Page 3: Advanced Problem Solving

This page continues with the solution process and introduces the concept of evaluating expressions with decimals.

Highlight: The solution process demonstrates how to handle multiple operations while maintaining mathematical accuracy.

Example: The complete solution shows how 12x - 13 + 10y simplifies to 0.

The page introduces two key steps for decimal operations:

1. Variable replacement with numerical values
2. Expression evaluation using PEMDAS

Page 4: Decimal Operations

This page focuses on working with decimal values in two-variable expressions.

Example: A detailed solution for 16q - 3s + 10 where q = 0.1 and s = 0.5 is provided, resulting in 10.1.

Highlight: The importance of performing operations in the correct order is emphasized, particularly when working with decimals.

Definition: When working with decimals, multiplication is performed first, followed by addition and subtraction from left to right.

The solution demonstrates how to systematically work through decimal calculations while maintaining precision and accuracy in the final answer.

Page 1: Introduction to Two-Variable Expressions

This page introduces the fundamental concepts for How to evaluate expressions with two variables using fractions. The content outlines a systematic four-step approach for solving these mathematical problems.

Definition: Order of Operations (PEMDAS) is a mathematical rule system that determines the sequence of operations when evaluating expressions.

Highlight: The four-step process includes: writing parentheses around variables, replacing variables with given values, performing multiplication/division, and completing addition/subtraction.

Example: The page introduces an expression 4 + 6m - 2n, where m = 2/3 and n = -2, demonstrating the initial setup of a two-variable problem.

Vocabulary: PEMDAS breakdown:

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction