Questions and Answers
To add or subtract algebraic fractions, or numerical fractions, the fractions must have a common denominator.
True
What is the least common denominator (LCD) of 5/6 and 3/8?
24
What is the LCD of 3/5, 5/16, and 9/20?
80
What is the LCD of 3/7b, 5/3c, and 11/21bc?
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What is the LCD of 3a/(a+1)^2, 2a/a+1, and 5a^3/(a+1)^3?
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What is the LCD of 6/a^2-7a+6 and 3/a^2-36?
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What is the LCD of 7/x^2+4x+4 and 5/4-x^2?
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What is the LCD of x/x^2-5x+4 and x+1/x^2-16?
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What is the LCD of x/x^3+y^3 and x/x+y?
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What is the equivalent numerator of 5/6 if the denominator is 24?
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What is the equivalent numerator of 3/5 if the denominator is 80?
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What is the equivalent numerator of 2/xy^2 if the denominator is x^3y^2?
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What is the equivalent numerator of 3a/(a+1)^2 if the denominator is (a + 1)³?
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What is the equivalent numerator of 6/a^2-7a+6 if the denominator is (a - 6)(a - 1)(a + 6)?
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What is the equivalent numerator of 2/x-2 if the denominator is (x-2)(x-1)(x-6)?
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What is the equivalent numerator of x-1/x^2-x-20 if the denominator is (x - 5)(x + 4)(x + 3)?
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Study Notes
Adding and Subtracting Algebraic Fractions
- To add or subtract algebraic fractions, having a common denominator is essential.
Finding the Least Common Denominator (LCD)
- For fractions 5/6 and 3/8, the LCD is 24.
- For fractions 3/5, 5/16, and 9/20, the LCD is 80.
- For fractions 3/7b, 5/3c, and 11/21bc, the LCD is 21bc.
- The LCD for 3a/(a+1)², 2a/(a+1), and 5a³/(a+1)³ is (a+1)³.
- For 6/(a² - 7a + 6) and 3/(a² - 36), the LCD is (a-6)(a-1)(a+6).
- For 7/(x² + 4x + 4) and 5/(4 - x²), the LCD is (x+2)²(2-x).
- For fractions x/(x² - 5x + 4) and (x+1)/(x² - 16), the LCD is (x-4)(x-1)(x+4).
- The LCD for x/(x³ + y³) and x/(x + y) is x³ + y³.
Equivalent Numerators
- For 5/6, if the denominator is changed to 24, the equivalent numerator is 20.
- For 3/5, changing the denominator to 80 results in an equivalent numerator of 48.
- The fraction 2/(xy²) changes to an equivalent numerator of 2x² if the denominator is x³y².
- For 3a/(a + 1)², the equivalent numerator with denominator (a + 1)³ is 3a(a + 1).
- For 6/(a² - 7a + 6), the equivalent numerator when using (a - 6)(a - 1)(a + 6) as the denominator is 6a + 36.
- The fraction 2/(x - 2) has an equivalent numerator of 2x² - 14x + 12 when the denominator is (x - 2)(x - 1)(x - 6).
- For x - 1/(x² - x - 20), the equivalent numerator when using (x - 5)(x + 4)(x + 3) as the denominator is x² + 2x - 3.
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Test your knowledge on adding and subtracting algebraic fractions with these flashcards. Each card will challenge you to determine common denominators for various fractions, enhancing your understanding of fraction operations. Perfect for reinforcing concepts in algebra.
