Answer key for identifying multiplication properties in equations.

You've uploaded an answer key for a math worksheet titled “Properties of Multiplication – Identify The Property” (Math Worksheet 8). The task is to:

> Identify the property used and rewrite the following equations under the correct multiplication property in the table below.

The worksheet lists 20 multiplication equations, and you’re supposed to classify each one under one of five properties:

- Zero Property
- Identity Property
- Commutative Property
- Associative Property
- Distributive Property

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✔ The image you uploaded IS THE ANSWER KEY, so all the equations are already correctly sorted into their respective categories.

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## 🔍 Let’s Break Down Each Property & Why Equations Belong Where They Do

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🟢 Zero Property of Multiplication

> Any number multiplied by 0 equals 0.

Equations:
- `148 × 0 = 0`
- `178 × 0 = 0`
- `97 × 0 = 0`
- `288 × 0 = 0`

✔️ All these show a number × 0 = 0 → Zero Property

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🟡 Identity Property of Multiplication

> Any number multiplied by 1 stays the same.

Equations:
- `114 × 1 = 114`
- `224 × 1 = 224`
- `300 × 1 = 300`

✔️ Multiplying by 1 doesn’t change the value → Identity Property

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🔵 Commutative Property of Multiplication

> Order doesn’t matter: a × b = b × a

Equations:
- `85 × 30 = 30 × 85`
- `35 × 105 = 105 × 35`
- `155 × 160 = 160 × 155`
- `1 × 345 = 345 × 1`

✔️ These show numbers swapped on either side of the equals sign → Commutative Property

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🟣 Associative Property of Multiplication

> Grouping doesn’t matter: (a × b) × c = a × (b × c)

Equations:
- `7 × (15 × 101) = (7 × 15) × 101`
- `98 × (13 × 13) = (98 × 13) × 13`
- `217 × (9 × 1) = (217 × 9) × 1`
- `(24 × 208) × 6 = 24 × (208 × 6)`
- `49 × (28 × 14) = (49 × 28) × 14`
- `72 × (1 × 55) = (72 × 1) × 55`

✔️ Parentheses moved around, but result unchanged → Associative Property

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🟠 Distributive Property of Multiplication Over Addition/Subtraction

> a × (b + c) = (a × b) + (a × c)
> or
> a × (b - c) = (a × b) - (a × c)

Equations:
- `63 × (79 + 2) = (63 × 79) + (63 × 2)` ← First example given
- `1 × (92 - 46) = (1 × 92) - (1 × 46)`
- `40 × (11 + 7) = (40 × 11) + (40 × 7)`
- `72 × (1 × 55) = (72 × 1) × 55` ← Wait! This one is actually Associative, not Distributive!

⚠️ Correction Needed: The equation `72 × (1 × 55) = (72 × 1) × 55` is Associative, NOT Distributive. It appears to be misclassified in the answer key.

Also, `1 × (92 - 46) = (1 × 92) - (1 × 46)` — while technically true, it's a trivial case since multiplying by 1 doesn’t change anything. Still, it fits the Distributive Property pattern.

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## ✔ Final Summary

| Property | Equations |
|------------------|---------------------------------------------------------------------------|
| Zero | 148×0=0, 178×0=0, 97×0=0, 288×0=0 |
| Identity | 114×1=114, 224×1=224, 300×1=300 |
| Commutative | 85×30=30×85, 35×105=105×35, 155×160=160×155, 1×345=345×1 |
| Associative | 7×(15×101)=(7×15)×101, 98×(13×13)=(98×13)×13, 217×(9×1)=(217×9)×1, (24×208)×6=24×(208×6), 49×(28×14)=(49×28)×14, 72×(1×55)=(72×1)×55 |
| Distributive | 63×(79+2)=(63×79)+(63×2), 1×(92-46)=(1×92)-(1×46), 40×(11+7)=(40×11)+(40×7) |

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## ❗ Important Note About the Answer Key

There is one error in the provided answer key:

> `72 × (1 × 55) = (72 × 1) × 55` → This is Associative, not Distributive.

It should be moved from the Distributive column to the Associative column.

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## 💡 Teaching Tip

When teaching this, emphasize:

- Zero Property → “Anything times zero is zero.”
- Identity → “Times 1? Same number!”
- Commutative → “Switch the order, same answer.”
- Associative → “Group differently, still works.”
- Distributive → “Multiply across the parentheses.”

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✔ Final Answer: The worksheet has been solved correctly in the answer key, except for one misclassification (`72 × (1 × 55) = (72 × 1) × 55` should be under Associative, not Distributive).

Let me know if you’d like a printable version or practice problems!