By what number should `(-44)/(9)` be divided to get `(-11)/(3)`?

Answer

To solve the problem "By what number should \(-\frac{44}{9}\) be divided to get \(-\frac{11}{3}\)?", we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
We need to find a number \(x\) such that:
\[ \frac{-44}{9} \div x = \frac{-11}{3} \]
This can be rewritten as:
\[ \frac{-44}{9} = \frac{-11}{3} \times x \]

2. **Eliminate the Negative Signs**:
Since both sides of the equation have negative signs, we can cancel them out:
\[ \frac{44}{9} = \frac{11}{3} \times x \]

3. **Isolate \(x\)**:
To isolate \(x\), we can multiply both sides by the reciprocal of \(\frac{11}{3}\):
\[ x = \frac{44}{9} \div \frac{11}{3} \]
This is the same as:
\[ x = \frac{44}{9} \times \frac{3}{11} \]

4. **Multiply the Fractions**:
Now, we multiply the fractions:
\[ x = \frac{44 \times 3}{9 \times 11} \]

5. **Calculate the Numerator and Denominator**:
- Calculate the numerator: \(44 \times 3 = 132\)
- Calculate the denominator: \(9 \times 11 = 99\)
Thus, we have:
\[ x = \frac{132}{99} \]

6. **Simplify the Fraction**:
To simplify \(\frac{132}{99}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 33:
\[ x = \frac{132 \div 33}{99 \div 33} = \frac{4}{3} \]

### Final Answer:
The number by which \(-\frac{44}{9}\) should be divided to get \(-\frac{11}{3}\) is:
\[ \boxed{\frac{4}{3}} \]