What are associative for rational numbers?

• A) Multiplication and addition
• B) Multiplication and subtraction
• C) Division and subtraction
• D) Division and subtraction

Associative properties refer to how numbers can be grouped in operations without changing the result. For rational numbers, the operations that exhibit this property are addition and multiplication.

Associative Properties Explained

Here’s a closer look at the two operations:

• Addition: For any rational numbers a, b, and c, the equation (a + b) + c = a + (b + c) holds true.
• Multiplication: Similarly, for multiplication, (a × b) × c = a × (b × c) is also valid.

Why Not Subtraction or Division?

Subtraction and division do not follow the associative property. For example:

• With subtraction: (5 - 3) - 2 ≠ 5 - (3 - 2)
• With division: (8 ÷ 4) ÷ 2 ≠ 8 ÷ (4 ÷ 2)

Thus, the correct answer to your question is A) Multiplication and addition.