Problem 77 - College Algebra Essentials

Question

State the name of the property illustrated. $$6+(2+7)=(6+2)+7$$

Step-by-Step Solution

Answer

The property illustrated is the Associative Property.

Step 1: Observe the equation

First, look closely at the equation \(6+(2+7)=(6+2)+7\). We see that the numbers being added remain the same on both sides, but the placement of the parenthesis, which dictates the order of operations, is different.

Step 2: Identify the property

Recall different mathematical properties, such as the commutative property, associative property, and distributive property. It becomes clear that the equation is demonstrating the associative property of addition.

Step 3: Definition of the property

The associative property of addition states that the way numbers are grouped does not change their sum. In other words, if you are adding three or more numbers, it doesn't matter how you group them, you will always get the same answer. This means that for any numbers a, b, and c: \(a+(b+c) = (a+b)+c\).