Expressions

What is an Expression?

Types of Expressions

• Numerical Expressions: These are expressions that contain only numbers and mathematical operations. For example, 5 + 3 * 2.
• Variable Expressions: These are expressions that contain variables (such as x, y, etc.) in addition to numbers and mathematical operations. For example, 2x + 3y - 7.
• Algebraic Expressions: These are expressions that contain variables, numbers, and mathematical operations. They often represent real-life situations or problems. For example, 3x + 2y - 5z.

Parts of an Expression

• Terms: These are the individual parts of the expression that are separated by addition or subtraction. For example, in the expression 3x + 2y - 5z, the terms are 3x, 2y, and -5z.
• Variables: These are symbols that represent unknown or changing quantities. They can be combined with numbers and operators to form expressions. For example, in the expression 2x + 3y - 7, x and y are variables.
• Coefficients: These are the numerical factors of the variables in an expression. For example, in the expression 4x + 2y, 4 and 2 are the coefficients of x and y, respectively.
• Constants: These are fixed values that do not change within a given context. For example, in the expression 2x + 3y - 7, 7 is a constant.

Operations with Expressions

Examples

1. Example 1: Numerical Expression
   • Expression: 5 + 3 * 2
   • Solution: 5 + 6 = 11
2. Example 2: Variable Expression
   • Expression: 2x + 3y - 7
   • This is a variable expression with terms 2x, 3y, and -7.
3. Example 3: Algebraic Expression
   • Expression: 3x + 2y - 5z
   • This is an algebraic expression with variables x, y, and z.

Study Guide

1. Understand the difference between numerical, variable, and algebraic expressions.
2. Identify the parts of an expression, including terms, variables, coefficients, and constants.
3. Practice simplifying and evaluating expressions using the order of operations.
4. Work on solving problems and real-life situations using algebraic expressions.