Problem Description:
The task involves using the
Associative Property of Addition to rewrite each addition fact. The Associative Property of Addition states that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. Mathematically, this is expressed as:
\[
(a + b) + c = a + (b + c)
\]
We will use this property to rewrite each given expression by changing the grouping of the numbers.
---
Step-by-Step Solution:
#### 1) \((12 + 3) + 5\)
Using the associative property, we can regroup the numbers:
\[
(12 + 3) + 5 = 12 + (3 + 5)
\]
So, the rewritten expression is:
\[
12 + (3 + 5)
\]
#### 2) \((10 + 3) + 7\)
Using the associative property, we can regroup the numbers:
\[
(10 + 3) + 7 = 10 + (3 + 7)
\]
So, the rewritten expression is:
\[
10 + (3 + 7)
\]
#### 3) \((14 + 6) + 2\)
Using the associative property, we can regroup the numbers:
\[
(14 + 6) + 2 = 14 + (6 + 2)
\]
So, the rewritten expression is:
\[
14 + (6 + 2)
\]
#### 4) \((5 + 8) + 6\)
Using the associative property, we can regroup the numbers:
\[
(5 + 8) + 6 = 5 + (8 + 6)
\]
So, the rewritten expression is:
\[
5 + (8 + 6)
\]
#### 5) \((12 + 5) + 2\)
Using the associative property, we can regroup the numbers:
\[
(12 + 5) + 2 = 12 + (5 + 2)
\]
So, the rewritten expression is:
\[
12 + (5 + 2)
\]
#### 6) \((11 + 4) + 2\)
Using the associative property, we can regroup the numbers:
\[
(11 + 4) + 2 = 11 + (4 + 2)
\]
So, the rewritten expression is:
\[
11 + (4 + 2)
\]
#### 7) \((9 + 3) + 2\)
Using the associative property, we can regroup the numbers:
\[
(9 + 3) + 2 = 9 + (3 + 2)
\]
So, the rewritten expression is:
\[
9 + (3 + 2)
\]
---
Final Answer:
\[
\boxed{
\begin{aligned}
1) & \quad 12 + (3 + 5) \\
2) & \quad 10 + (3 + 7) \\
3) & \quad 14 + (6 + 2) \\
4) & \quad 5 + (8 + 6) \\
5) & \quad 12 + (5 + 2) \\
6) & \quad 11 + (4 + 2) \\
7) & \quad 9 + (3 + 2)
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of properties of addition worksheet 2nd.