Pre-Algebra Lecture Notes

Key Topics Covered

• Adding and Subtracting Integers
• Multiplication and Division
• Order of Operations (PEMDAS)
• Evaluating Algebraic Expressions
• Solving Linear Equations
• Working with Fractions
• Exponents and Factoring
• Greatest Common Factor (GCF)
• Simplifying Fractions
• Multiplying and Dividing Monomials
• Understanding Percentages
• Solving for Similar Triangles

Adding and Subtracting Integers

• Use a number line to assist with addition and subtraction.
• Adding: Move right on the number line.
• Subtracting: Move left on the number line.
• Examples:
  • 5 + 3 = 8
  • -4 + 5 = 1
  • 7 - 5 = 2
  • -4 - 2 = -6
  • -6 - (-3) = -6 + 3 = -3

Multiplication and Division of Integers

• Multiplication can be thought of as repeated addition.
• Division is the opposite of multiplication.
• Signs:
  • Positive × Positive = Positive
  • Negative × Positive = Negative
  • Negative × Negative = Positive
• Examples:
  • 8 × 3 = 24
  • 9 × 4 = 36
  • -5 × 3 = -15
  • -6 × -8 = 48
  • 54 ÷ 6 = 9
  • -45 ÷ 9 = -5

Order of Operations (PEMDAS)

• PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
• Priority:
  • Parentheses → Exponents → Multiplication/Division → Addition/Subtraction
• Examples:
  • 8 - 5 × 4: Perform multiplication first.
  • (8 - 5) × 4: Solve inside parentheses first.

Evaluating Algebraic Expressions

• Substitute given values for variables.
• Perform operations using the order of operations.
• Examples:
  • 4x + 3y - 2z with x=5, y=2, z=3
  • x² - y² ÷ 4z + 8 with x=8, y=6, z=4

Solving Linear Equations

• Isolate the variable on one side of the equation.
• Use inverse operations to simplify.
• Examples:
  • x + 4 = 11 → x = 7
  • 3y = 18 → y = 6
  • 2/3x = 9 → x = 13.5

Working with Fractions

• Simplify by factoring and canceling common terms.
• Cross multiplication can solve equations with two fractions.
• Examples:
  • 14x²y / 63xy = 2x / 9
  • x² / x⁵ = 1 / x³

Exponents and Factoring

• Exponents: Repeated multiplication of the same number.
• Negative exponents: Indicate reciprocal.
• Factoring: Break down numbers to their prime factors.
• Examples:
  • 2³ = 8
  • Negative exponents: x⁻² = 1/x²

Greatest Common Factor (GCF)

• Find common prime factors of given numbers.
• Examples:
  • GCF of 8 and 12 is 4
  • GCF of 27, 36, 45 is 9

Simplifying Fractions

• Factor fully and cancel common factors.
• Convert improper fractions and decimals.

Multiplying and Dividing Monomials

• Multiplying: Add exponents of like bases.
• Dividing: Subtract exponents of like bases.
• Examples:
  • x² × x³ = x⁵
  • y⁷ / y² = y⁵

Understanding Percentages

• Percentage calculations: Convert percentage to decimal for calculations.
• Mental math: Break percentages into known parts (10%, 5%, etc.) and sum.
• Examples:
  • 15% of 300 = 45
  • 25% of 400 = 100

Solving for Similar Triangles

• Use proportions to solve for unknowns in similar triangles.
• Example setup:
  • Triangle 1 height/base = Triangle 2 height/base

Additional Resource

• Udemy Course: Offers a comprehensive guide on topics covered, including additional sections on graphing, quadratic equations, and more advanced algebra topics.