Questions: Multiple Choice Question Given the equation -1/2+1/3+2/4, select the LCD: 6 8 12 10

Multiple Choice Question Given the equation -1/2+1/3+2/4, select the LCD: 6 8 12 10
Transcript text: Multiple Choice Question Given the equation $-\frac{1}{2}+\frac{1}{3}+\frac{2}{4}$, select the LCD: 6 8 12 10
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Solution

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Solution Steps

To solve this problem, we need to find the least common denominator (LCD) of the fractions involved in the equation. The fractions are \(-\frac{1}{2}\), \(\frac{1}{3}\), and \(\frac{2}{4}\). The LCD is the smallest number that is a multiple of all the denominators (2, 3, and 4). We will calculate the least common multiple (LCM) of these numbers to find the LCD.

Step 1: Identify the Denominators

The given fractions are: \[ -\frac{1}{2}, \quad \frac{1}{3}, \quad \frac{2}{4} \] The denominators of these fractions are \(2\), \(3\), and \(4\).

Step 2: Calculate the Least Common Denominator (LCD)

To find the least common denominator, we need to determine the least common multiple (LCM) of the denominators \(2\), \(3\), and \(4\).

The LCM can be calculated as follows:

  • The prime factorization of \(2\) is \(2^1\).
  • The prime factorization of \(3\) is \(3^1\).
  • The prime factorization of \(4\) is \(2^2\).

The LCM takes the highest power of each prime: \[ \text{LCM}(2, 3, 4) = 2^2 \cdot 3^1 = 4 \cdot 3 = 12 \]

Final Answer

The least common denominator (LCD) is \[ \boxed{12} \]

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