Commutative & associative properties of addition & multiplication - what about subtraction & division?
In this basic lesson I explain briefly what the commutative and associative properties of addition & multiplication mean. Then we check if subtraction & division also have those properties — turns out they don't. It's easy to prove that by using specific numbers and checking that the expressions given in the properties are not equal. For example, since 10 − 5 is not equal to 5 − 10, subtraction is not commutative.
After that, we check if two given expressions are equal for all values of the variable, using our knowledge of the properties of the operations. For example, is a + 5 equal to 5 + a?
Lastly, I simplify various expressions using the commutative and associative properties of addition and multiplication — and also the definition of multiplication.
See also
Math Mammoth Grade 7 curriculum (pre-algebra)