Which of the following statements is not true?

Options

A. Both addition and multiplication are associative for whole numbers.
B. Zero is the identity for muliplication of whole numbers.
C. Addition and multiplication both are commutative for whole numbers.
D. Multiplication is distributive over addition for whole numbers.

Answer

To determine which statement is not true, we will analyze each of the four statements one by one.

### Step 1: Analyze the First Statement
**Statement:** Both addition and multiplication are associative for whole numbers.

**Explanation:** The associative property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. For example:
- For addition: (a + b) + c = a + (b + c)
- Let’s take a = 2, b = 3, c = 5:
- (2 + 3) + 5 = 5 + 5 = 10
- 2 + (3 + 5) = 2 + 8 = 10
- For multiplication: (a × b) × c = a × (b × c)
- Let’s take a = 2, b = 3, c = 5:
- (2 × 3) × 5 = 6 × 5 = 30
- 2 × (3 × 5) = 2 × 15 = 30

**Conclusion:** This statement is true.

### Step 2: Analyze the Second Statement
**Statement:** 0 is the identity for multiplication of whole numbers.

**Explanation:** The identity element for a mathematical operation is a number that, when used in the operation with any number, does not change that number. For multiplication, the identity element is 1, not 0.
- For example:
- 2 × 1 = 2 (identity)
- 2 × 0 = 0 (not identity)

**Conclusion:** This statement is false.

### Step 3: Analyze the Third Statement
**Statement:** Addition and multiplication are commutative for whole numbers.

**Explanation:** The commutative property states that changing the order of the numbers does not change the sum or product.
- For addition: a + b = b + a
- Example: 2 + 3 = 5 and 3 + 2 = 5
- For multiplication: a × b = b × a
- Example: 2 × 3 = 6 and 3 × 2 = 6

**Conclusion:** This statement is true.

### Step 4: Analyze the Fourth Statement
**Statement:** Multiplication is distributive over addition for whole numbers.

**Explanation:** The distributive property states that a × (b + c) = (a × b) + (a × c).
- Example: Let a = 13, b = 100, c = 2
- 13 × (100 + 2) = 13 × 102 = 1326
- (13 × 100) + (13 × 2) = 1300 + 26 = 1326

**Conclusion:** This statement is true.

### Final Conclusion
The only statement that is not true is the second statement: **0 is the identity for multiplication of whole numbers.**

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