Math Vocabulary #2

Less Than

(1) One expression is less than another if its value is not as large. We indicate this relationship with the less than symbol "<". For example, 1 + 1 is less than 4 + 5. We write 1 + 1 < 4 + 5. (2) We sometimes say that one amount is a certain quantity less than another amount. For example, a student movie ticket might cost two dollars less than an adult ticket.

Solve

(1) To find all the solutions to an equation or an inequality (or a system of equations or inequalities). For example, solving 2y - 8x = 16 for y gives y = 4x + 8. The equation y = 4x + 8 has the same solutions as 2y - 8x = 16, but y = 4x + 8 expresses y in terms of x and some constants.

Equation

A mathematical sentence in which two expressions appear on either side of an "equals" sign (=), stating that the two expressions are equivalent. For example, the equation 7x + 4.2 = -8 states that the expression 7x + 4.2 has the value -8. In this course, an equation is often used to represent a rule relating two quantities. For example, a rule for finding the area y of a tile pattern with figure number x might be written y = 4x - 3.

Zero

A number often used to represent "having none of a quantity". Zero is neither negative nor positive. Zero is the additive identity.

Term

A single number, variable, or product of numbers and variables. A monomial is a term. Also a component of a sequence.

Variable

A symbol used to represent one or more numbers. In this course, letters of the English alphabet are used as variables. For example, in the expression 3x - (8.6xy + z), the variables are x, y, and z.

Algebra Tiles

An algebra tile is a manipulative whose area represents a constant or variable quantity. The algebra tiles used in this course consist of large squares with dimensions x-by-x and y-by-y, rectangles with dimensions x-by-1, y-by-1, and x-by-y, and small squares with dimensions 1-by-1. These tiles are named by their areas: x, x2, y2, x, y, xy, and 1, respectively. The smallest squares are called "unit tiles". In this text, shaded tiles will represent positive quantities while unshaded tiles will represent negative quantities.

Expression

An expression is a combination of individual terms separated by plus or minus signs. Numerical expressions combine numbers and operation symbols; algebraic (variable) expressions include variables. For example, 4 + (5 - 3) is a numerical expression. In an algebraic expression, if each of the following terms, 6xy2, 24, and , are combined, the result may be 6xy2 + 24 −. An expression does not have an "equals" sign.

Equation Mat

An organizing tool used to visually represent two equal expressions using algebra tiles. For example, the Equation Mat below represents the equation 2x − 1 − (−x + 3) = 6 − 2x.

Combining Like Terms

Combining two or more like terms simplifies an expression by summing constants and summing those variable terms in which the same variables are raised to the same power. For example, combining like terms in the expression 3x + 7 + 5x − 3 + 2x2 + 3y2 gives 8x + 4 + 2x2 + 3y2. When working with algebra tiles, combining like terms involves putting together tiles with the same dimensions.

Real Numbers

Irrational numbers together with rational numbers form the set of the real numbers. For example, the following are all real numbers:. All real numbers are represented on the number line.

Greater Than

One expression is greater than another if its value is larger. We indicate this relationship with the greater than symbol ">". For example, 4 + 5 is greater than 1 + 1. We write 4 + 5 > 1 + 1.

Solutions

The number or numbers that when substituted into an equation or inequality make the equation or inequality true. For example, x = 4 is a solution to the equation 3x - 2 = 10 because 3x - 2 equals 10 when x = 4. A solution to a two-variable equation is sometimes written as an ordered pair (x, y). For example, x = 3 and y = -2 is a solution to the equation y = x - 5; this solution can be written as (3, -2).

Order of Operations

The specific order in which certain operations are to be carried out to evaluate or simplify expressions. The order is: parentheses (or other grouping symbols), exponents (powers or roots), multiplication and division (from left to right), and addition and subtraction (from left to right).

Evaluate

To evaluate an expression, substitute the value(s) given for the variable(s) and perform the operations according to the Order of Operations. For example, evaluating 2x + y - 10 when x = 4 and y = 3 gives the value 1.

Simplify

To simplify an expression is to write a less complicated expression with the same value. A simplified expression has no parentheses and no like terms. For example, the expression 3 - (2x + 7) - 4x can be simplified to -4 - 6x. When working with algebra tiles, a simplified expression uses the fewest possible tiles to represent the original expression.

Legal Moves

When working with an equation mat or expression comparison mat, there are certain "legal" moves you can make with the algebra tiles that keep the relationship between the two sides of the mat intact. For example, removing an x tile from the positive region of each side of an equation mat is a legal move; it keeps the expressions on each side of the mat equal. The legal moves are those justified by the properties of the real numbers.