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This guide introduces the fundamental concepts of algebra, focusing on variables, expressions, and their evaluation. A variable, often represented by letters like "n", signifies an unknown quantity. Algebraic expressions consist of numbers, variables, and at least one operation (e.g., addition, subtraction). For example, to evaluate the expression n + 3 when n = 4, simply replace n with 4, resulting in 7. The guide also explains the omission of multiplication symbols in expressions and the importance of coefficients. Mastering these basics will help bridge the gap between word problems and algebraic representation.
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Learning Target TSW evaluate simple algebraic expressions.
Variable A symbol that represents an unknown quantity. Most of the time, a letter will be used. Example: n+2 In this case, “n” is the variable.
Algebra The branch of mathematics that involves expressions with variables.
Algebraic Expressions Contain numbers, variables, and at least one operation. Examples: 12 + c m - 8
Evaluating Algebraic Expressions Evaluate n+3 if n=4. The expression is n+3. To evaluate, you replace n with 4. n+3 becomes 4+3. n+3 when n=4 equals 7 when the expression is evaluated.
Algebraic Expressions Involving Multiplication In algebra, the multiplication symbol is often omitted. You will see things like the following examples: 6d means 6 times d 8st means 8 times s times t mn means m times n The numerical factor of a multiplication expression that contains a variable is called a coefficient. In the previous example, “6” is the coefficient in the expression “6d”.
Important Information In most algebraic expressions, the fraction bar is used as a grouping symbol. You should evaluate expressions in the numerator and denominator separately before dividing.
Defining a Variable When translating a verbal phrase (word problem) into an algebraic expression: Describe the situation using only the most important words. Choose a variable that represents the unknown quantity. Write an algebraic expression that represents the verbal description.
