Associative Property Of Addition Worksheets - Worksheet School - Free Printable

Let's solve this step by step using the Associative Property of Addition.

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🔷 What is the Associative Property?

The associative property of addition states that:

> (a + b) + c = a + (b + c)

This means that when adding three or more numbers, the way you group them does not change the sum.

So, for example:
- (2 + 3) + 4 = 5 + 4 = 9
- 2 + (3 + 4) = 2 + 7 = 9

Both are equal → This illustrates the associative property.

But note: The associative property only applies to addition and multiplication, not subtraction or division.

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Now, let’s go through each option and determine if the two expressions are equal based on the associative property.

We will evaluate both sides and see if they are equal.

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✔ A. 7 + (5+3) ___ (7+5) + 3

Left:
7 + (5+3) = 7 + 8 = 15

Right:
(7+5) + 3 = 12 + 3 = 15

✔ Equal → Yes, because grouping changed, but sum is same.

✔️ Equal

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✔ B. 4 + (9+2) ___ (4+9) + 2

Left:
4 + (9+2) = 4 + 11 = 15

Right:
(4+9) + 2 = 13 + 2 = 15

✔ Equal

✔️ Equal

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✔ C. (1+1) + 6 ___ 1 + (1+6)

Left:
(1+1) + 6 = 2 + 6 = 8

Right:
1 + (1+6) = 1 + 7 = 8

✔ Equal

✔️ Equal

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✘ D. (2+4) + 8 ___ 2 + (8+4)

Left:
(2+4) + 8 = 6 + 8 = 14

Right:
2 + (8+4) = 2 + 12 = 14

Wait — both are 14?

Yes! But let's check the grouping.

Is this associative?

Left: (2+4)+8 = 6+8 = 14
Right: 2+(8+4) = 2+12 = 14

But the associative property says:
(a + b) + c = a + (b + c)

Here, left is: (2+4)+8 → (a+b)+c with a=2, b=4, c=8
Right is: 2+(8+4) → a+(b+c), but b=8, c=4 → so it's not the same order!

Wait — in the right side, it's 2 + (8+4) → which is not the same as 2 + (4+8), but since addition is commutative, 8+4 = 4+8.

But the associative property allows changing grouping as long as the numbers stay the same.

So even though the order seems different, we can use commutativity and associativity together.

But strictly speaking, (2+4)+8 = 2+(4+8) → yes, that's associative.

But here it's 2+(8+4) → same as 2+(4+8) due to commutativity.

So the total sum is still the same.

✔ So numerically, both sides are equal.

✔️ Equal

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✔ E. 3 + (6+7) ___ (3+6) + 6

Wait — look closely:

Left: 3 + (6+7) = 3 + 13 = 16

Right: (3+6) + 6 = 9 + 6 = 15

✘ Not equal!

So this one is not equal.

Because:
Left: 3 + (6+7) = 3 + 13 = 16
Right: (3+6) + 6 = 9 + 6 = 15

→ Different results

🚫 Not equal

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✔ F. (9+8) + 4 ___ 8+4 + 9

Left: (9+8) + 4 = 17 + 4 = 21

Right: 8 + 4 + 9 = 12 + 9 = 21

But wait — the expression is written as:
"8+4 + 9" — no parentheses.

So it's just 8 + 4 + 9 = 21

But the left is (9+8)+4 = 17+4 = 21

Same result.

But is this associative?

Actually, the associative property would say:
(9+8)+4 = 9+(8+4)

But here the right side is 8+4+9, which is not grouped as 8+(4+9) or (8+4)+9?

But since addition is associative and commutative, all ways of adding these numbers give same result.

So numerically, both sides are equal.

But the original equation is:

(9+8) + 4 vs 8+4 + 9

Left: (9+8)+4 = 17+4 = 21
Right: 8+4+9 = 21

So yes, equal.

✔️ Equal

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✔ G. 3 + (3+4) ___ (4+3) + 1

Left: 3 + (3+4) = 3 + 7 = 10

Right: (4+3) + 1 = 7 + 1 = 8

✘ Not equal!

10 ≠ 8

🚫 Not equal

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✔ H. (7+8) + 2 ___ (8+2) + 5

Left: (7+8)+2 = 15 + 2 = 17

Right: (8+2)+5 = 10 + 5 = 15

17 ≠ 15

🚫 Not equal

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✔ I. 8 + (2+2) ___ (8+2) + 1

Left: 8 + (2+2) = 8 + 4 = 12

Right: (8+2) + 1 = 10 + 1 = 11

12 ≠ 11

🚫 Not equal

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✔ J. (3+3) + 5 ___ (3+5) + 3

Left: (3+3) + 5 = 6 + 5 = 11

Right: (3+5) + 3 = 8 + 3 = 11

✔ Equal

✔️ Equal

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✔ Final Answers:

| Letter | Equal? |
|--------|--------|
| A | ✔️ Yes |
| B | ✔️ Yes |
| C | ✔️ Yes |
| D | ✔️ Yes |
| E | ✘ No |
| F | ✔️ Yes |
| G | ✘ No |
| H | ✘ No |
| I | ✘ No |
| J | ✔️ Yes |

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✔ Summary:

Use the associative property to check if the grouping changes but the sum remains the same.

Only if the numbers are the same and only grouping changes, then they are equal.

If numbers are different or extra numbers appear, then not equal.

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✔ Correct Answers:

A, B, C, D, F, J → Equal

E, G, H, I → Not equal

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