Questions and Answers
What is an algebraic fraction?
Fraction with algebraic terms and expressions in the denominator and/or numerator.
Calculate $\frac{2x}{5} + \frac{4y}{5}$?
$\frac{2x + 4y}{5}$
What is the LCD of $\frac{3x}{10}$ and $\frac{2y}{15}$?
30
Convert $\frac{2x}{7}$ to an equivalent fraction with a denominator of 21.
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What does $\frac{3x}{11} + \frac{5x}{11}$ equal?
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What does $\frac{4a}{3} + \frac{2a}{5}$ equal?
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What does $\frac{6k}{5} - \frac{3k}{10}$ equal?
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Study Notes
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.
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Description
This set of flashcards focuses on key concepts related to adding and subtracting algebraic fractions in algebra. It covers definitions, calculations, and techniques for finding the least common denominator (LCD). Perfect for students looking to reinforce their understanding of algebraic fractions.
