The rational number `(-8)/(35) ` is divided by a number and the result is `(-4)/(5)` What is the number ?

Answer

To solve the problem step by step, we need to find the number \( x \) such that when the rational number \(-\frac{8}{35}\) is divided by \( x \), the result is \(-\frac{4}{5}\).

### Step-by-Step Solution:

1. **Set Up the Equation**:
We know that dividing \(-\frac{8}{35}\) by \( x \) gives us \(-\frac{4}{5}\). We can set up the equation as follows:
\[ -\frac{8}{35} \div x = -\frac{4}{5} \]

2. **Rewrite Division as Multiplication**:
Dividing by \( x \) is the same as multiplying by its reciprocal. Therefore, we can rewrite the equation:
\[ -\frac{8}{35} \times \frac{1}{x} = -\frac{4}{5} \]

3. **Eliminate the Negative Signs**:
Since both sides of the equation have negative signs, we can eliminate them:
\[ \frac{8}{35} \times \frac{1}{x} = \frac{4}{5} \]

4. **Cross-Multiply**:
To solve for \( x \), we can cross-multiply:
\[ 8 \times 5 = 4 \times 35 \times x \]
This simplifies to:
\[ 40 = 140x \]

5. **Solve for \( x \)**:
Now, we can isolate \( x \) by dividing both sides by 140:
\[ x = \frac{40}{140} \]

6. **Simplify the Fraction**:
We can simplify \(\frac{40}{140}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 20:
\[ x = \frac{2}{7} \]

### Final Answer:
The number \( x \) is \(\frac{2}{7}\).