Matching Properties Activity worksheet for identifying mathematical 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 maybe there's a typo? Let’s double-check.

Actually, if it were:
> \( 8/9 + 0 = 8/9 \)

That would be Identity Property of Addition.

But as written:
\( 8/9 + 1 = 8/9 \) → This is false, so likely a typo.

But looking at the original image: It says:

> ① \( 8/9 + 1 = 8/9 \)

This is incorrect. But perhaps it's meant to be:

> \( 8/9 + 0 = 8/9 \)

Which would be Identity Property of Addition.

But wait — the next one is:

> ② \( x + 0 = x \) → That’s clearly Identity Property of Addition

So maybe ① is actually supposed to be something else?

Wait — look again at the image:

It says:
> ① \( 8/9 + 1 = 8/9 \) ← This is false

But perhaps it's a typo and should be:
> \( 8/9 + 0 = 8/9 \) → Then it would be Identity Property of Addition

But since ② is already \( x + 0 = x \), that's probably the correct one for Identity Property of Addition.

So maybe ① is incorrect, but let's assume it's a typo and skip for now.

Alternatively, maybe it's:

> \( 8/9 \times 1 = 8/9 \)

That would make sense and be Identity Property of Multiplication

Ah! Likely, the + is a typo and should be ×.

So:
> ① \( 8/9 \times 1 = 8/9 \) → Identity Property of Multiplication

✔ That makes sense.

So we’ll assume it’s a typo: multiplication, not addition.

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Now, let's re-evaluate each item carefully.

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#### ① \( 8/9 \times 1 = 8/9 \) → Identity Property of Multiplication

Because multiplying by 1 leaves the number unchanged.

✔ Match: Identity Property of Multiplication

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#### ② \( x + 0 = x \) → Identity Property of Addition

Adding zero doesn’t change the value.

✔ Match: Identity Property of Addition

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#### ③ \( 6 + (-6) = 0 \) → Additive Inverse

A number plus its opposite equals zero.

✔ Match: Additive Inverse

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#### ④ \( 28 + 7 = 7 + 28 \) → Commutative Property of Addition

Order doesn’t matter when adding.

✔ Match: Commutative Property

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#### ⑤ \( 100 + 0 = 100 \) → Identity Property of Addition

Again, adding zero.

✔ Match: Identity Property of Addition

But wait — ② is already using this property.

But both ② and ⑤ use the same property — that’s okay; multiple problems can have the same property.

So yes, ⑤ also matches Identity Property of Addition

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#### ⑥ \( m + 8 = 8 + m \) → Commutative Property of Addition

Same as ④, just variables.

✔ Match: Commutative Property

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#### ⑦ \( x + (9 - 3) = (x + 9) - 3 \)

Let’s simplify both sides:

Left: \( x + (9 - 3) = x + 6 \)

Right: \( (x + 9) - 3 = x + 6 \)

So both sides equal \( x + 6 \)

But what property is this?

This is not distributive, associative, etc.

Wait — it's showing that subtraction is not associative, but here it's being treated as if it is.

But actually:

\( x + (9 - 3) = x + 6 \)

\( (x + 9) - 3 = x + 6 \)

So they’re equal due to properties of operations, but what specific property?

This looks like Associative Property of Addition?

But subtraction isn't associative.

Wait — rewrite:

\( x + (9 - 3) = x + 6 \)

\( (x + 9) - 3 = x + 6 \)

But \( 9 - 3 = 6 \), and \( x + 9 - 3 = x + 6 \)

This is more about order of operations and subtraction as addition of negative.

But notice:

\( x + (9 - 3) = x + 9 - 3 \)

And \( (x + 9) - 3 = x + 9 - 3 \)

So both are equivalent.

But this is not a standard named property unless we think of subtraction as addition.

Alternatively, this might be illustrating Associative Property of Addition if we write:

\( x + (-3 + 9) = (x + 9) + (-3) \)

Then: \( x + (9 + (-3)) = (x + 9) + (-3) \)

Yes! So:

\( x + (9 - 3) = x + (9 + (-3)) \)

And \( (x + 9) - 3 = (x + 9) + (-3) \)

So: \( x + (9 + (-3)) = (x + 9) + (-3) \)

That’s the Associative Property of Addition!

✔ Match: Associative Property of Addition

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#### ⑧ \( 25 + 2 = 50 \)

Wait — 25 + 2 = 27, not 50 → False!

This is not true.

But maybe it's a typo?

Perhaps it's \( 25 \times 2 = 50 \)? That would make sense.

If so: \( 25 \times 2 = 50 \)

But that’s just multiplication — no special property unless it's related to closure.

But 25 × 2 = 50 — both integers → Closure Property of Multiplication

Because multiplying two integers gives an integer.

So likely, it's meant to be:

> ⑧ \( 25 \times 2 = 50 \) → Closure Property of Multiplication

✔ Match: Closure Property of Multiplication

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#### ⑨ \( 8 \times 1/8 = 1 \)

This is a number times its reciprocal = 1 → Multiplicative Inverse

✔ Match: Multiplicative Inverse

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Summary of Matches:

| Problem | Expression | Property |
|--------|------------|---------|
| ① | \( 8/9 \times 1 = 8/9 \) | Identity Property of Multiplication |
| ② | \( x + 0 = x \) | Identity Property of Addition |
| 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 | \( 25 \times 2 = 50 \) | Closure Property of Multiplication |
| ⑨ | \( 8 \times 1/8 = 1 \) | Multiplicative Inverse |

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Final Answer (Matching):

1. \( 8/9 \times 1 = 8/9 \) → Identity Property of Multiplication
2. \( x + 0 = x \) → Identity Property of Addition
3. \( 6 + (-6) = 0 \) → Additive Inverse
4. \( 28 + 7 = 7 + 28 \) → Commutative Property
5. \( 100 + 0 = 100 \) → Identity Property of Addition
6. \( m + 8 = 8 + m \) → Commutative Property
7. \( x + (9 - 3) = (x + 9) - 3 \) → Associative Property of Addition
8. \( 25 \times 2 = 50 \) → Closure Property of Multiplication
9. \( 8 \times 1/8 = 1 \) → Multiplicative Inverse

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⚠️ Note: There are likely typos in the original worksheet:

- ①: Should be multiplication, not addition
- ⑧: Should be \( 25 \times 2 = 50 \), not \( 25 + 2 = 50 \)
- ⑦: May be tricky, but best interpreted via associative property after rewriting subtraction as addition

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✔ Corrected Matching (as per reasoning):

| Number | Expression | Property |
|--------|------------|----------|
| ① | \( \frac{8}{9} \times 1 = \frac{8}{9} \) | Identity Property of Multiplication |
| ② | \( x + 0 = x \) | Identity Property of Addition |
| ③ | \( 6 + (-6) = 0 \) | Additive Inverse |
| ④ | \( 28 + 7 = 7 + 28 \) | Commutative Property |
| ⑤ | \( 100 + 0 = 100 \) | Identity Property of Addition |
| ⑥ | \( m + 8 = 8 + m \) | Commutative Property |
| ⑦ | \( x + (9 - 3) = (x + 9) - 3 \) | Associative Property of Addition |
| ⑧ | \( 25 \times 2 = 50 \) | Closure Property of Multiplication |
| ⑨ | \( 8 \times \frac{1}{8} = 1 \) | Multiplicative Inverse |

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Final Answer:

Match each number to the correct property:

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

✔ All matched correctly based on corrected interpretations.