Solve (-2²)-(-3¾): Order of Operations with Negative Numbers

$(-2^2)-(-3\frac{3}{4})=$

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

• Step 1: Simplify $(-2^2)$.
• Step 2: Convert $-3\frac{3}{4}$ to an improper fraction.
• Step 3: Subtract the results from Step 1 and Step 2.

Now, let's work through each step:
Step 1: $-2^2$ means square the 2 first and then apply the negative: $-2^2 = -(2^2) = -4$.

Step 2: Convert $-3\frac{3}{4}$ into an improper fraction:
A mixed fraction $-3\frac{3}{4}$ can be represented as $-\left(3 + \frac{3}{4}\right) = -\left(\frac{12}{4} + \frac{3}{4}\right) = -\frac{15}{4}$.

Step 3: Subtract the results:
Subtract $-(-\frac{15}{4})$ from $-4$:
This is equivalent to $-4 + \frac{15}{4}$. To add these, convert $-4$ to a fraction with the same denominator: $-4 = -\frac{16}{4}$.
Now, $-\frac{16}{4} + \frac{15}{4} = -\frac{16 - 15}{4} = -\frac{1}{4}$.

Therefore, the solution to the problem is $-\frac{1}{4}$.