Properties of Operation Worksheet - WordMint - Free Printable

This image presents a matching exercise: you are to match each numbered property of operation (on the left) with its correct algebraic example (lettered A–K on the right).

Let’s go through each one carefully and explain why each matches.

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1. Associative Property of Addition

> This means that when adding three or more numbers, the way you group them doesn’t change the sum:
> `(a + b) + c = a + (b + c)`

✔ Match: B

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2. Commutative Property of Addition

> This means that changing the order of addends doesn’t change the sum:
> `a + b = b + a`

✔ Match: D

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3. Additive Identity Property of 0

> Adding zero to any number leaves it unchanged:
> `a + 0 = 0 + a = a`

✔ Match: K

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4. Existence of Additive Inverses

> Every number has an opposite (additive inverse) such that their sum is zero:
> `a + (-a) = (-a) + a = 0`

✔ Match: F

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5. Associative Property of Multiplication

> Grouping doesn’t matter in multiplication:
> `(a * b) * c = a * (b * c)`

✔ Match: G

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6. Commutative Property of Multiplication

> Order doesn’t matter in multiplication:
> `a * b = b * a`

✔ Match: E

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7. Multiplicative Identity Property of 1

> Multiplying any number by 1 leaves it unchanged:
> `a * 1 = 1 * a = a`

✔ Match: A

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8. Existence of Multiplicative Inverses

> Every non-zero number has a reciprocal such that their product is 1:
> `a * (1/a) = (1/a) * a = 1`
> *(Note: This assumes a ≠ 0)*

✔ Match: I

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9. Distributive Property of Multiplication over Addition

> Multiplication distributes over addition:
> `a * (b + c) = a * b + a * c`

✔ Match: H

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10. Distributive Property of Multiplication over Subtraction

> Similarly, multiplication distributes over subtraction:
> `a * (b - c) = a * b - a * c`

✔ Match: J

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11. Distributive Property to Combine Like Terms

> This refers to using distribution (or reverse distribution) to combine like terms. For example:
> `a + (a + b) = (a + a) + b = 2a + b`
> *(This is really applying associative property and then combining like terms — but the example given fits this description best.)*

✔ Match: C

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## ✔ Final Matching Answers:

1. → B
2. → D
3. → K
4. → F
5. → G
6. → E
7. → A
8. → I
9. → H
10. → J
11. → C

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## 💡 Explanation Summary:

- Associative: Grouping doesn’t matter → parentheses can move.
- Commutative: Order doesn’t matter → swap operands.
- Identity: Adding 0 or multiplying by 1 leaves number unchanged.
- Inverse: Adding opposite or multiplying by reciprocal gives identity (0 or 1).
- Distributive: Multiply across a sum/difference → distribute the multiplier.
- Combine Like Terms: Often uses distributive property in reverse (factoring) or associative to regroup.

This is a foundational algebra concept — understanding these properties helps simplify expressions, solve equations, and reason about mathematical structures.

Let me know if you’d like a visual chart or flashcards for memorization!