Pre-Algebra Review Vocabulary - Order of Operations & Basic Concepts

Vocabulary flashcards covering key terms from the lecture notes on order of operations, algebra basics, and number types.

order of operations

The rules for the sequence of operations in an expression: parentheses/grouping symbols, exponents or roots, multiplication and division (from left to right), and addition and subtraction (from left to right).

sum

The result of adding two or more numbers.

5 more

A phrase meaning to increase a number by 5; addition by 5.

difference

The result of subtracting numbers; how much one quantity is less than another.

5 less

A phrase meaning to subtract 5; decrease by 5.

product

The result of multiplying numbers.

quotient

The result of dividing numbers.

commutative property of addition

Changing the order of addends does not change the sum (a + b = b + a).

commutative property of multiplication

Changing the order of factors does not change the product (a · b = b · a).

associative property of addition

Grouping addends differently does not change the sum ((a + b) + c = a + (b + c)).

associative property of multiplication

Grouping factors differently does not change the product ((a · b) · c = a · (b · c)).

distributive property

Multiplication distributes over addition:

a · (b + c) = a·b + a·c.

equation

A mathematical statement that two expressions are equal, indicated by an equals sign.

variable

A symbol (often x) that represents an unknown or changeable value.

coefficient

A number multiplying a variable; in x, the implied/invisible coefficient is 1 (as in 1·x). In 2x, the coefficient is 2 (as in 2·x).

like terms

Terms that have the same variable raised to the same exponent (for example [3x and 5x] or [3x²y and -4x²y] that can be combined through addition or subtraction. )

term

A single part of an algebraic expression that can be a number/constant, variable, or both. (For example, 3x, -4, or xy.)

expression

A combination of terms, constants, variables, and operations separated by addition, +, or subtraction symbols. (For example, [3x + 4 - 2y] or [5 - 3y.] ).

solve

To find the value(s) of the variable(s) that satisfy an equation or inequality.

simplify

To rewrite an expression in a simpler or more compact form, often by combining like terms or performing operations such as addition or multiplication. This makes the expression easier to understand or evaluate. .

evaluate

To find the numerical value of an expression by substituting given values for variables.

inequality

A relation showing one side is greater than, less than, or equal to the other (uses

independent variable

The input variable that can be varied (often x in a function/equation).

dependent variable

The output variable that depends on the input (often y in a function/equation).

input-output table

A table listing input values and their corresponding output values for a function.

coordinate pair

An ordered pair (x, y) representing a point on the coordinate plane.

relation

A set of ordered pairs; can be represented as a table, graph, or mapping. It describes how two variables are related, typically involving a dependent and independent variable.

coordinate plane

The two-dimensional plane with an x-axis and a y-axis used to graph points and equations.

origin

The point (0, 0) where the x- and y-axes intersect.

x-axis

The horizontal axis of the coordinate plane. It is perpendicular to the y-axis and is used to represent the domain of values in graphing functions or data. The axis may be labeled with a different variable to represent the context of a problem.

y-axis

The vertical axis of the coordinate plane. It is perpendicular to the x-axis and is used to represent the range of values in graphing functions or data. The axis may be labeled with a different variable to represent the context of a problem.

base

The number that is raised to a power in exponent notation (e.g., 3 in 3²).

exponent

The power to which the base is raised (the superscript). For example, the 2 in 3². It indicates how many times the base will be multiplied by itself. In the expression 3² it indicates that the based is multiplied by itself two times, so 3· 3 = 3².

power

The result of raising a base to a given exponent. Sometimes used as a synonym for exponent.

root

A value that, when raised to a certain power, yields a given number (e.g., square root, cube root). It is the inverse operation of exponentiation. For example if 3² = 9, then the square root of 9 is 3. √ 9 = 3

index number (indices)

The small number in the radical/root symbol indicating which root is taken. If there is no index number, the implied root is 2 and it will be a square root or for cube root it would be 3.

radical

The symbol or operation for taking a root, such as √ or nth root.

grouping symbols

Symbols like parentheses (), brackets [], braces {}, radicals √ and fraction bars, used to group terms and indicate what comes first in order of operations.

integers

All positive and negative whole numbers, including zero.

real numbers

All rational and irrational numbers; numbers that can be located on the number line.

whole numbers

Non-negative integers: {0, 1, 2, 3, …}.

rational numbers

Numbers that can be expressed as a ratio of two integers (p/q with q ≠ 0). For example, 2/3 or 3/5.

irrational numbers

Numbers that cannot be expressed as a ratio of integers; decimals that do not terminate or repeat. For example pi or the square root of 2.

decimal

A number written with a decimal point separating the whole (left of the decimal) and fractional (right of the decimal) parts.

place value (ones, tens, hundreds)

The value to the left of a decimal of a digit based on its position in a number (ones, tens, hundreds, etc.).

decimal place value (tenths, hundredths, thousandths)

Place values to the right of the decimal point (tenths, hundredths, thousandths, etc.).

difference between a mathematical operation and the result

The operation is the process (e.g., addition); the result is the value produced (e.g., the sum).