The image you've uploaded is a worksheet on the
Associative Property of Addition, which states:
>
(a + b) + c = a + (b + c)
This means that when adding three or more numbers, the way in which the numbers are grouped does
not affect the sum. The order of the numbers stays the same, but the grouping (parentheses) changes.
---
✔ Let's go through the problems and solutions step by step.
---
🔹 Top Section: Answers (Already Filled In)
These are examples of how the associative property works.
1.
(2 + 5) + 4 = 2 + (5 + 4)
→ Left: (7) + 4 = 11
→ Right: 2 + (9) = 11
✔
2.
6 + (10 + 3) = (6 + 10) + 3
→ Left: 6 + 13 = 19
→ Right: 16 + 3 = 19
✔
3.
(7 + 8) + 3 = 7 + (8 + 3)
→ Left: 15 + 3 = 18
→ Right: 7 + 11 = 18
✔
4.
2 + (9 + 5) = (2 + 9) + 5
→ Left: 2 + 14 = 16
→ Right: 11 + 5 = 16
✔
5.
7 + (6 + 2) = (7 + 6) + 2
→ Left: 7 + 8 = 15
→ Right: 13 + 2 = 15
✔
6.
9 + (10 + 12) = (9 + 10) + 12
→ Left: 9 + 22 = 31
→ Right: 19 + 12 = 31
✔
✔ All these equations demonstrate the associative property — changing the grouping doesn’t change the result.
---
🔹 Example Box
It shows two examples:
-
(1 + 2) + 3 = 1 + (2 + 3)
→ 3 + 3 = 1 + 5 → 6 = 6
✔
-
4 + (2 + 8) = (4 + 2) + 8
→ 4 + 10 = 6 + 8 → 14 = 14
✔
These show that regrouping doesn't change the sum.
---
🔹 Bottom Section: Practice Problems (Solved)
Let’s verify each one:
1.
(5 + 6) + 7 = 5 + (6 + 7)
→ Left: 11 + 7 = 18
→ Right: 5 + 13 = 18
✔
2.
8 + (9 + 3) = (8 + 9) + 3
→ Left: 8 + 12 = 20
→ Right: 17 + 3 = 20
✔
3.
(10 + 2) + 5 = 10 + (2 + 5)
→ Left: 12 + 5 = 17
→ Right: 10 + 7 = 17
✔
4.
11 + (3 + 4) = (11 + 3) + 4
→ Left: 11 + 7 = 18
→ Right: 14 + 4 = 18
✔
All correct!
---
✔ Summary: What is the Associative Property?
- It applies to
addition (and multiplication).
- It says:
You can group numbers differently without changing the sum.
- The
order of numbers remains the same; only the
grouping changes.
- This is useful for simplifying calculations.
For example:
> (15 + 5) + 3 = 15 + (5 + 3)
> 20 + 3 = 15 + 8 → 23 = 23
---
🎯 Final Answer:
✔ All answers provided in the worksheet are correct and illustrate the
Associative Property of Addition perfectly.
If you were asked to solve this worksheet, you would fill in the blanks so that both sides of the equation have the same numbers, just grouped differently — which has already been done correctly here.
Let me know if you'd like a printable version or want to create similar problems! 😊
Parent Tip: Review the logic above to help your child master the concept of associative property worksheet grade 4.
