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Reference

Concept

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 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 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.

$×,$a mid-line dot

$⋅,$or by placing one factor adjacent to the other, using parentheses to separate the two.

$2×32⋅32(3) =6=6=6 $

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.
$2×3=63×2=6 $

Because of this property, it is very common to refer to both as factors.Concept

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.

$÷.$However, there are other ways to represent it. Another common notation is using a a diagonal bar or using fraction notation.

$6÷26/226 =3=3=3 $

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.

$10÷55÷10 =2=0.5 $

Concept

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 $7$ and exponent $4.$

In this example, $7$ is multiplied by itself $4$ times.$7_{4}=47⋅7⋅7⋅7 $

Most powers are read in the same way, whether they are numeric or algebraic. Expression | Example $1$ | Example $2$ |
---|---|---|

$2_{2}$ | $2$ to the second power |
$2$ squared |

$7_{3}$ | $7$ to the third power |
$7$ cubed |

$5_{4}$ | $5$ raised to the power of $4$ |
$5$ raised to the fourth power |

$m_{4}$ | $m$ raised to the power of $4$ |
$m$ raised to the fourth power |

$x_{9}$ | $x$ to the power of $9$ |
$x$ to the ninth power |

This table contains two special cases — when a number or variable is raised to the power of $2$ or $3,$ the power can be read as squared

or cubed,

respectively.

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