NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False QuestionsQuestion 78
Class 6 - Mathematics - Unit 1: Number System - True or False Questions
Question. 78
Sum of two consecutive odd numbers is always divisible by 4.
Answer:
true
Detailed Answer with Explanation:
Let the two consecutive odd numbers be \(2k+1\) and \(2k+3\), where \(k\) is any whole number.
Add them step by step:
\((2k+1) + (2k+3)\)
= \(2k + 1 + 2k + 3\)
= \((2k + 2k) + (1 + 3)\)
= \(4k + 4\)
Now factor out 4:
= \(4(k+1)\)
Because the sum is \(4 \times (k+1)\), it is a multiple of 4. So, the statement is true.