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Evaluate

(an expression) To find the numerical value of. 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. (Also see the expression.)

Coefficient

(numerical) A number multiplying a variable or product of variables. For example, -7 is the coefficient of −7xy2.

Constant Term

A number that is not multiplied by a variable. In the expression 2x + 3(5 − 2x) + 8, the number 8 is a constant term. The number 3 is not a constant term, because it is multiplied by a variable inside the parentheses.

Ratio

A ratio compares two quantities by division. A ratio may be written using a colon but is more often written as a fraction. For example, the comparison may be made of the ratio of female students in a particular school to the total number of students in the school. This ratio could be written as 1521 : 2906 or as the fraction shown below.

Rule

A rule is an equation or inequality that represents the relationship between two numerical quantities. We often use a rule to represent the relationship between quantities in a table, a pattern, a real-world situation, or a graph.

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.

Term

A term is a single number, variable, or the product of numbers and variables, such as -45, 1.2x, and 3xy2.

Combining Like Terms

Combining two or more like terms simplify 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 involve putting together tiles with the same dimensions.

Equivalent Expressions

Two expressions are equivalent if they have the same value. For example, 2 + 3 is equivalent to 1 + 4.

Area

For this course, the area is the number of square units needed to fill up a region on a flat surface. In later courses, the idea will be extended to cones, spheres, and more complex surfaces. (Also see the surface area.)

Dimension

The dimensions of a figure that is a flat region or space tell how far that the figure extends in each direction. For example, the dimensions of a rectangle might be 16 cm wide by 7 cm high.

Quotient

The result of a division problem.

Product

The result of multiplying. For example, the product of 4 and 5 is 20.

Order of Operations

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

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 may be simplified to -4 - 6x. When working with algebra tiles, a simplified expression uses the fewest possible tiles to represent the original expression.