Algebra Review Video

Introduction

• Purpose: Review basic algebra concepts for students returning to school.
• Key topics: Operations with fractions, like terms, solving equations, and inequalities.

Operations with Fractions

• Addition & Subtraction:
  • Fractions must have the same denominator.
  • Example: For ( \frac{3}{4} + \frac{2}{5} ), find common denominator (20), adjust fractions, and then add.
  • Example: ( \frac{5}{6} - \frac{4}{7} ), find common denominator (42), adjust fractions, then subtract.
• Multiplication:
  • Multiply directly across numerators and denominators.
  • Example: ( \frac{7}{5} \times \frac{4}{3} = \frac{28}{15} ).
  • Simplify if possible: ( \frac{18}{20} = \frac{9}{10} ) by canceling common factors.
• Division:
  • Keep, Change, Flip: Keep the first fraction, change division to multiplication, and flip the second fraction.
  • Example: ( \frac{36}{52} \div \frac{27}{65} ) becomes ( \frac{36}{52} \times \frac{65}{27} ).

Like Terms

• Addition & Subtraction: Combine only like terms (same variables raised to the same power).
  • Example: Combine (5x) and (-7x), not (5x) and (3x^2).

Exponent Rules

• Multiplication: Add exponents ((x^m \times x^n = x^{m+n})).
• Division: Subtract exponents ((x^m \div x^n = x^{m-n})).
• Power of a Power: Multiply exponents (((x^m)^n = x^{m \cdot n})).

Distributive Property

• Single Term: Distribute single term over sum or difference.
• FOIL Method: Use for multiplying two binomials.
• General Distribution: Used for products of polynomials of any size.

Solving Equations

• Basic Equations: Isolate variable by inverse operations.
• Equations with Fractions: Clear fractions by multiplying by common denominators.
• Multi-step Equations: Simplify through distribution and combining like terms.
• Equations with Variables on Both Sides: Isolate variables on one side and constants on the other.

Solving Inequalities

• Treat inequalities like equations but reverse inequality when multiplying/dividing by a negative.
• Graph solutions on a number line and express using interval notation.

Tips for Algebra Success

• Practice by solving homework problems and reviewing examples.
• Use online courses for additional explanations and practice quizzes.

Additional Resources

• Udemy Course: Comprehensive algebra course available with quizzes and practice problems.
• Topics Covered: Includes arithmetic, fractions, equations, inequalities, polynomials, factoring, quadratic equations, exponential functions, and more.