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5 3 plus 2 15 plus 10 is an example of the associative property for addition true or false?
False.
Which of the basic rules of arithmetic are true when you restrict the number system to the positive integers?
Closure with respect to addition and multiplication. Cummutative, Associative properties of addition and of multiplication. Distributive property of multiplication over addition.
Why does the commutative and associative properties don't hold true for subtraction and division but the identity properties do?
Consider the main operations to be addition and multiplication. In that case, subtraction is defined in terms of addition, for example, a - b = a + (-b) (where the last "-b" refers to the additive inverse of b), while a / b = a times 1/b (where 1/b is the multiplicative inverse of b). Now, assuming that commutative, etc. properties hold for addition and multiplication, check what happens with a subtraction. That should clarify everything. For example: a - b = a + (-b) whereas: b - a = b + (-a) which happens NOT to be the same as a - b, but rather its additive inverse.
What is associate property of multiplication?
According the associative property of multiplication, given any three elements a, b and c belonging to a set, (ab)c = a(bc) and so without ambiguity either can be written as abc. By contrast, (a/b)/c is not equal to a/(b/c). The first is a/bc, the second is ac/b which is true only if c2 = 1 ie c = -1 or c = 1
What is the associtive property of addition?
The associative property of addition states that given any three elements in the domain, their sum does not depend on the order in which the operation of addition is carried out. So, if x, y and z are three elements, then (x + y) + z = x + (y+ z) and either can be written as x + y + z without ambiguity. Note that this is not true for subtraction. (5 - 3) - 2 = 2 - 2 = 0 but 5 - (3 - 2) = 5 - 1 = 4
