Solve -14/7 + (-3) - 1/2 - (-1/4): Combined Operations with Fractions

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

• Step 1: Simplify $-\frac{14}{7}$.
• Step 2: Perform arithmetic operations in sequence, converting all parts as necessary.
• Step 3: Combine the fractions into a single fraction and simplify.

Now, let's work through each step:
Step 1: Simplify $-\frac{14}{7}$. Since $14 \div 7 = 2$, $-\frac{14}{7} = -2$.

Step 2: We rewrite the expression properly:
$-2 + (-3) - \frac{1}{2} - (-\frac{1}{4})$.

Simplify and operate on each part:
Convert $-3$ to a fraction with a denominator of 1: $-\frac{3}{1}$.
Evaluate the subtraction of a negative: $-(-\frac{1}{4}) = \frac{1}{4}$.

Rewrite the expression using fractions:
$-\frac{2}{1} + (-\frac{3}{1}) - \frac{1}{2} + \frac{1}{4}$.

Step 3: Add and subtract the fractions using a common denominator. The least common denominator for 1, 2, and 4 is 4.
$-\frac{2}{1} = -\frac{8}{4}$,
$-\frac{3}{1} = -\frac{12}{4}$,
$-\frac{1}{2} = -\frac{2}{4}$.

Combining these, we get:
$-\frac{8}{4} - \frac{12}{4} - \frac{2}{4} + \frac{1}{4} = \frac{-8 - 12 - 2 + 1}{4}$.

Simplify the numerator: $-8 - 12 - 2 + 1 = -21$.
Thus, we have:
$\frac{-21}{4}$.

Therefore, the solution to the problem is $-\frac{21}{4}$, which corresponds to choice 3.