The image you uploaded is related to an interactive lesson on
multi-digit addition and specifically highlights the
Commutative Property of addition. Let's break down the problem and explain the solution:
---
Problem Explanation:
The image shows two addition problems:
1. \( 414 + 312 = 726 \)
2. \( 312 + 414 = 726 \)
The lesson emphasizes the
Commutative Property of addition, which states that the order in which numbers are added does not affect the sum. In other words:
\[
a + b = b + a
\]
---
Solution:
#### Step 1: Understand the Commutative Property
The Commutative Property of addition tells us that when adding two or more numbers, changing the order of the numbers will not change the result. For example:
\[
414 + 312 = 726
\]
and
\[
312 + 414 = 726
\]
Both expressions yield the same sum, \( 726 \).
#### Step 2: Verify the Addition
Let’s verify both additions step by step:
1.
First Addition: \( 414 + 312 \)
- Align the numbers by place value:
\[
\begin{array}{c@{}c@{}c@{}c}
& 4 & 1 & 4 \\
+ & 3 & 1 & 2 \\
\hline
\end{array}
\]
- Add the digits from right to left:
- Ones place: \( 4 + 2 = 6 \)
- Tens place: \( 1 + 1 = 2 \)
- Hundreds place: \( 4 + 3 = 7 \)
- Result: \( 414 + 312 = 726 \)
2.
Second Addition: \( 312 + 414 \)
- Align the numbers by place value:
\[
\begin{array}{c@{}c@{}c@{}c}
& 3 & 1 & 2 \\
+ & 4 & 1 & 4 \\
\hline
\end{array}
\]
- Add the digits from right to left:
- Ones place: \( 2 + 4 = 6 \)
- Tens place: \( 1 + 1 = 2 \)
- Hundreds place: \( 3 + 4 = 7 \)
- Result: \( 312 + 414 = 726 \)
#### Step 3: Confirm the Property
Both calculations confirm that:
\[
414 + 312 = 726
\]
and
\[
312 + 414 = 726
\]
Thus, the order of the addends does not affect the sum, demonstrating the Commutative Property.
---
Final Answer:
\[
\boxed{726}
\]
Parent Tip: Review the logic above to help your child master the concept of interactive 3 digit subtraction.
