Both addition and multiplication of numbers are operations which are

### Concept & Logic This question tests foundational properties of basic arithmetic operations. * **Commutative Property:** The order of numbers does not change the result. ($a \ast b = b \ast a$) * **Associative Property:** The grouping of numbers does not change the result. ($(a \ast b) \ast c = a \ast (b \ast c)$) ### Step-by-Step Solution * **Test Addition:** * Commutativity: $2 + 3 = 5$, and $3 + 2 = 5$. Therefore, $a + b = b + a$. (Addition is commutative). * Associativity: $(2 + 3) + 4 = 5 + 4 = 9$, and $2 + (3 + 4) = 2 + 7 = 9$. Therefore, $(a+b)+c = a+(b+c)$. (Addition is associative). * **Test Multiplication:** * Commutativity: $2 \times 3 = 6$, and $3 \times 2 = 6$. Therefore, $a \times b = b \times a$. (Multiplication is commutative). * Associativity: $(2 \times 3) \times 4 = 6 \times 4 = 24$, and $2 \times (3 \times 4) = 2 \times 12 = 24$. Therefore, $(ab)c = a(bc)$. (Multiplication is associative). ### Exam Strategy & Shortcut **Fact Recall:** You don't need to test these in an exam. It is a universal mathematical axiom that both standard addition and multiplication are unconditionally commutative and associative across real numbers. Conversely, subtraction and division are *neither*. ### Common Pitfall Students sometimes confuse associative and commutative properties. Commutative is about the *commute* or moving of elements (order). Associative is about who you *associate* with (grouping/brackets). However, since both apply here, knowing the difference just ensures you are confident in your choice. ### Final Answer Therefore, the correct answer is **commutative and associative**.