Expressions and Formulas

1. Expressions

• Definition: An expression is a combination of numbers, variables, and mathematical operations (like addition, subtraction, multiplication, division, exponents).

  • Example: 3x + 5, 2y - 7, x² + 4x

• Key Features:

  • No equal sign: Expressions don't state that two things are equal.

  • Can be simplified: By combining like terms, applying the distributive property, etc.

  • Can be evaluated: If given values for the variables, you can calculate the expression's value.

2. Formulas

• Definition: A formula is a special type of equation that expresses a relationship between two or more variables.

  • Example:

    • Area of a rectangle: A = l * w (where A is area, l is length, and w is width)

    • Perimeter of a square: P = 4s (where P is perimeter and s is side length)

• Key Features:

  • Equations: Formulas always involve an equal sign.

  • Represent relationships: They show how different quantities are connected.

  • Used for calculations: Formulas are essential for solving problems in various fields like physics, chemistry, finance, and more.

3. Variables

• Definition: A variable is a symbol (usually a letter) that represents an unknown or changing quantity.

  • Example: In the expression 3x + 5, "x" is a variable.

• Importance:

  • Flexibility: Variables allow us to represent general rules and patterns.

  • Problem-solving: By manipulating variables, we can solve equations and find unknown values.

4. Order of Operations (PEMDAS)

• Crucial for Evaluation: The order of operations is a set of rules that determine the sequence in which calculations are performed within an expression:

  • Parentheses/Brackets: Perform operations within parentheses first.

  • Exponents: Evaluate any terms with exponents.

  • Multiplication and Division: Perform multiplication and division from left to right.

  • Addition and Subtraction: Perform addition and subtraction from left to right.