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Questions and Answers
To add or subtract algebraic fractions, or numerical fractions, the fractions must have a common denominator.
To add or subtract algebraic fractions, or numerical fractions, the fractions must have a common denominator.
True (A)
What is the least common denominator (LCD) of 5/6 and 3/8?
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?
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?
What is the LCD of 3/7b, 5/3c, and 11/21bc?
What is the LCD of 3a/(a+1)^2, 2a/a+1, and 5a^3/(a+1)^3?
What is the LCD of 3a/(a+1)^2, 2a/a+1, and 5a^3/(a+1)^3?
What is the LCD of 6/a^2-7a+6 and 3/a^2-36?
What is the LCD of 6/a^2-7a+6 and 3/a^2-36?
What is the LCD of 7/x^2+4x+4 and 5/4-x^2?
What is the LCD of 7/x^2+4x+4 and 5/4-x^2?
What is the LCD of x/x^2-5x+4 and x+1/x^2-16?
What is the LCD of x/x^2-5x+4 and x+1/x^2-16?
What is the LCD of x/x^3+y^3 and x/x+y?
What is the LCD of x/x^3+y^3 and x/x+y?
What is the equivalent numerator of 5/6 if the denominator is 24?
What is the equivalent numerator of 5/6 if the denominator is 24?
What is the equivalent numerator of 3/5 if the denominator is 80?
What is the equivalent numerator of 3/5 if the denominator is 80?
What is the equivalent numerator of 2/xy^2 if the denominator is x^3y^2?
What is the equivalent numerator of 2/xy^2 if the denominator is x^3y^2?
What is the equivalent numerator of 3a/(a+1)^2 if the denominator is (a + 1)³?
What is the equivalent numerator of 3a/(a+1)^2 if the denominator is (a + 1)³?
What is the equivalent numerator of 6/a^2-7a+6 if the denominator is (a - 6)(a - 1)(a + 6)?
What is the equivalent numerator of 6/a^2-7a+6 if the denominator is (a - 6)(a - 1)(a + 6)?
What is the equivalent numerator of 2/x-2 if the denominator is (x-2)(x-1)(x-6)?
What is the equivalent numerator of 2/x-2 if the denominator is (x-2)(x-1)(x-6)?
What is the equivalent numerator of x-1/x^2-x-20 if the denominator is (x - 5)(x + 4)(x + 3)?
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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