Statistics

Statistics

Order of Operations

In math, order is everything! There is a unique order of operations we use to solve all mathematical equations. The order of operations (sometimes called operator precedence) is a rule used to clarify which procedures should be performed first in a given mathematical expression. The order of operations--or precedence--is used throughout mathematics, science, technology, and computer programming, and is expressed here. It states the order in which problems should be solved:

1. Terms inside parentheses or brackets 2. Exponents and roots

3. Multiplication and division 4. Addition and subtraction

This means that if a mathematical expression is preceded by one operator and followed by another, the operator higher on the list should be applied first.

Examples

(1 − 3) + 7 = −2 + 7 = 5

• • •

(2 × 3) + (4 × 1) = 6 + 4 = 10 (4 ÷ 2)– (3– 2) × 2 = 2– 1 × 2 = 2

Always remember to perform the functions inside parenthesis first then read the problem left to right to complete it.

1.2 Algebra

For your exam, you will have to apply the concepts of elementary algebra. This is the most basic form of algebra. In arithmetic, only numbers and their arithmetical operations (such as + , − , × , ÷ ) occur. In algebra, numbers are often denoted by symbols (such as , , , , or ). This is useful for the following reasons: • It allows the reference to "unknown" numbers, the formulation of equations and the study of how to solve these (for instance, "Find a number such that 3 + 1 = 10 " or going a bit further "Find a number x such that + = ") • It allows the formulation of functional relationships. (For instance, "If you sell tickets, then your profit will be 3 − 10 dollars, or ( ) = 3 − 10 , where is the function, and is the number to which the function is applied.") • It allows the general formulation of arithmetical laws (such as + = + for all and )

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