- \( 3+4=4+3 \)

The equation you provided: - \(3 + 4 = 4 + 3\) demonstrates the **commutative property of addition** in mathematics. This property states that the order in which two numbers are added does not affect the sum. In other words, for any two numbers \(a\) and \(b\): \[ a + b = b + a \] **Example:** \[ 3 + 4 = 4 + 3 = 7 \] Both expressions yield the same result, **7**, regardless of the order of the addends. ### Importance of the Commutative Property 1. **Simplifies Calculations:** Knowing that numbers can be rearranged makes mental math and algebraic manipulations easier. 2. **Foundation for Algebra:** This property is fundamental in solving equations and understanding more complex mathematical concepts. 3. **Real-World Applications:** From computing totals to balancing equations in chemistry, the commutative property is widely applicable. ### Other Commutative Properties While you've shown the commutative property for addition, it's worth noting that multiplication also follows this property: \[ a \times b = b \times a \] **Example:** \[ 2 \times 5 = 5 \times 2 = 10 \] However, not all mathematical operations are commutative. For instance, subtraction and division do not generally follow the commutative property: \[ 5 - 3 \neq 3 - 5 \quad \text{and} \quad \frac{6}{2} \neq \frac{2}{6} \] Understanding which operations are commutative helps in accurately performing and simplifying mathematical expressions.