By what number should `(-33)/(8)` be divided to get `(-11)/(2)` ?

Answer

To solve the problem, we need to find the number \( x \) by which \(-\frac{33}{8}\) should be divided to obtain \(-\frac{11}{2}\).

Let's denote the equation as follows:

\[ -\frac{33}{8} \div x = -\frac{11}{2} \]

### Step 1: Rewrite the Division as Multiplication
We can rewrite the division as multiplication by the reciprocal:

\[ -\frac{33}{8} = -\frac{11}{2} \cdot x \]

### Step 2: Isolate \( x \)
To isolate \( x \), we can rearrange the equation:

\[ x = -\frac{33}{8} \div -\frac{11}{2} \]

### Step 3: Dividing by a Fraction
Dividing by a fraction is the same as multiplying by its reciprocal. Thus, we have:

\[ x = -\frac{33}{8} \cdot -\frac{2}{11} \]

### Step 4: Simplify the Expression
Now, we can simplify the multiplication:

\[ x = \frac{33 \cdot 2}{8 \cdot 11} \]

Calculating the numerator and denominator:

\[ x = \frac{66}{88} \]

### Step 5: Reduce the Fraction
Now, we can simplify \(\frac{66}{88}\):

\[ x = \frac{66 \div 22}{88 \div 22} = \frac{3}{4} \]

### Final Answer
Thus, the number by which \(-\frac{33}{8}\) should be divided to get \(-\frac{11}{2}\) is:

\[ \boxed{\frac{3}{4}} \]