Untitled Quiz

Algebraic Expressions

• Expressions such as 4q, 15+r, and 2a+6 represent combinations of variables and constants, indicating operations like multiplication and addition.
• 5 times a number can be expressed as 5x, where x represents the number.
• More complex expressions include 18 decreased by 3 times d which can be written as 18-3d, and Three times a number plus 16, expressed as 3x+16.

Evaluating Numerical Expressions

• Simple calculations: 35-3×8 evaluates to 11, and 29-3(9-4) resolves to 14.
• Operations involving fractions and multiplication yield results such as 18/9+2×6 which also equals 14.
• The expression (4+5)6 simplifies to 54, while 7(2+1) computes to 21.

Properties of Operations

• Commutative Properties:
  • Addition: (A + b = b + a)
  • Multiplication: (A \times b = b \times a)
• Associative Properties:
  • Addition: (A + (B + C) = (A + B) + C)
  • Multiplication: (A \times (B \times C) = (A \times B) \times C)
• Distributive Property: Allows distribution over addition: (A \times (B + C) = A \times B + A \times C).

Identity and Inverse Properties

• Additive Identity: For any a, (a + 0 = a).
• Multiplicative Identity: For any a, (a \times 1 = a).
• Additive Inverse: (a + (-a) = 0), implying for every number, there’s a corresponding negative that sums to zero.
• Multiplicative Inverse: For non-zero a, (a \times (1/a) = 1).
• Zero Property: (a \times 0 = 0).

Properties of Equality

• Reflexive Property: (A = A) shows equality with itself.
• Symmetric Property: If (A = B), then (B = A).
• Transitive Property: If (A = B) and (B = C), then (A = C).

Algebra Basics

• Expressions: Non-equation forms that imply simplification without an equal sign.
• Equations: Mathematical statements that equate two expressions, directing to solve for the unknowns.

Further Algebra Concepts

• No Solution and Identities: Equations like (N(3+2)+6=5n+(10-3)) yield no solution, whereas consistent terms define identities.
• Domain: Refers to the values of the independent variable, the first numbers in ordered pairs of a relation.
• Range: Represents the dependent variable outputs, being the second numbers in ordered pairs.
• Independent Variable: The variable chosen freely in a function.
• Dependent Variable: Its value is contingent upon the independent variable.

Calculating with PEMDAS

• The acronym PEMDAS stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

These rules govern the order of operations in simplifying expressions and solving equations.