17 3rd Grade Multiplication Properties Worksheet - Free PDF at ... - Free Printable

Let's solve each problem step by step and identify the property of addition used in each case.

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🔷 Addition Properties Recap:

1. Commutative Property:
The order of numbers doesn’t change the sum.
Example: $ a + b = b + a $

2. Associative Property:
The grouping of numbers doesn’t change the sum.
Example: $ (a + b) + c = a + (b + c) $

3. Identity Property (of Addition):
Adding zero to any number doesn’t change it.
Example: $ a + 0 = a $

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Now, let’s go through each problem:

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1)

$ 8 + 5 + 9 + 9 = \quad 8 + 9 + 5 + 9 = $
- Left: $ 8 + 5 + 9 + 9 = 31 $
- Right: $ 8 + 9 + 5 + 9 = 31 $
→ The order of numbers changed.

✔ Property: Commutative

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2)

$ 71 + (26 + 25) = \quad (71 + 26) + 25 = $
- Left: $ 71 + 51 = 122 $
- Right: $ 97 + 25 = 122 $
→ The grouping changed.

✔ Property: Associative

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3)

$ 59 + 63 = \quad 63 + 59 = $
- Both equal $ 122 $
→ Order changed.

✔ Property: Commutative

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4)

$ 22 + 13 = \quad 13 + 22 = $
- Both equal $ 35 $
→ Order changed.

✔ Property: Commutative

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5)

$ 100 + 50 + 1 = \quad 1 + 100 + 50 = $
- Left: $ 151 $
- Right: $ 151 $
→ Order changed.

✔ Property: Commutative

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6)

$ (28 + 35) + 7 = \quad 28 + (35 + 7) = $
- Left: $ 63 + 7 = 70 $
- Right: $ 28 + 42 = 70 $
→ Grouping changed.

✔ Property: Associative

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7)

$ 104 + (28 + 12) = \quad (104 + 28) + 12 = $
- Left: $ 104 + 40 = 144 $
- Right: $ 132 + 12 = 144 $
→ Grouping changed.

✔ Property: Associative

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8)

$ 77 + 44 + 7 = \quad 7 + 77 + 44 = $
- Left: $ 128 $
- Right: $ 128 $
→ Order changed.

✔ Property: Commutative

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9)

$ 29 + 0 + 1 = \quad 1 + 0 + 29 = $
- Both: $ 30 $
→ Zero is involved; order changed.

✔ Property: Commutative (also involves identity, but since order changes, commutative is primary)

> Note: Identity property would be if only one side has zero and others are same, like $ a + 0 = a $. Here, both sides have same numbers rearranged.

So, Commutative is correct.

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10)

$ (27 + 67) + 19 = \quad 27 + (67 + 19) = $
- Left: $ 94 + 19 = 113 $
- Right: $ 27 + 86 = 113 $
→ Grouping changed.

✔ Property: Associative

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11)

$ 8 + 5 = \quad 5 + 8 = $
- Both equal $ 13 $
→ Order changed.

✔ Property: Commutative

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12)

$ 9 + (5 + 1) = \quad (9 + 5) + 1 = $
- Left: $ 9 + 6 = 15 $
- Right: $ 14 + 1 = 15 $
→ Grouping changed.

✔ Property: Associative

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✔ Final Answers:

| # | Left Side | Right Side | Sum | Property |
|---|----------|------------|-----|---------|
| 1 | 8+5+9+9 | 8+9+5+9 | 31 | Commutative |
| 2 | 71+(26+25) | (71+26)+25 | 122 | Associative |
| 3 | 59+63 | 63+59 | 122 | Commutative |
| 4 | 22+13 | 13+22 | 35 | Commutative |
| 5 | 100+50+1 | 1+100+50 | 151 | Commutative |
| 6 | (28+35)+7 | 28+(35+7) | 70 | Associative |
| 7 | 104+(28+12) | (104+28)+12 | 144 | Associative |
| 8 | 77+44+7 | 7+77+44 | 128 | Commutative |
| 9 | 29+0+1 | 1+0+29 | 30 | Commutative |
|10 | (27+67)+19 | 27+(67+19) | 113 | Associative |
|11 | 8+5 | 5+8 | 13 | Commutative |
|12 | 9+(5+1) | (9+5)+1 | 15 | Associative |

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📝 Summary:

- Commutative Property: Used when order of addends changes.
- Associative Property: Used when grouping (parentheses) changes.
- Identity Property is not directly asked here, but appears implicitly with zero (e.g., #9), though the main focus is on commutative/associative.

Let me know if you'd like this formatted as a printable answer sheet!