NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False Questions
Question 74

Question. 74

A whole number divided by another whole number greater than 1 never gives the quotient equal to the former.

Answer:

true

Detailed Answer with Explanation:

We want to see if the quotient (result of division) can be the same as the first number.

  1. Let the first number be \(a\) (the dividend) and the second number be \(b\) (the divisor) with \(b > 1\).
  2. When we divide, we can write: \(a = b \times q + r\) where \(q\) is the quotient and \(0 \le r < b\).
  3. If \(r = 0\), then \(q = \dfrac{a}{b}\). Since \(b \ge 2\), we have \(\dfrac{a}{b} \le \dfrac{a}{2}\), so \(q < a\).
  4. If \(r > 0\), then \(q = \left\lfloor \dfrac{a}{b} \right\rfloor\). This means \(q < \dfrac{a}{b} \le \dfrac{a}{2}\), so again \(q < a\).
  5. In both cases, the quotient is strictly less than \(a\), not equal to \(a\).

Therefore, dividing a whole number by a number greater than 1 never gives a quotient equal to the first number.

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