NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice Questions

Question 20

Goal: Find the statement that is not true for whole numbers.

First, recall these ideas:

• Identity for addition: adding 0 keeps a number the same.
  \(a + 0 = a\)
• Identity for multiplication: multiplying by 1 keeps a number the same.
  \(a \times 1 = a\)
• Commutative: order does not matter.
  Addition: \(a + b = b + a\)
  Multiplication: \(a \times b = b \times a\)
• Associative: grouping does not matter.
  Addition: \((a + b) + c = a + (b + c)\)
  Multiplication: \((a \times b) \times c = a \times (b \times c)\)
• Distributive: multiply first number with each part inside brackets.
  \(a \times (b + c) = a \times b + a \times c\)

Check each option with small examples:

A. Associative (True)

Addition example:

\((2 + 3) + 4 = 5 + 4 = 9\)

\(2 + (3 + 4) = 2 + 7 = 9\)

Multiplication example:

\((2 \times 3) \times 4 = 6 \times 4 = 24\)

\(2 \times (3 \times 4) = 2 \times 12 = 24\)

B. “Zero is the identity for multiplication.” (Not true)

Test with \(5\):

\(5 \times 0 = 0\) ≠ \(5\)

This changes the number, so 0 cannot be the identity.

The correct multiplicative identity is 1:

\(5 \times 1 = 5\)

C. Commutative (True)

Addition: \(3 + 5 = 8\) and \(5 + 3 = 8\)

Multiplication: \(3 \times 5 = 15\) and \(5 \times 3 = 15\)

D. Distributive (True)

\(2 \times (3 + 4) = 2 \times 7 = 14\)

\(2 \times 3 + 2 \times 4 = 6 + 8 = 14\)

Conclusion: Option B is the only statement that is not true.