Skip to main content
Back

Least Common Denominators quiz

Control buttons has been changed to "navigation" mode.
1/15
  • What is the first step in finding the least common denominator (LCD) for rational expressions?
    The first step is to factor each denominator completely into prime factors and variables.
  • How do you determine which powers of each factor to use when finding the LCD?
    You use the highest power of each unique factor present in any denominator.
  • What is the LCD of 30x and 20x^2?
    The LCD is 60x^2, found by multiplying the highest powers of all unique factors: 3, 2^2, 5, and x^2.
  • Why do you only write each unique prime factor once when finding the LCD?
    Because the LCD requires only the highest power of each unique factor, not repeated factors.
  • How do you handle variables like x when finding the LCD?
    Include the variable raised to its highest power found in any denominator.
  • What is the process for finding the LCD of denominators like x + 5 and x^2 + 7x + 10?
    Factor each denominator completely, then multiply the unique factors together to get the LCD.
  • How do you factor x^2 + 7x + 10?
    It factors into (x + 2)(x + 5) because 2 and 5 multiply to 10 and add to 7.
  • What is the LCD for denominators x + 5 and (x + 2)(x + 5)?
    The LCD is (x + 2)(x + 5), including each unique factor once.
  • What is the next step after finding the LCD when writing equivalent rational expressions?
    Identify the missing factors in each denominator compared to the LCD.
  • How do you rewrite a rational expression to have the LCD as its denominator?
    Multiply both the numerator and denominator by the missing factors needed to reach the LCD.
  • If the LCD is 60, what missing factor does 30 need to reach the LCD?
    30 needs a factor of 2 to reach 60, since 30 × 2 = 60.
  • If the LCD is 60, what missing factor does 20 need to reach the LCD?
    20 needs a factor of 3 to reach 60, since 20 × 3 = 60.
  • How do you rewrite 1/30x to have a denominator of 60x^2?
    Multiply numerator and denominator by 2x, resulting in 2x/60x^2.
  • How do you rewrite 1/20x^2 to have a denominator of 60x^2?
    Multiply numerator and denominator by 3, resulting in 3/60x^2.
  • Why is finding the LCD important when adding or subtracting rational expressions?
    It allows you to rewrite expressions with a common denominator, making addition or subtraction possible.