Name the multiplication property of rational numbers shown below :
(iv) `(-7)/(5)xx(5)/(-7)=1`

Answer

To solve the question, we need to identify the multiplication property of rational numbers demonstrated by the equation:

\[ \frac{-7}{5} \times \frac{5}{-7} = 1 \]

### Step-by-step Solution:

1. **Identify the Rational Numbers**:
We have two rational numbers:
- The first number is \(\frac{-7}{5}\)
- The second number is \(\frac{5}{-7}\)

2. **Understand the Multiplication**:
We are multiplying these two rational numbers together:
\[ \frac{-7}{5} \times \frac{5}{-7} \]

3. **Multiply the Numerators and Denominators**:
When multiplying fractions, we multiply the numerators together and the denominators together:
\[ \text{Numerator: } -7 \times 5 = -35 \]
\[ \text{Denominator: } 5 \times -7 = -35 \]
Therefore, we have:
\[ \frac{-35}{-35} \]

4. **Simplify the Fraction**:
Since both the numerator and denominator are the same (and negative), we can simplify:
\[ \frac{-35}{-35} = 1 \]

5. **Identify the Property**:
The property illustrated here is that when a number is multiplied by its multiplicative inverse (or reciprocal), the result is 1. In this case, \(\frac{-7}{5}\) is multiplied by its multiplicative inverse \(\frac{5}{-7}\).

### Conclusion:
The multiplication property of rational numbers shown in the equation \(\frac{-7}{5} \times \frac{5}{-7} = 1\) is known as the **Multiplicative Inverse**.

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