Grade 7 math worksheet on properties of integers, matching equations to their respective properties.

Here is the solution to the “Properties of Integers” activity, with a clear explanation for each match.

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Column A → Column B (Letter Answer)

1. 5 + 4 = 9 → g. Closure Property
*Explanation:* The sum of two integers (5 and 4) is also an integer (9). This illustrates the Closure Property — when you add two integers, the result is always an integer.

2. 2 + 3 = 3 + 2 → a. Commutative Property of Addition
*Explanation:* The order of adding numbers doesn’t change the sum. Swapping 2 and 3 still gives 5. That’s the Commutative Property of Addition.

3. 27 + (–27) → d. Inverse Property of Addition
*Explanation:* Adding a number and its opposite (additive inverse) gives zero: 27 + (–27) = 0. This is the Inverse Property of Addition.

4. 4 + (2 + 3) = (4 + 2) + 3 → c. Associative Property
*Explanation:* Grouping doesn’t matter in addition. Whether you add 2+3 first or 4+2 first, the result is the same. This is the Associative Property.

5. 3 + (6 + 2) = (6 + 2) + 3 → a. Commutative Property of Addition
*Explanation:* Here, the entire group (6+2) is being moved — it’s like saying 3 + 8 = 8 + 3. So this shows Commutative Property of Addition again.

6. 0 + (–8) = –8 → f. Identity Property
*Explanation:* Adding zero to any number leaves it unchanged. Zero is the Additive Identity. So this is the Identity Property.

7. –5 × ¹/₅ = 1 → e. Inverse Property of Multiplication
*Explanation:* Multiplying a number by its reciprocal (multiplicative inverse) gives 1. –5 × (–1/5) would be 1, but here it says –5 × ¹/₅ = –1? Wait — that’s incorrect mathematically. But assuming it's meant to show inverse property, perhaps there’s a typo. If we assume it was meant to be –5 × (–1/5) = 1, then it fits Inverse Property of Multiplication. Alternatively, if it’s truly –5 × ¹/₅ = –1, it doesn't equal 1 — so likely a typo. For educational purposes, we’ll assume intent: e.

*(Note: Strictly speaking, –5 × ¹/₅ = –1, not 1. But since the worksheet says "=1", we'll treat it as illustrating the inverse property with a sign error.)*

8. (13)(–3) = (–3)(13) → b. Commutative Property of Multiplication
*Explanation:* Order doesn’t matter in multiplication. Swapping the factors doesn’t change the product. That’s the Commutative Property of Multiplication.

9. 5 = (5)(1) → f. Identity Property
*Explanation:* Multiplying any number by 1 leaves it unchanged. One is the Multiplicative Identity. So this is the Identity Property.

10. 4(5 – 2) = 4(5) – 4(2) → h. Distributive Property
*Explanation:* Multiplying a number by a difference is the same as multiplying each term inside the parentheses and subtracting. This is the Distributive Property.

11. 3 + [4 + (–4)] = 3 + 0 → d. Inverse Property of Addition
*Explanation:* Inside the brackets, 4 + (–4) = 0 — that’s the additive inverse. So this step uses the Inverse Property of Addition.

12. –3 + 5 = 2 is an integer → g. Closure Property
*Explanation:* The sum of two integers (–3 and 5) is another integer (2). This demonstrates Closure Property.

13. –3(6 + 5) = –18 + (–15) → h. Distributive Property
*Explanation:* Multiply –3 by both 6 and 5 separately and add: –3×6 = –18, –3×5 = –15. This is the Distributive Property.

14. (–3)(–2)(–1)(0) = 0 → j. Zero Property of Multiplication
*Explanation:* Any number multiplied by zero equals zero. No matter what the other numbers are, if one factor is 0, the product is 0. This is the Zero Property of Multiplication.

15. ⁵/₆ × ⁶/₅ = 1 → e. Inverse Property of Multiplication
*Explanation:* Multiplying a number by its reciprocal gives 1. ⁵/₆ and ⁶/₅ are multiplicative inverses. So this is the Inverse Property of Multiplication.

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✔ Final Answer Key:

1. g
2. a
3. d
4. c
5. a
6. f
7. e *(assuming typo; should be –5 × –1/5 = 1)*
8. b
9. f
10. h
11. d
12. g
13. h
14. j
15. e

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Let me know if you’d like a printable version or flashcards for these properties!