Name the property of multiplication illustrated by the following statements:
(i) `(-15)/(8)xx(-12)/(7) = (-12)/(7)xx (-15)/(8)`
(ii) `((-2)/(3) xx (7)/(9)) xx (-9)/(5) = (-2)/(3)xx ((7)/(9)xx (-9)/(5))`
(iii) `(-3)/(4) xx ((-5)/(6)+(7)/(8))= ((-3)/(4)xx (-5)/(6))+((-3)/(4)xx (7)/(8))`
(iv) `(-16)/(9) xx 1 = 1 xx (-16)/(9) = (-16)/(9)`
(v) `(-11)/(15)xx (15)/(-11) =(15)/(-11)xx (-11)/(15) = 1`
(vi) `(-7)/(5) xx 0 =0`

Answer

To solve the question, we will identify the property of multiplication illustrated by each of the given statements step by step.

### Step-by-Step Solution:

1. **Statement (i)**:
\[ \frac{-15}{8} \times \frac{-12}{7} = \frac{-12}{7} \times \frac{-15}{8} \]
- This statement shows that the order of multiplication does not change the product.
- **Property**: **Commutative Law of Multiplication**.

2. **Statement (ii)**:
\[ \left(\frac{-2}{3} \times \frac{7}{9}\right) \times \frac{-9}{5} = \frac{-2}{3} \times \left(\frac{7}{9} \times \frac{-9}{5}\right) \]
- This statement shows that when multiplying three numbers, the way in which the numbers are grouped does not change the product.
- **Property**: **Associative Law of Multiplication**.

3. **Statement (iii)**:
\[ \frac{-3}{4} \times \left(\frac{-5}{6} + \frac{7}{8}\right) = \left(\frac{-3}{4} \times \frac{-5}{6}\right) + \left(\frac{-3}{4} \times \frac{7}{8}\right) \]
- This statement shows that multiplication distributes over addition.
- **Property**: **Distributive Property**.

4. **Statement (iv)**:
\[ \frac{-16}{9} \times 1 = 1 \times \frac{-16}{9} = \frac{-16}{9} \]
- This statement shows that multiplying any number by 1 gives the same number.
- **Property**: **Multiplicative Identity Property**.

5. **Statement (v)**:
\[ \frac{-11}{15} \times \frac{15}{-11} = \frac{15}{-11} \times \frac{-11}{15} = 1 \]
- This statement shows that a number multiplied by its reciprocal equals 1.
- **Property**: **Multiplicative Inverse Property**.

6. **Statement (vi)**:
\[ \frac{-7}{5} \times 0 = 0 \]
- This statement shows that any number multiplied by 0 results in 0.
- **Property**: **Multiplicative Property of Zero**.

### Summary of Properties:
- (i) Commutative Law of Multiplication
- (ii) Associative Law of Multiplication
- (iii) Distributive Property
- (iv) Multiplicative Identity Property
- (v) Multiplicative Inverse Property
- (vi) Multiplicative Property of Zero