Properties of Operation in Integers worksheet - Free Printable

Let's solve this step by step. The task is to match each expression in Column A with the correct property of integers listed in Column B.

We’ll go through each item in Column A and identify which property it illustrates.

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🔹 Definitions of Properties (for reference):

- a. Commutative Property of Addition: $ a + b = b + a $
- b. Commutative Property of Multiplication: $ a \times b = b \times a $
- c. Associative Property: $ (a + b) + c = a + (b + c) $ or $ (a \times b) \times c = a \times (b \times c) $
- d. Inverse Property of Addition: $ a + (-a) = 0 $
- e. Inverse Property of Multiplication: $ a \times \frac{1}{a} = 1 $ (for $ a \neq 0 $)
- f. Identity Property:
- Addition: $ a + 0 = a $
- Multiplication: $ a \times 1 = a $
- g. Closure Property: The sum or product of two integers is also an integer.
- h. Distributive Property: $ a(b + c) = ab + ac $
- i. Zero Property of Addition: $ a + 0 = a $ → This is actually the same as Identity Property of Addition, but sometimes listed separately.
- j. Zero Property of Multiplication: $ a \times 0 = 0 $

Note: Zero Property of Addition (i) is redundant with Identity Property (f), but since both are listed, we'll use them accordingly.

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Now let’s match each:

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1. 5 + 4 = 9
→ This is just a simple addition, no rearrangement or grouping.
But 9 is the result, and it shows that adding two integers gives another integer.
✔ g. Closure Property
✔️ Answer: g

2. 2 + 3 = 3 + 2
→ Order changed in addition → Commutative Property of Addition
✔ a. Commutative Property of Addition
✔️ Answer: a

3. 27 + (–27)
→ This is $ a + (-a) $ → Sum is zero.
✔ d. Inverse Property of Addition
✔️ Answer: d

4. 4 + (2 + 3) = (4 + 2) + 3
→ Grouping changed → Associative Property of Addition
✔ c. Associative Property
✔️ Answer: c

5. 3 + (6 + 2) = (6 + 2) + 3
→ Left side: $ 3 + (6+2) $, right: $ (6+2) + 3 $ → order changed between 3 and (6+2)
→ So it's commutative: $ a + b = b + a $, where $ a=3 $, $ b=8 $
✔ a. Commutative Property of Addition
✔️ Answer: a

6. 0 + (–8) = –8
→ Adding zero doesn’t change the number → Identity Property of Addition
✔ f. Identity Property
✔️ Answer: f

7. –5 × (1/5) = 1
→ Multiplying a number by its reciprocal gives 1 → Inverse Property of Multiplication
✔ e. Inverse Property of Multiplication
✔️ Answer: e

8. (13)(–3) = (–3)(13)
→ Order changed in multiplication → Commutative Property of Multiplication
✔ b. Commutative Property of Multiplication
✔️ Answer: b

9. 5 = (5)(1)
→ Multiplying by 1 gives the same number → Identity Property of Multiplication
✔ f. Identity Property
✔️ Answer: f

10. 4(5 – 2) = 4(5) – 4(2)
→ Distributing 4 over subtraction → Distributive Property
✔ h. Distributive Property
✔️ Answer: h

11. 3 + [4 + (–4)] = 3 + 0
→ Here, $ 4 + (-4) = 0 $ → inverse of addition
→ Then $ 3 + 0 = 3 $ → identity
But the key idea is adding a number and its opposite → Inverse Property of Addition
✔ d. Inverse Property of Addition
✔️ Answer: d

12. –3 + 5 = 2 is an integer
→ Two integers added give an integer → Closure Property
✔ g. Closure Property
✔️ Answer: g

13. –3(6 + 5) = –18 + (–15)
→ Left: $ -3(11) = -33 $
Right: $ -18 + (-15) = -33 $
→ This is distributing $ -3 $ over $ 6+5 $ → Distributive Property
✔ h. Distributive Property
✔️ Answer: h

14. (–3)(–2)(–1)(0) = 0
→ Any number multiplied by 0 is 0 → Zero Property of Multiplication
✔ j. Zero Property of Multiplication
✔️ Answer: j

15. (5/6) × (6/5) = 1
→ Reciprocals multiplying to 1 → Inverse Property of Multiplication
✔ e. Inverse Property of Multiplication
✔️ Answer: e

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✔ Final Answers (Column A → Letter):

1. g
2. a
3. d
4. c
5. a
6. f
7. e
8. b
9. f
10. h
11. d
12. g
13. h
14. j
15. e

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📝 Summary Table:

| # | Answer |
|---|--------|
| 1 | g |
| 2 | a |
| 3 | d |
| 4 | c |
| 5 | a |
| 6 | f |
| 7 | e |
| 8 | b |
| 9 | f |
|10 | h |
|11 | d |
|12 | g |
|13 | h |
|14 | j |
|15 | e |

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✔ All matched correctly! Let me know if you want this printed or formatted for submission.