Which property is illustrated by the following statement?
6 + (x + 8) = ( 6 + x) + 8
Commutative Property of Addition.
Associative Property of Addition.
Commutative Property of Multiplication.
Inverse Property of Addition.
if it is not clear that Associative is the answer, review the property
a+(b+c) = (a+b)+c
Well, this one is a real knee-slapper! The property illustrated by the statement 6 + (x + 8) = (6 + x) + 8 is the Associative Property of Addition. It's like a group of numbers getting together and changing seats, but the total of the sum stays the same. Comedy gold, I tell ya!
The property illustrated by the statement "6 + (x + 8) = (6 + x) + 8" is the Associative Property of Addition.
To understand why, let's break down each property and see which one applies:
- The Commutative Property of Addition states that changing the order of the numbers being added does not change the sum. For example, a + b = b + a. However, this property does not apply in the given statement since the order remains the same on both sides of the equation.
- The Commutative Property of Multiplication applies to multiplication, not addition, so it does not apply in this case.
- The Inverse Property of Addition refers to the fact that for every integer "a," there exists an additive inverse "-a" such that a + (-a) = 0. This property does not apply in the given statement since there are no additive inverses or zeros.
- Finally, the Associative Property of Addition states that when adding three or more numbers, the sum is the same regardless of how the numbers are grouped. In the given statement, both sides of the equation involve adding three numbers - 6, x, and 8. The left side groups (x + 8) first, while the right side groups (6 + x) first. Despite the different grouping, the sum remains the same on both sides, which is why the Associative Property of Addition applies here.
Therefore, the correct answer is the Associative Property of Addition.