name the property that is illustrated by the statement below: 5+(6+3)=(5+6)+3
associative
identity
commutative
distributive
associative
The property illustrated by the statement is the Associative Property.
The property illustrated by the statement "5+(6+3)=(5+6)+3" is the associative property.
To understand why, let's break it down step by step:
Step 1: 5 + (6+3)
Step 2: The inner parentheses (6+3) are evaluated to give 9. So, we have 5+9.
Step 3: The final result is 14.
Now, let's look at the other side of the equation:
Step 1: (5+6)+3
Step 2: The inner parentheses (5+6) are evaluated to give 11. So, we have 11+3.
Step 3: The final result is also 14.
The associative property states that the way in which numbers are grouped does not affect the result of an addition or multiplication operation. In this case, re-grouping the numbers using parentheses on both sides of the equation results in the same final answer of 14. This confirms that the equation demonstrates the associative property.