Name the property that is illustrated by the statement below:
`2\ +\ \left(7\ +\ 3\right)\ =\ \left(2\ +\ 7\right)\ +\ 3`
The property that is illustrated by the statement is the associative property of addition.
The property illustrated by the statement is the associative property of addition.
The property illustrated by the statement is the Associative Property of Addition.
To understand why, you can break down the equation step by step:
1. The left side of the equation, `2 + (7 + 3)`, represents adding 7 and 3 first, which equals 10. Then, you add 2 to that result, which makes the sum 12.
2. The right side of the equation, `(2 + 7) + 3`, represents adding 2 and 7 first, which equals 9. Then, you add 3 to that result, making the sum 12.
Since the left side and the right side of the equation give the same final result (both equal 12), it demonstrates the Associative Property of Addition. This property states that when adding three or more numbers, the grouping of the numbers does not affect the total.
In other words, you can change the grouping of the numbers without changing the sum. This property is helpful in simplifying mathematical expressions and evaluating equations.