is
4(7)(5)= 4(5)(7) associative property or commutative?
I don't really get the difference between the two properties.
The property being referred to in the given equation is the commutative property of multiplication. To understand the difference between the commutative property and the associative property, let's break it down:
1. Commutative Property: This property applies to operations like addition and multiplication. It states that changing the order of the numbers being added or multiplied does not affect the result. For example, in the equation 4 * 5, you can switch the order to get the same result: 5 * 4. This also applies to addition, where the order of numbers can be changed without affecting the result.
2. Associative Property: Similar to the commutative property, the associative property also applies to addition and multiplication. This property states that changing the grouping of numbers being added or multiplied will not change the result. For example, in the equation (2 + 3) + 4, you can group the numbers in a different way and still get the same result: 2 + (3 + 4).
Now let's apply these properties to the given equation, 4(7)(5) = 4(5)(7):
To determine whether it is commutative or associative, we need to examine if changing the order of the multiplication affects the result.
In this equation, we have 4 multiplied by 7, then multiplied by 5. And on the right side, we have 4 multiplied by 5, then multiplied by 7.
Since the order of the multiplication has changed, and yet the equation is still true, we can conclude that this is an example of the commutative property of multiplication.
In summary, the difference between the commutative and associative properties is that the commutative property allows you to change the order of the numbers being added or multiplied, while the associative property allows you to change the grouping of the numbers being added or multiplied.
Actually, what yu've written is a bit of both.
Commutative is:
4 + 5 = 5 + 4
Associative is:
(4 + 5) + 2 = 4 + (5 + 2)
So 4 * (7*5) = (4*7) * 5 is Associative.
but
5*7 = 7*5 is Commutative.