Algebra Review Video Notes

Adding and Subtracting Fractions

• Key concept: Common denominators necessary.
• Example:
  • 3/4 + 2/5
  • Need the same denominator (common denominator = 20)
  • Adjust fractions: multiply 3/4 by 5/5 and 2/5 by 4/4
  • Add adjusted fractions: 15/20 + 8/20 = 23/20
• Example:
  • 5/6 - 4/7
  • Multiply by other denominator: 5/6 by 7 and 4/7 by 6
  • Common denominator: 42
  • Subtract: 35/42 - 24/42 = 11/42

Multiplying Fractions

• Key concept: No need for common denominator.
• Example:
  • 7/5 * 4/3
  • Multiply across: 7 * 4 = 28 and 5 * 3 = 15
  • Result: 28/15
• Example:
  • 3/5 * 6/4
  • Multiply across: 3 * 6 = 18 and 5 * 4 = 20
  • Simplify: 18/20 → 9/10
• Simplify large numbers beforehand
  • Example: 28/63 * 56/35
  • Factorize and cancel first, then multiply
  • Result: 32/45*

Dividing Fractions

• Key concept: Use keep-change-flip strategy.
• Example:
  • 36/52 ÷ 27/65
  • Keep first fraction, change division to multiplication, flip second fraction
  • Simplify first, then multiply
  • Result: 5/3

Like Terms

• Key concept: Combine like terms for simplification.
• Example:
  • 5x + 3x² – 7x + 4x³ + 8x²
  • Combine like terms: 5x and -7x, 3x² and 8x²
  • Result: -2x + 11x² + 4x³

Multiplying Variables

• Key concept: Add exponents when multiplying, subtract when dividing.
• Example: x⁴ * x⁷ = x¹¹
• Example: x⁷ ÷ x⁴ = x³
• Raising powers: Multiply exponents
  • Example: (x³)⁴ = x¹²*

Solving Linear Equations

• Key concept: Isolate the variable.
• Example: Addition/Subtraction
  • x + 8 = 15
  • Subtract 8 both sides: x = 7
• Example: Multiplication/Division
  • 3x = 15
  • Divide by 3 both sides: x = 5
• Examples with fractions
  • Multiply by reciprocal to isolate variable
  • 2/3x = 8
  • Multiply by 3/2 on both sides: x = 12
• Multi-Step Equations: Combine steps to isolate the variable
  • 3x + 5 = 11
  • Subtract 5: 3x = 6
  • Divide by 3: x = 2

Inequalities

• Key concept: Solve similar to equations, but flip inequality when multiplying/dividing by a negative number.
• Graphing and Interval Notation
  • x > 2: Open circle on 2, shade right. Interval: (2, ∞)
  • x ≤ 1: Closed circle on 1, shade left. Interval: (-∞, 1]
• Solving: Treat similar to equations
  • Example: 5 + 3x > 14
  • Subtract 5: 3x > 9
  • Divide by 3: x > 3

Multiplying Polynomials

• FOIL method for binomials
  • (2x + 3)(3x - 5)
  • First: 2x*3x = 6x²
  • Outer: 2x*(-5) = -10x
  • Inner: 3*3x = 9x
  • Last: 3*(-5) = -15
  • Combine: 6x² – x – 15

Solving Equations with Fractions and Decimals

• Equations with fractions: Clear fractions first
  • 2/3x + 5 = 8
  • Multiply all terms by 3
  • Result: 2x + 15 = 24
  • Solve for x: x = 3
• Equations with decimals: Clear decimals first
  • 0.2 + 0.3x = 0.8
  • Multiply all terms by 10
  • Result: 2 + 3x = 8
  • Solve for x: x = 2

Tip: Practice often and review problems to master algebra concepts.

Exam preparation: Utilize quizzes and textbook problems for practice.