By what number should `(-24)` be multiplied to get `(8)/(13)`?

Answer

To solve the problem of finding the number by which \(-24\) should be multiplied to get \(\frac{8}{13}\), we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
Let the unknown number be \(x\). The equation can be set up as:
\[ -24 \times x = \frac{8}{13} \]

2. **Isolate \(x\)**:
To find \(x\), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by \(-24\):
\[ x = \frac{8}{13} \div -24 \]

3. **Convert Division to Multiplication**:
Dividing by \(-24\) is the same as multiplying by its reciprocal. The reciprocal of \(-24\) is \(-\frac{1}{24}\):
\[ x = \frac{8}{13} \times -\frac{1}{24} \]

4. **Multiply the Fractions**:
Now, we multiply the fractions:
\[ x = \frac{8 \times -1}{13 \times 24} = \frac{-8}{312} \]

5. **Simplify the Fraction**:
We can simplify \(\frac{-8}{312}\). Both the numerator and the denominator can be divided by 8:
\[ x = \frac{-1}{39} \]

### Final Answer:
Thus, the number by which \(-24\) should be multiplied to get \(\frac{8}{13}\) is:
\[ \boxed{-\frac{1}{39}} \]