Question

Can you discuss the differences between the associative and commutative properties

Answer 1

Commutative talks about the inherent order of the numbers and associative is about the order of grouping.

Explanation:

The commutative property is basically that: A + B = B + A or A * B = B * A

In other words, for commutative, whatever order you write the sum, it doesn't matter because you'll get the same result. However, this only works if the mathematical symbol is addition or multiplication; it doesn't work for division and subtraction.

The associative property says that: A + B + C = A + (B + C) = (A + B) + C or A * B * C = A * (B * C) = (A * B) * C.

In other words, for associative, wherever you place the parentheses, or however you group the numbers, it doesn't matter because you're going to get the same answer. However, again, this only works for all addition or all multiplication, not division or subtraction.

Basically, the difference is that commutative talks about the inherent order of the numbers and associative is about the order of grouping. Regardless, both say that you get the same result no matter what kind of order you put the numbers in.

Answer 2

Commutative property:

a + b = b + a

Or

a × b = b × a

Basically it's between two values and order doesn't matter

Associative property:

(a + b) + c = a + (b + c)

If you have more than two terms, you can start solving with any two