Скачать или смотреть NCERT Class 8 Mathematics Ch-5 | Is Tathagat's Claim True about Remainder Sum

🎓 Test a Mathematical Claim with Proof!

In this NCERT Class 8 Mathematics Chapter 5 "Number Play" video, we investigate Tathagat's claim: "If you have several numbers that leave remainder 2 when divided by 6, and you add any three such numbers, the sum will ALWAYS be a multiple of 6. Is his claim TRUE or FALSE?" Using concrete examples and rigorous algebraic proof, you'll learn how to test mathematical claims systematically. Perfect for developing mathematical reasoning and proof-writing skills!

📌 WHAT YOU'LL LEARN:
✅ What "remainder 2 when divided by 6" means
✅ Testing claims with concrete examples
✅ The algebraic representation: n = 6k + 2
✅ Adding numbers with the same remainder
✅ Pattern recognition in remainders
✅ How remainders add up
✅ Complete algebraic proof from start to finish
✅ Why examples support but don't prove a claim
✅ The power of mathematical proof
✅ Building confidence in mathematical reasoning

🎯 KEY CONCEPTS COVERED:
• Understanding remainders deeply
• Algebraic representation of numbers with specific remainders
• The formula n = 6k + 2 for numbers leaving remainder 2
• Adding three numbers and analyzing their remainders
• Combining like terms algebraically
• Factoring out common factors (6)
• The connection between remainders and divisibility
• Mathematical proof techniques
• Verification through substitution
• Critical thinking about mathematical claims

💡 PERFECT FOR:
Class 8 Mathematics students
Chapter 5: Number Play curriculum
Students ages 13-14 (Grade 8)
Students learning mathematical proof
Competitive exam preparation (NTSE, IMO)
Visual learners who need clear explanations
Test preparation for school exams
Anyone developing reasoning skills
Students building proof-writing abilities
Teachers seeking engaging proof examples

THE CLAIM: 📢

Tathagat's Statement: "If you add any three numbers that leave remainder 2 when divided by 6, the sum will always be a multiple of 6."

THE INVESTIGATION: 🔍

Example 1: 2 + 8 + 14 = 24
24 ÷ 6 = 4 (exactly) ✓ Multiple of 6!

Example 2: 8 + 20 + 32 = 60
60 ÷ 6 = 10 (exactly) ✓ Multiple of 6!

Example 3: 14 + 26 + 44 = 84
84 ÷ 6 = 14 (exactly) ✓ Multiple of 6!

THE ALGEBRAIC PROOF: 📐

Step 1: Let the three numbers be:
n₁ = 6a + 2
n₂ = 6b + 2
n₃ = 6c + 2

Step 2: Add them:
n₁ + n₂ + n₃ = (6a + 2) + (6b + 2) + (6c + 2)

Step 3: Rearrange:
= 6a + 6b + 6c + 2 + 2 + 2
= 6a + 6b + 6c + 6

Step 4: Factor out 6:
= 6(a + b + c + 1)

Step 5: Conclusion:
Since the sum equals 6 × (a + b + c + 1), it is ALWAYS a multiple of 6!

THE ANSWER: ✅ TATHAGAT'S CLAIM IS TRUE!

LEARNING FEATURES: ✨

Multiple concrete examples before proof. Clear algebraic representation. Step-by-step derivation using TransformMatchingTex. Color-coded mathematical expressions. Verification with actual numbers. Complete logical reasoning chain. Summary of proof structure. Voiceover explanation for clarity.

WHY THIS MATTERS: 💡

This video teaches the essence of mathematical proof:
1. Test your idea with examples
2. Look for a pattern or property
3. Write the claim precisely
4. Prove it algebraically
5. Verify your proof

These are the skills that transform you from a calculator into a MATHEMATICIAN! You learn to think critically and prove your ideas rigorously.

THE POWER OF ALGEBRA: 🚀

Without algebra, you'd need to test INFINITE examples. With algebra, you prove it works for ALL numbers! This is why algebra is so powerful in mathematics.

CRITICAL THINKING: 🧠

Tathagat made a claim. Instead of blindly believing him, we:
1. Tested with examples (good evidence)
2. Proved it algebraically (proof)
3. Verified our proof (validation)

This is the scientific method in mathematics!

STUDY TIPS: 📝

Try proving with different divisors (4, 5, 7, etc.). Test claims before watching the proof. Create your own claim and test it. Use the algebraic method for any remainder claim. Practice writing proofs step by step.

WHY THIS IS DIFFERENT: 🌟

Most textbooks say "Tathagat's claim is true." We ask WHY and HOW, proving it rigorously. This deeper understanding leads to real mathematical confidence!

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