Solve: (-1/6) - (+4 2/4) Mixed Number Subtraction

$(-\frac{1}{6})-(+4\frac{2}{4})=$

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Simplify the improper fraction, if possible.
• Step 3: Find a common denominator for the fractions.
• Step 4: Subtract the fractions by rewriting them with a common denominator.
• Step 5: Simplify the result, if needed.

Now, let's work through each step:
Step 1: $+4\frac{2}{4}$ is first converted to an improper fraction:

$4\frac{2}{4} = 4 + \frac{2}{4}$. Since $\frac{2}{4}$ can be simplified to $\frac{1}{2}$, it becomes $4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}$. Thus, $+4\frac{2}{4} = \frac{9}{2}$.

Step 2: Simplification has already been done in the conversion.

Step 3: Determine a common denominator for $-\frac{1}{6}$ and $\frac{9}{2}$. The least common denominator between 6 and 2 is 6.

Step 4: Rewrite each fraction with the common denominator:

• $-\frac{1}{6}$ remains as $-\frac{1}{6}$.
• $\frac{9}{2}$ needs to be converted to have a denominator of 6: $\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}$.

Now, perform the subtraction:

$-\frac{1}{6} - \frac{27}{6} = \frac{-1 - 27}{6} = \frac{-28}{6}$.

Step 5: Simplify the result: $\frac{-28}{6} = \frac{-14}{3}$. This can be expressed as a mixed number $-4\frac{2}{3}$.

Therefore, the solution to the problem is $-4\frac{2}{3}$, which matches the correct choice: $-4\frac{2}{3}$.