commutative property

Putting on your left sock then your right gives the same result as the other way around — the order did not matter. The commutative property says that for addition and for multiplication, swapping the order of two numbers does not change the answer: a + b = b + a, and a × b = b × a. So 3 + 5 and 5 + 3 are both 8.

This freedom is so familiar that we use it without noticing, rearranging a long sum to add the easy pairs first, or reordering factors to make a product simpler. In algebra it lets you write 2x rather than x2, and rearrange terms while keeping an expression's value intact.

Crucially, subtraction and division are not commutative. 7 − 3 = 4 but 3 − 7 = −4, and 8 ÷ 2 = 4 but 2 ÷ 8 = 1/4. Order genuinely matters for those operations, so you may never reorder a difference or a quotient the way you would a sum or a product.