NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False Questions
Question 75

Question. 75

Every multiple of a number is greater than or equal to the number.

Answer:

false

Detailed Answer with Explanation:

Step 1: A multiple of a number \(n\) is any number of the form \(k \times n\), where \(k\) is a whole number \(0, 1, 2, \dots\).

Step 2: Take \(k = 0\). Then \(0 \times n = 0\). So \(0\) is a multiple of \(n\).

Step 3: If \(n > 0\), we know \(0 < n\).

Step 4: This shows there exists a multiple of \(n\) (namely \(0\)) that is less than \(n\), not \(\ge n\).

Conclusion: The statement is false.

Extra note (optional): For a negative number (e.g., \(n = -3\)), the multiple \(2 \times n = -6\) is also less than \(n\), so the statement still fails.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – True or False Questions | Detailed Answers