend seperately and ask how many times the divisor will go into it. If the number is too small put the second number onto it (for example, if your number is 183, and 1 is too small, then you look at the number 18). Let’s say the divisor will go into the number 3 times. Write 3 on the top of the line and subtract your divisor * 3 from the number you used to find that. Sometimes the difference is 0, but usually it isn’t. Keep on adding the next number in the dividend with it until you get to the last number, at which point you must add on the remainder in a decimal point. Long division is also a way to convert fractions into decimals if changing the denominator to 100 is impossible. When you do this, the numerator becomes the dividend and the denominator becomes the divisor.