Arithmetric

ARITHMETIC

Contents:

Rules.
Commutative Law.
Associative Law.
Distributive Law.
Order of Operations.
Example.

Rules: There are four rules of arithmetic:

Addition: the sum of to or more numbers.
Subtraction: the difference between two numbers.
Multiplication: the product of two or more numbers.
Division: the quotient of two numbers.

Commutative Law: For addition and multiplication, numbers may be added or multiplied together in any order. eg. 6 + 3 = 9 and 3 + 6 = 9....and 6 x 3 = 18 and 3 x 6 = 18. For subtraction and division the order is most important and must not be changed as this results in an incorrect answer. eg. 6 3 = 3 and 3 6 = 3....and 6 3 = 2 and 3 6 = .

Associative Law: For addition and multiplication, the operations may be performed in any order. eg. 6 + 4 + 3 = 13 and 6 + (4 + 3) = 13 and (6 + 4) + 3 = 13....and 6 x 4 x 3 = 72 and 6 x (4 x 3) = 72 and (6 x 4) x 3 = 72. For subtraction and division these operations are not associative. eg. 843 = 1 and 8(43) = 7 and (84)3 = 1. Not all of these answers are the same....and 842 = 1 and 8(42) = 4 and (84)2 = 1. Again not all of the answers are the same.

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Distributive Law: For multiplication and division each term within the brackets is multiplied or divided by the external factor. eg. 6 x (3 + 2) = (6 x 3) + (6 x 2) = 30 ....and =+= 4. For powers and roots the operations are not distributive eg. (2 + 3)= 5not 2+ 3....and 6 2 =4 not 62.

Order of Operations: Many operations may appear in an arithmetric expression, when this occurs there is order of precedence, the priority is:

Brackets
Powers and Roots.
Multiplication and Division.
Addition and Subtraction.

When two operations of the same precedence appear errors will be avoided by starting from the left each time.

Example: 3 + 5 (32) x 2+ 16 2 = ?