Match the following columns on whole numbers:
`{:(" Column A", " Column B"), ((a) 137+63=63+137,"(i) Associativity of multiplication"),((b) (16xx25)" is a whole number", "(ii) Commutativity of multiplication"),((c) 365xx18=18xx365, "(iii) Distributive law of multiplication"), (," over addition"),((d)(86xx14)xx25=86xx(14xx25),"(iv) Commutativity of addition"),((e) 23xx(80+5)=(23xx80)+(23xx5), "(v) Closure property for multiplication"):} `

Answer

To solve the question of matching the properties of whole numbers in Column A with their corresponding descriptions in Column B, we will analyze each statement in Column A and identify the correct property from Column B.

### Step-by-Step Solution:

1. **Match (a) 137 + 63 = 63 + 137**
- This statement demonstrates the property where the order of addition does not affect the sum. This is known as the **Commutative Property of Addition**.
- **Match:** (a) → (iv)

2. **Match (b) (16 × 25) is a whole number**
- The multiplication of two whole numbers (16 and 25) results in a whole number, which illustrates the **Closure Property for Multiplication**.
- **Match:** (b) → (v)

3. **Match (c) 365 × 18 = 18 × 365**
- This statement shows that the order of multiplication does not affect the product, which is known as the **Commutative Property of Multiplication**.
- **Match:** (c) → (ii)

4. **Match (d) (86 × 14) × 25 = 86 × (14 × 25)**
- This statement indicates that when multiplying three numbers, the grouping of the numbers does not affect the product, which is known as the **Associative Property of Multiplication**.
- **Match:** (d) → (i)

5. **Match (e) 23 × (80 + 5) = (23 × 80) + (23 × 5)**
- This statement illustrates the property that allows multiplication to be distributed over addition, known as the **Distributive Law of Multiplication over Addition**.
- **Match:** (e) → (iii)

### Final Matches:
- (a) → (iv) Commutativity of addition
- (b) → (v) Closure property for multiplication
- (c) → (ii) Commutativity of multiplication
- (d) → (i) Associativity of multiplication
- (e) → (iii) Distributive law of multiplication over addition