Math associative property worksheet - Free Printable

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

🔷 What is the Associative Property of Addition?

The associative property states that when adding three or more numbers, the way the numbers are grouped does not change the sum. In other words:

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

We'll use this to fill in the blanks in each problem.

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✔ Problem 1:

(33 + __) + 15 = ___
33 + (21 + 15) = ___

- From the second line:
$ 33 + (21 + 15) = 33 + 36 = 69 $

- So, the first expression must also equal 69:
$ (33 + \boxed{21}) + 15 = 69 $

Now check:
$ (33 + 21) + 15 = 54 + 15 = 69 $ ✔

Answer:
1. $ (33 + \boxed{21}) + 15 = \boxed{69} $
$ 33 + (21 + 15) = \boxed{69} $

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✔ Problem 2:

__ + (9 + 2) = ___
(17 + 9) + 2 = ___

- Second line:
$ (17 + 9) + 2 = 26 + 2 = 28 $

- First line:
$ \boxed{17} + (9 + 2) = 17 + 11 = 28 $

So, both sides equal 28.

Answer:
2. $ \boxed{17} + (9 + 2) = \boxed{28} $
$ (17 + 9) + 2 = \boxed{28} $

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✔ Problem 3:

154 + (__ + __) = ___
(154 + 48) + 30 = ___

- Second line:
$ (154 + 48) + 30 = 202 + 30 = 232 $

- So first line must be:
$ 154 + (\boxed{48} + \boxed{30}) = 154 + 78 = 232 $

Answer:
3. $ 154 + (\boxed{48} + \boxed{30}) = \boxed{232} $
$ (154 + 48) + 30 = \boxed{232} $

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✔ Problem 4:

(__ + 81) + 8 = ___
25 + (81 + 8) = ___

- Second line:
$ 25 + (81 + 8) = 25 + 89 = 114 $

- First line:
$ (\boxed{25} + 81) + 8 = 106 + 8 = 114 $

Answer:
4. $ (\boxed{25} + 81) + 8 = \boxed{114} $
$ 25 + (81 + 8) = \boxed{114} $

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✔ Problem 5:

(__ + 9) + 7 = ___
13 + (__ + 7) = ___

- We know from the associative property that grouping doesn’t matter.
Let’s assume the number in the first blank is 13, so we can match:

$ (13 + 9) + 7 = 22 + 7 = 29 $

Then second line:
$ 13 + (\boxed{9} + 7) = 13 + 16 = 29 $

So both expressions equal 29.

Answer:
5. $ (\boxed{13} + 9) + 7 = \boxed{29} $
$ 13 + (\boxed{9} + 7) = \boxed{29} $

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✔ Problem 6:

4 + (__ + 75) = ___
(__ + 33) + __ = ___

We need to find numbers such that both expressions are equal and follow the associative property.

Let’s suppose the missing number in the first blank is 33, then:

- $ 4 + (33 + 75) = 4 + 108 = 112 $

Now second line:
We want $ (\boxed{4} + 33) + \boxed{75} = 37 + 75 = 112 $

Perfect!

Answer:
6. $ 4 + (\boxed{33} + 75) = \boxed{112} $
$ (\boxed{4} + 33) + \boxed{75} = \boxed{112} $

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✔ Problem 7:

__ + (__ + 22) = ___
(99 + 44) + __ = ___

- Second line:
$ (99 + 44) + \boxed{22} = 143 + 22 = 165 $

- So first line:
$ \boxed{99} + (\boxed{44} + 22) = 99 + 66 = 165 $

Answer:
7. $ \boxed{99} + (\boxed{44} + 22) = \boxed{165} $
$ (99 + 44) + \boxed{22} = \boxed{165} $

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✔ Problem 8:

10 + (__ + __) = ___
(__ + 15) + 20 = ___

Let’s suppose the missing numbers are 15 and 20, then:

- First line:
$ 10 + (\boxed{15} + \boxed{20}) = 10 + 35 = 45 $

- Second line:
$ (\boxed{10} + 15) + 20 = 25 + 20 = 45 $

Perfect match!

Answer:
8. $ 10 + (\boxed{15} + \boxed{20}) = \boxed{45} $
$ (\boxed{10} + 15) + 20 = \boxed{45} $

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✔ Final Answers:

1. $ (33 + \boxed{21}) + 15 = \boxed{69} $
$ 33 + (21 + 15) = \boxed{69} $

2. $ \boxed{17} + (9 + 2) = \boxed{28} $
$ (17 + 9) + 2 = \boxed{28} $

3. $ 154 + (\boxed{48} + \boxed{30}) = \boxed{232} $
$ (154 + 48) + 30 = \boxed{232} $

4. $ (\boxed{25} + 81) + 8 = \boxed{114} $
$ 25 + (81 + 8) = \boxed{114} $

5. $ (\boxed{13} + 9) + 7 = \boxed{29} $
$ 13 + (\boxed{9} + 7) = \boxed{29} $

6. $ 4 + (\boxed{33} + 75) = \boxed{112} $
$ (\boxed{4} + 33) + \boxed{75} = \boxed{112} $

7. $ \boxed{99} + (\boxed{44} + 22) = \boxed{165} $
$ (99 + 44) + \boxed{22} = \boxed{165} $

8. $ 10 + (\boxed{15} + \boxed{20}) = \boxed{45} $
$ (\boxed{10} + 15) + 20 = \boxed{45} $

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✔ All problems use the associative property: changing grouping doesn't change the sum.