हिंदी में जवाब दो: Explain why the sum of any three consecutive whole numbers is always divisible by 3. Illustrate your reasoning with two examples.
Get the complete, step-by-step math solution for: "हिंदी में जवाब दो: Explain why the sum of any three consecutive whole numbers is always divisible by 3. Illustrate your reasoning with two examples.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Representing Consecutive Whole Numbers
Let's represent any whole number as n. Then, the next two consecutive whole numbers will be n+1 and n+2. These three expressions represent any three consecutive whole numbers.
Step 2: Finding the Sum
Now, we need to find the sum of these three consecutive whole numbers. We add the three expressions together.
Step 3: Simplifying the Sum
When we add n, n+1, and n+2, we get 3n+3. We can factor out 3 from this expression, which gives us 3(n+1).
Step 4: Conclusion on Divisibility
Since the sum can be written as 3(n+1), it means the sum is always a multiple of 3. Therefore, the sum of any three consecutive whole numbers is always divisible by 3.
Step 5: Example 1
Let's take an example with the numbers 4, 5, and 6. Their sum is 4+5+6=15. When we divide 15 by 3, we get 5, which confirms that 15 is divisible by 3.
Step 6: Example 2
For another example, consider the numbers 10, 11, and 12. Their sum is 10+11+12=33. Dividing 33 by 3 gives us 11, again showing that the sum is divisible by 3.