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Reference

Mathematical Operations

Concept

Addition

Addition is one of the four basic arithmetic operations. It combines two quantities, called addends, giving as a result their total amount, called the sum. This operation is represented with the plus sign .

It is important to notice that the order in which the operation is performed does not affect the result. This property is known as the Commutative Property of Addition.

Concept

Subtraction

Subtraction is one of the four basic arithmetic operations. It is the opposite of addition. Subtraction represents the operation of removing a quantity, called the subtrahend, from another quantity, called the minuend. The result is called the difference. This operation is represented using the minus sign .

Subtraction is not commutative; this means that the order in which subtraction is performed matters, as different orders lead to different results.

Concept

Multiplication

Multiplication is one of the four basic arithmetic operations. It can be thought of as repeated addition. Multiplying two numbers is equivalent to adding as many copies of one of the numbers, called the multiplicand, as many times as indicated by the other number, called the multiplier. The result is called the product.

As indicated in the diagram above, multiplication can be represented with the sign . However, there are other ways to represent this operation. Another common notation is using a mid-line dot .
It is important to notice that the order in which the operation is performed does not affect the result. This property is known as the Commutative Property of Multiplication.
Because of this property, both the multiplicand and multiplier could play each other's role. Thus, it is very common to refer to both indistinctly as factors.

Concept

Division

Division is one of the four basic arithmetic operations. It is the opposite of multiplication and is indicated by using the sign This operation represents the process of calculating how many times one quantity, called the divisor, is contained within another quantity, called the dividend. The result is called the quotient of the division.

As already stated, division can be represented with the sign However, there are other ways to represent it. Another common notation is using a a diagonal bar or using fraction notation.
If the result of a division is not an integer, the quotient is the number of times the divisor is contained in the dividend, and the part of the dividend that remains is called the remainder.

Division is not commutative. This means that changing the order in which the operation is performed leads to different results.

Concept

Power

A power is the product of a repeated factor. A power expression consists of two parts. The base is the repeated factor and the exponent indicates how many times the base is used as a factor. Consider, for example, the power expression with base and exponent

A power expression 7^4 where 7 is the base and 4 is the exponent
In this example, is multiplied by itself times.
Most powers are read in the same way, whether they are numeric or algebraic.
Expression Example Example
to the second power squared
to the third power cubed
raised to the power of raised to the fourth power
raised to the power of raised to the fourth power
to the power of to the ninth power

This table contains two special cases — when a number or variable is raised to the power of or the power can be read as squared or cubed, respectively.