Algebra Class Flashcards: Adding & Subtracting Fractions

Algebraic Fractions

• An algebraic fraction is defined as a fraction that includes algebraic terms in either the numerator or the denominator.

Adding Algebraic Fractions

• Example of calculating the sum: ( \frac{2x}{5} + \frac{4y}{5} ) simplifies to ( \frac{2x + 4y}{5} ).
• When adding fractions with the same denominator, simply combine the numerators.

Least Common Denominator (LCD)

• The LCD of ( \frac{3x}{10} ) and ( \frac{2y}{15} ) is 30, determined by identifying the least common multiple (LCM) of the denominators 10 and 15.

Converting Fractions

• To convert ( \frac{2x}{7} ) into an equivalent fraction with a denominator of 21, multiply both numerator and denominator by 3, resulting in ( \frac{6x}{21} ).

Example of Adding Fractions with Different Denominators

• For ( \frac{4a}{3} + \frac{2a}{5} ):
  • Identify the LCD (15).
  • Convert each fraction:
    • Multiply ( \frac{4a}{3} ) by ( \frac{5}{5} ) to get ( \frac{20a}{15} ).
    • Multiply ( \frac{2a}{5} ) by ( \frac{3}{3} ) to get ( \frac{6a}{15} ).
  • Summing gives ( \frac{26a}{15} ).

Example of Subtracting Fractions

• To solve ( \frac{6k}{5} - \frac{3k}{10} ):
  • Identify the LCD as 10.
  • Convert ( \frac{6k}{5} ) by multiplying by ( \frac{2}{2} ) to get ( \frac{12k}{10} ).
  • Proceed with subtraction: ( \frac{12k}{10} - \frac{3k}{10} = \frac{9k}{10} ).

Key Takeaways

• Always identify the LCD when adding or subtracting algebraic fractions.
• Convert fractions to have the same denominator before performing operations.
• Simplifying the final result is important after calculations.