Properties Worksheets | Properties of Mathematics Worksheets - Free Printable

Let's solve the problem by identifying the properties of mathematics described in each statement. We'll go through each one, explain it, and name the correct mathematical property.

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1) The product of any number and one is that number. For example a × 1 = a.

- Explanation: Multiplying any number by 1 gives the same number.
- Property: Multiplicative Identity Property

✔ Answer: *Multiplicative Identity Property*

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2) Adding 0 to any number leaves it unchanged. For example a + 0 = a.

- Explanation: Adding zero does not change the value of a number.
- Property: Additive Identity Property

✔ Answer: *Additive Identity Property*

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3) If you subtract the same number from both sides of an equation, the equation is still true. For example if a = b, then a - c = b - c.

- Explanation: This maintains equality when subtracting the same value from both sides.
- Property: Subtraction Property of Equality

✔ Answer: *Subtraction Property of Equality*

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4) When three or more numbers are multiplied, the product is the same regardless of the order of the multiplicands. For example (a × b) × c = a × (b × c)

- Explanation: Grouping doesn’t affect the result when multiplying.
- Property: Associative Property of Multiplication

✔ Answer: *Associative Property of Multiplication*

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5) When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (a + b) + c = a + (b + c)

- Explanation: Grouping doesn't affect addition.
- Property: Associative Property of Addition

✔ Answer: *Associative Property of Addition*

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6) If you add the same number to both sides of an equation, the equation is still true. For example if a = b, then a + c = b + c.

- Explanation: Adding the same value to both sides keeps the equation balanced.
- Property: Addition Property of Equality

✔ Answer: *Addition Property of Equality*

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7) Multiplying any number by 0 yields 0. For example a × 0 = 0.

- Explanation: Any number times zero equals zero.
- Property: Multiplicative Property of Zero

✔ Answer: *Multiplicative Property of Zero*

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8) If you divide the same number to both sides of an equation, the equation is still true. For example if a = b, then a / c = b / c.

- Explanation: Dividing both sides by the same nonzero number preserves equality.
- Property: Division Property of Equality

✔ Answer: *Division Property of Equality*

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9) If you multiply the same number to both sides of an equation, the equation is still true. For example if a = b, then a × c = b × c.

- Explanation: Multiplying both sides by the same number keeps the equation valid.
- Property: Multiplication Property of Equality

✔ Answer: *Multiplication Property of Equality*

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10) The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a × (b + c) = a × b + a × c

- Explanation: Distributing multiplication over addition.
- Property: Distributive Property of Multiplication over Addition

✔ Answer: *Distributive Property*

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11) The multiplicative inverse of a number, a is 1/a so that a × 1/a = 1.

- Explanation: A number multiplied by its reciprocal gives 1.
- Property: Multiplicative Inverse Property

✔ Answer: *Multiplicative Inverse Property*

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12) When two numbers are added, the sum is the same regardless of the order of the addends. For example a + b = b + a

- Explanation: Order doesn't matter in addition.
- Property: Commutative Property of Addition

✔ Answer: *Commutative Property of Addition*

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13) The sum of any number and zero is the original number. For example a + 0 = a.

- Explanation: Same as #2 — adding zero doesn’t change the number.
- Property: Additive Identity Property

✔ Answer: *Additive Identity Property*

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14) When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example a × b = b × a

- Explanation: Order doesn't matter in multiplication.
- Property: Commutative Property of Multiplication

✔ Answer: *Commutative Property of Multiplication*

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15) The additive inverse of a number, a is -a so that a + (-a) = 0.

- Explanation: A number plus its opposite equals zero.
- Property: Additive Inverse Property

✔ Answer: *Additive Inverse Property*

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✔ Final Answers:

| Number | Property Name |
|--------|----------------|
| 1 | Multiplicative Identity Property |
| 2 | Additive Identity Property |
| 3 | Subtraction Property of Equality |
| 4 | Associative Property of Multiplication |
| 5 | Associative Property of Addition |
| 6 | Addition Property of Equality |
| 7 | Multiplicative Property of Zero |
| 8 | Division Property of Equality |
| 9 | Multiplication Property of Equality |
| 10 | Distributive Property |
| 11 | Multiplicative Inverse Property |
| 12 | Commutative Property of Addition |
| 13 | Additive Identity Property |
| 14 | Commutative Property of Multiplication |
| 15 | Additive Inverse Property |

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These are all fundamental properties used in algebra and arithmetic. Understanding them helps simplify expressions and solve equations logically.