The sum of any number and zero is the original number. For example a+0=a
Commutative or Associative?
Example of Commutative 3x4=4x3 (a x b + b x a)
Example of Associative : (5+10)+20, 5+(10+20)
(a+b)+c=a+(b+c)
In this scenario, the property is commutative.
To determine whether a mathematical property is commutative or associative, you need to understand their definitions:
1. Commutative Property: This property holds when the order of the numbers being added or multiplied doesn't affect the result. In other words, the numbers can be rearranged without changing the outcome.
2. Associative Property: This property exists when the grouping of numbers being added or multiplied doesn't influence the result. You can change the grouping of the numbers without affecting the final answer.
Let's consider the given example: a + 0 = a
Since addition is commutative, it doesn't matter whether we write a + 0 or 0 + a. Both expressions will yield the same result, which is simply 'a.' The order of the operands doesn't affect the outcome, so it follows the commutative property.
On the other hand, the example you provided for the associative property is incorrect. The associative property applies to addition and multiplication, not to the combination of both operations. So, (5 + 10) + 20 and 5 + (10 + 20) are both valid examples of the associative property in action.
Remember, when determining whether a property is commutative or associative, you need to consider which operation is being performed (addition, multiplication) and check if changing the order or grouping affects the outcome.
The property described is an example of the Commutative property, as it states that the order of the numbers being added or multiplied does not affect the result.
An example of Commutative property in addition is: 3 + 5 = 5 + 3
An example of Commutative property in multiplication is: 2 x 8 = 8 x 2
The Associative property, on the other hand, states that the grouping of numbers being added or multiplied does not affect the result.
An example of Associative property in addition is: (2 + 4) + 3 = 2 + (4 + 3)
An example of Associative property in multiplication is: (6 x 2) x 4 = 6 x (2 x 4)