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Variable A symbol, usually a letter, that represents one or more numbers. x = 3
Algebraic Expression A mathematical phrase that can include numbers, variables and operation symbols. 3x
More Than Indicates addition. x + 7
Less Than Indicates subtraction. x - 7
Difference Indicates subtraction. x - 7
Product Indicates multiplication. 7n
Quotient Indicates division. n/7
Equation A mathematical sentence that uses an equal sign. c = 12n
Open Sentence An equation that contains one or more variables. c = 12n
Simplify To simplify a numerical expression, you replace it with its simplest name. For example, 2 * 8 + 2 * 3 is simplified to 22.
Exponent Tells how many times a number (the base) is used as a factor. In the expression "2 to the 4th power" the exponent is 4.
Base The number that is used as a factor in a power. In the expression "2 to the 4th power" the base is 2.
Power A power has two parts, a base and an exponent.
Order of Operation 1. Perform any operations inside grouping symbols. 2. Simplify powers. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right.
Evaluate You evaluate an algebraic expression by substituting a given number for each variable. Then simplify the numerical expression using the order of operations.
Natural Numbers The numbers in the set 1, 2, 3, . . .
Whole Numbers The numbers in the set 0, 1, 2, 3, . . .
Integers Numbers that can be written without fractions or decimals. They include zero and negative numbers. -2, -1, 0, 1, 2, . . .
Rational Numbers Any number that can be written in the form a/b, where a and b are integers and b is not 0. All integers are rational numbers because any integer can also be written as n/1.
Irrational Numbers Cannot be expressed in the form a/b, where a and b are integers. These are numbers where the decimal expression is nonrepeating and nonterminating. Pi is an example.
Real Numbers Real Numbers is the set of irrational and rational numbers.
Counterexample Any example that proves a statement false is a counterexample. You need only one counterexample to prove that a statement is false. (A proof to show that a statement is true may be more complicated.)
Inequality A mathematical sentence that compares the value of two expressions using an inequality symbol, such as < or >.
Created by: noahegerton