Math worksheet matching equations to their corresponding properties.

Let's solve the Matching Properties Activity step by step. The task is to match each equation or expression on the left with the correct property of math on the right.

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Step 1: Understand Each Property

Here are the properties listed on the right:

1. Closure Property of Multiplication – When you multiply two numbers, the result is also a number in the same set (e.g., integers, real numbers).
2. Zero Property of Multiplication – Any number multiplied by zero equals zero.
3. Identity Property of Addition – Adding zero to any number leaves it unchanged.
4. Additive Inverse – A number plus its opposite equals zero.
5. Identity Property of Multiplication – Multiplying by 1 leaves a number unchanged.
6. Distributive Property – \( a(b + c) = ab + ac \)
7. Commutative Property – Order doesn't matter: \( a + b = b + a \), \( ab = ba \)
8. Multiplicative Inverse – A number times its reciprocal equals 1.
9. Associative Property of Addition – Grouping doesn’t matter: \( (a + b) + c = a + (b + c) \)

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Now let’s go through each problem on the left and determine which property applies.

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Problem ①: \( 8/9 + 1 = 8/9 \)

Wait — this is not true!
\( 8/9 + 1 = 17/9 \), not \( 8/9 \).
But if it were:
👉 \( 8/9 + 0 = 8/9 \), that would be Identity Property of Addition.

But as written: \( 8/9 + 1 = 8/9 \) → False.

But maybe it's a typo? Let’s check again.

Wait — actually, looking at the image, it says:

> ① \( 8/9 + 1 = 8/9 \)

That can't be right. Unless it's supposed to be:

👉 \( 8/9 \times 1 = 8/9 \) → That would be Identity Property of Multiplication.

Possibly a typo: + should be ×.

Let’s assume it's meant to be:
> ① \( 8/9 \times 1 = 8/9 \)

✔ This matches: Identity Property of Multiplication

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Problem ②: \( x \cdot 0 = 0 \)

Any number times zero is zero.

✔ Zero Property of Multiplication

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Problem ③: \( 6 + (-6) = 0 \)

A number plus its opposite equals zero.

✔ Additive Inverse

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Problem ④: \( 28 + 7 = 7 + 28 \)

Order of addition changes, but sum stays the same.

✔ Commutative Property of Addition

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Problem ⑤: \( 100 + 0 = 100 \)

Adding zero doesn't change the number.

✔ Identity Property of Addition

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Problem ⑥: \( m + 8 = 8 + m \)

Again, order of addition changes.

✔ Commutative Property of Addition

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Problem ⑦: \( x + (9 + 3) = (x + 9) + 3 \)

Grouping changes, but the sum remains the same.

This is Associative Property of Addition

✔ Associative Property of Addition

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Problem ⑧: \( -2 + 2 = 0 \)

Negative and positive of the same number add to zero.

✔ Additive Inverse

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Problem ⑨: \( 8 \cdot 1/8 = 1 \)

A number times its reciprocal equals 1.

✔ Multiplicative Inverse

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Now, let’s double-check all:

| Problem | Equation | Property |
|--------|---------|----------|
| ① | \( 8/9 \times 1 = 8/9 \) | Identity Property of Multiplication |
| ② | \( x \cdot 0 = 0 \) | Zero Property of Multiplication |
| ③ | \( 6 + (-6) = 0 \) | Additive Inverse |
| ④ | \( 28 + 7 = 7 + 28 \) | Commutative Property of Addition |
| ⑤ | \( 100 + 0 = 100 \) | Identity Property of Addition |
| ⑥ | \( m + 8 = 8 + m \) | Commutative Property of Addition |
| ⑦ | \( x + (9 + 3) = (x + 9) + 3 \) | Associative Property of Addition |
| ⑧ | \( -2 + 2 = 0 \) | Additive Inverse |
| ⑨ | \( 8 \cdot 1/8 = 1 \) | Multiplicative Inverse |

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✔ Final Matching:

- ① → Identity Property of Multiplication
- ② → Zero Property of Multiplication
- ③ → Additive Inverse
- ④ → Commutative Property of Addition
- ⑤ → Identity Property of Addition
- ⑥ → Commutative Property of Addition
- ⑦ → Associative Property of Addition
- ⑧ → Additive Inverse
- ⑨ → Multiplicative Inverse

> ⚠️ Note: If the first problem was truly written as \( 8/9 + 1 = 8/9 \), then it's incorrect. But since it's likely a typo (should be multiplication), we assume it's meant to be \( 8/9 \times 1 = 8/9 \).

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🟩 Summary of Answers:

| Number | Matched Property |
|-------|------------------|
| ① | Identity Property of Multiplication |
| ② | Zero Property of Multiplication |
| ③ | Additive Inverse |
| ④ | Commutative Property of Addition |
| ⑤ | Identity Property of Addition |
| ⑥ | Commutative Property of Addition |
| ⑦ | Associative Property of Addition |
| ⑧ | Additive Inverse |
| ⑨ | Multiplicative Inverse |

You can now cut and paste these matches accordingly.

Let me know if you'd like a printable version or visual matching guide!