Write an equivalent expression to 𝑥+(𝑦+𝑧), using the Associative Property of Addition.

Answer 1

According to the Associative Property of Addition, the way in which numbers are grouped in addition does not change their sum. This property states that \( (a + b) + c = a + (b + c) \).

To rewrite the expression \( x + (y + z) \) using the Associative Property, you can regroup the terms. The equivalent expression would be:

\[ (x + y) + z \]

Both \( x + (y + z) \) and \( (x + y) + z \) yield the same result due to the associative nature of addition.

Answer 2

can you break down in a simpler way and make the answer clearer

Answer 3

Sure! Let’s break it down step by step:

1. Understanding the Original Expression: You start with the expression \( x + (y + z) \). Here, \( y + z \) is grouped together.

2. Associative Property of Addition: This property tells us that when we add three or more numbers, we can change the grouping without changing the result. In simpler terms, it means we can add the numbers in any order.

3. Rearranging the Grouping: You can take the expression \( x + (y + z) \) and regroup it. Instead of adding \( y + z \) first, you can add \( x + y \) first.

4. Final Equivalent Expression: After regrouping, your new expression becomes \( (x + y) + z \).

So, the equivalent expression using the Associative Property of Addition is:

\[ (x + y) + z \]

This means both expressions \( x + (y + z) \) and \( (x + y) + z \) will give you the same result when you evaluate them.