Associative Property of Addition worksheet with exercises for students to practice and identify the property.

Let's solve the worksheet step by step, explaining each part and applying the Associative Property of Addition.

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🔷 What is the Associative Property of Addition?

The associative property of addition states that when adding three or more numbers, the way the numbers are grouped does not change the sum.
In symbols:
> (a + b) + c = a + (b + c)

This means you can group numbers differently without changing the result.

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## ✔ Part 1: Show the associative property using parentheses

We need to rewrite each expression using different grouping (parentheses), but keep the same numbers and operations.

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1. 2 + 4 + 6

Original: 2 + 4 + 6
We can group as: (2 + 4) + 6 = 6 + 6 = 12
Or: 2 + (4 + 6) = 2 + 10 = 12

✔ Answer: (2 + 4) + 6 or 2 + (4 + 6)
But since it asks to "show" the associative property, we write one version with different grouping.

👉 Answer: (2 + 4) + 6

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2. 3 + 5 + 7

Grouping: (3 + 5) + 7 = 8 + 7 = 15
Or: 3 + (5 + 7) = 3 + 12 = 15

👉 Answer: (3 + 5) + 7

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3. 9 + 1 + 4

(9 + 1) + 4 = 10 + 4 = 14
or 9 + (1 + 4) = 9 + 5 = 14

👉 Answer: (9 + 1) + 4

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4. 7 + 8 + 3

(7 + 8) + 3 = 15 + 3 = 18
or 7 + (8 + 3) = 7 + 11 = 18

👉 Answer: (7 + 8) + 3

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## ✔ Part 2: Determine the answer, then rewrite using the associative property

We compute the original expression, then rewrite it in a different grouping using parentheses.

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5. (2 + 6) + 10 = ?

First: (2 + 6) = 8 → 8 + 10 = 18

Now use associative property:
→ 2 + (6 + 10) = 2 + 16 = 18

👉 Answer:
(2 + 6) + 10 = 18
Rewritten: 2 + (6 + 10)

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6. (5 + 5) + 6 = ?

(5 + 5) = 10 → 10 + 6 = 16

Rewrite: 5 + (5 + 6) = 5 + 11 = 16

👉 Answer:
(5 + 5) + 6 = 16
Rewritten: 5 + (5 + 6)

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7. 3 + (4 + 5) = ?

(4 + 5) = 9 → 3 + 9 = 12

Rewrite: (3 + 4) + 5 = 7 + 5 = 12

👉 Answer:
3 + (4 + 5) = 12
Rewritten: (3 + 4) + 5

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8. (0 + 4) + 12 = ?

(0 + 4) = 4 → 4 + 12 = 16

Rewrite: 0 + (4 + 12) = 0 + 16 = 16

👉 Answer:
(0 + 4) + 12 = 16
Rewritten: 0 + (4 + 12)

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## ✔ Part 3: Identify whether the commutative or associative property is being used

- Commutative Property: Order changes → a + b = b + a
- Associative Property: Grouping changes → (a + b) + c = a + (b + c)

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9. (2 + 2) + 6 = 2 + (2 + 6)

Here, the grouping changed: from ((2+2)+6) to (2+(2+6))
→ This is associative property.

✔ Answer: Associative

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10. (6 + 8) + 3 = (8 + 6) + 3

Left side: (6 + 8) + 3
Right side: (8 + 6) + 3 → order of 6 and 8 switched

So, 6 and 8 were swapped, which is commutative property.

✔ Answer: Commutative

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11. (2 + 5) + 4 = 2 + (5 + 4)

Grouping changed: ((2+5)+4) → (2+(5+4))

✔ Answer: Associative

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12. 3 + (7 + 10) = 3 + (10 + 7)

Inside the parentheses: (7 + 10) → (10 + 7) → order changed

So, this is commutative property applied inside the parentheses.

✔ Answer: Commutative

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## ✔ Final Answers:

Part 1:

1. (2 + 4) + 6
2. (3 + 5) + 7
3. (9 + 1) + 4
4. (7 + 8) + 3

Part 2:

5. (2 + 6) + 10 = 18 → 2 + (6 + 10)
6. (5 + 5) + 6 = 16 → 5 + (5 + 6)
7. 3 + (4 + 5) = 12 → (3 + 4) + 5
8. (0 + 4) + 12 = 16 → 0 + (4 + 12)

Part 3:

9. Associative
10. Commutative
11. Associative
12. Commutative

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