Question

what does commutative property mean

Answer 1

The commutative property is a fundamental property in mathematics that applies to certain operations, such as addition and multiplication. It states that the order in which two numbers are added or multiplied does not affect the result.

1. **Commutative Property of Addition**: This means that for any numbers \( a \) and \( b \):
\[
a + b = b + a
\]
For example, \( 3 + 5 = 5 + 3 = 8 \).

2. **Commutative Property of Multiplication**: This states that for any numbers \( a \) and \( b \):
\[
a \times b = b \times a
\]
For example, \( 4 \times 6 = 6 \times 4 = 24 \).

It's important to note that not all operations are commutative. For example, subtraction and division do not satisfy the commutative property:
- \( 5 - 3 \neq 3 - 5 \)
- \( 6 \div 2 \neq 2 \div 6 \)

The commutative property is often utilized in algebra and helps simplify expressions and solve equations.