If a, b and c are rational numbers, then associativity of rational numbers under multiplication is given by

Options

A. `a xx b = b xx a `
B. `a + ( b + c) = (a + b ) + c`
C. ` a xx ( b xx c) = (a xx b) xx c`
D. ` a xx ( b + c) = (a xx b) + (a xx c)`

Answer

To determine the associativity of rational numbers under multiplication, we need to understand the property of associativity. The associativity property states that when multiplying three numbers, the way in which the numbers are grouped does not affect the product.

### Step-by-Step Solution:

1. **Understanding Associativity**: The property of associativity for multiplication states that for any three numbers \(a\), \(b\), and \(c\):
\[ (a \times b) \times c = a \times (b \times c) \]
This means that whether we multiply \(a\) and \(b\) first, or \(b\) and \(c\) first, the result will be the same.

2. **Applying to Rational Numbers**: Since \(a\), \(b\), and \(c\) are rational numbers, we can apply the same property:
\[ (a \times b) \times c = a \times (b \times c) \]
This holds true for rational numbers as well.

3. **Identifying the Correct Option**: In the context of the question, we need to find the correct representation of this property among the given options. The correct representation of the associativity property under multiplication should be:
\[ (a \times b) \times c = a \times (b \times c) \]
We need to check the options provided to find one that matches this expression.

4. **Checking the Options**:
- If option A has addition instead of multiplication, it is incorrect.
- If option B has addition, it is also incorrect.
- If option C correctly states the multiplication with the proper grouping, then it is the correct answer.

5. **Conclusion**: After analyzing the options, we find that option C correctly represents the associativity of rational numbers under multiplication.

### Final Answer:
The associativity of rational numbers under multiplication is given by:
\[ (a \times b) \times c = a \times (b \times c) \]
The correct option is **C**.