Math Expression Calculator

Understanding Mathematical Expressions

What are Mathematical Expressions?

Mathematical expressions are combinations of numbers, variables, and mathematical operations that represent a value. They can range from simple arithmetic to complex algebraic formulas.

Basic Components of Mathematical Expressions

• Numbers: Constant values (e.g., 1, 2, 3.14)
• Variables: Symbols representing unknown or changing values (e.g., x, y, z)
• Operators: Symbols indicating mathematical operations (+, -, *, /, ^, sqrt)
• Parentheses: Used to group parts of an expression and indicate order of operations

Order of Operations (PEMDAS)

When evaluating mathematical expressions, we follow the order of operations, often remembered by the acronym PEMDAS:

1. Parentheses
2. Exponents (including square roots)
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Example Calculation

Let's evaluate the expression: 12 * (4 * 3)^2

1. First, we evaluate what's inside the parentheses: (4 * 3) = 12
2. Now our expression looks like: 12 * 12^2
3. We perform exponentiation: 12^2 = 144
4. Finally, we multiply: 12 * 144 = 1728
5. Therefore, 12 * (4 * 3)^2 = 1728

Visual Representation

This diagram shows the step-by-step evaluation of the expression 12 * (4 * 3)^2, resulting in 1728.