Solve: -1/2 + 3/4 - 1/5 - 4/5 Fraction Addition and Subtraction

To solve this problem, we must simplify the expression $-\frac{1}{2} + \frac{3}{4} + (-\frac{1}{5}) + (-\frac{4}{5})$.

First, we need to find the least common denominator (LCD) for the fractions 2, 4, and 5. The LCD is 20.

Next, we convert each fraction to an equivalent fraction with the common denominator of 20:

• $-\frac{1}{2}$ becomes $-\frac{10}{20}$
• $\frac{3}{4}$ becomes $\frac{15}{20}$
• $-\frac{1}{5}$ becomes $-\frac{4}{20}$
• $-\frac{4}{5}$ becomes $-\frac{16}{20}$

Now we perform the addition and subtraction:

$-\frac{10}{20} + \frac{15}{20} - \frac{4}{20} - \frac{16}{20}$

Combine the numerators:

$-10 + 15 - 4 - 16 = -15$

Thus, the resulting fraction is:

$-\frac{15}{20}$

We simplify $-\frac{15}{20}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

$-\frac{15}{20} = -\frac{3}{4}$

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