Properties of Operation in Integers worksheet - Free Printable

Problem: Matching Properties of Integers

The task is to match each statement in Column A with the correct property of integers listed in Column B. Here's a detailed explanation and solution for each statement.

---

Column A Statements and Their Matching Properties

#### 1. \( 5 + 4 = 9 \)
- Explanation: This is a basic addition of two integers, showing that the result is also an integer.
- Property: g. Closure Property (Addition of integers results in another integer.)
- Answer: g

#### 2. \( 2 + 3 = 3 + 2 \)
- Explanation: The order of addition does not affect the result.
- Property: a. Commutative Property of Addition
- Answer: a

#### 3. \( 27 + (-27) = 0 \)
- Explanation: Adding a number to its additive inverse results in zero.
- Property: d. Inverse Property of Addition
- Answer: d

#### 4. \( 4 + (2 + 3) = (4 + 2) + 3 \)
- Explanation: The grouping of numbers does not affect the result of addition.
- Property: c. Associative Property
- Answer: c

#### 5. \( 3 + (6 + 2) = (6 + 2) + 3 \)
- Explanation: This shows both the associative and commutative properties of addition. However, the primary focus here is on the grouping (associativity).
- Property: c. Associative Property
- Answer: c

#### 6. \( 0 + (-8) = -8 \)
- Explanation: Adding zero to any integer leaves the integer unchanged.
- Property: f. Identity Property
- Answer: f

#### 7. \( -5 \times \frac{1}{5} = 1 \)
- Explanation: Multiplying a number by its multiplicative inverse results in 1.
- Property: e. Inverse Property of Multiplication
- Answer: e

#### 8. \( (13)(-3) = (-3)(13) \)
- Explanation: The order of multiplication does not affect the result.
- Property: b. Commutative Property of Multiplication
- Answer: b

#### 9. \( 5 = (5)(1) \)
- Explanation: Multiplying any integer by 1 leaves the integer unchanged.
- Property: f. Identity Property
- Answer: f

#### 10. \( 4(5 - 2) = 4(5) - 4(2) \)
- Explanation: Distributing a factor over a sum or difference.
- Property: h. Distributive Property
- Answer: h

#### 11. \( 3 + [4 + (-4)] = 3 + 0 \)
- Explanation: Adding a number to its additive inverse results in zero, and then adding zero to any number leaves it unchanged.
- Property: d. Inverse Property of Addition (primary) and f. Identity Property (secondary)
- Answer: d

#### 12. \( -3 + 5 = 2 \) is an integer
- Explanation: The result of adding two integers is always an integer.
- Property: g. Closure Property (Addition of integers results in another integer.)
- Answer: g

#### 13. \( -3(6 + 5) = -18 + (-15) \)
- Explanation: Distributing a factor over a sum.
- Property: h. Distributive Property
- Answer: h

#### 14. \( (-3)(-2)(-1)(0) = 0 \)
- Explanation: Multiplying any number by zero results in zero.
- Property: j. Zero Property of Multiplication
- Answer: j

#### 15. \( \frac{5}{6} \times \frac{6}{5} = 1 \)
- Explanation: Multiplying a number by its multiplicative inverse results in 1.
- Property: e. Inverse Property of Multiplication
- Answer: e

---

Final Answer

Matching the statements in Column A with the properties in Column B:

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

\[
\boxed{g, a, d, c, c, f, e, b, f, h, d, g, h, j, e}
\]