Скачать или смотреть NCERT Class 8 Mathematics Ch-5 | Find Numbers with Specific Remainders Algebraic Expression

🎓 Master Remainder Problems with Algebraic Expressions!

In this NCERT Class 8 Mathematics Chapter 5 "Number Play" video, we solve: Find numbers that leave remainder 2 when divided by 3 AND remainder 2 when divided by 4. Then write an algebraic expression to describe ALL such numbers. Perfect for understanding remainders, LCM, and building algebraic thinking!

📌 WHAT YOU'LL LEARN:
✅ What are remainders and how to find them
✅ Testing numbers against multiple conditions
✅ Finding numbers that satisfy BOTH conditions simultaneously
✅ Discovering patterns in number sequences
✅ Understanding LCM (Least Common Multiple)
✅ Writing algebraic expressions for number sequences
✅ The formula: LCM × n + r (where r is remainder)
✅ Applying the formula to find general solutions
✅ Verification of algebraic expressions
✅ Real-world applications of remainder problems

🎯 KEY CONCEPTS COVERED:
• Understanding remainders when dividing numbers
• Testing single and multiple conditions
• Finding common elements in two sets
• Pattern recognition in sequences
• Discovering the constant difference (related to LCM)
• The role of LCM in remainder problems
• Algebraic representation of sequences
• Generalization from specific to general
• Building and verifying formulas

💡 PERFECT FOR:
Class 8 Mathematics students
Chapter 5: Number Play curriculum
Students ages 13-14 (Grade 8)
Students learning algebraic thinking
Competitive exam preparation (NTSE, IMO)
Visual learners who need animated explanations
Test preparation for school exams
Anyone developing problem-solving skills
Students learning modular arithmetic basics
Foundation building for number theory

THE PROBLEM BREAKDOWN: 🔍

Find numbers that leave remainder 2 when divided by 3 AND remainder 2 when divided by 4.

Step 1: Numbers leaving remainder 2 when ÷3: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38...

Step 2: Numbers leaving remainder 2 when ÷4: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38...

Step 3: Common numbers (in BOTH lists): 2, 14, 26, 38, 50...

Step 4: Find the pattern: Difference is always 12! Why? Because LCM(3,4) = 12

Step 5: Write algebraic expression: 12n + 2 (where n = 0, 1, 2, 3, ...)

THE SOLUTION: 🌟

Numbers: 2, 14, 26, 38, 50, 62, 74...

Algebraic Expression: 12n + 2 where n = 0, 1, 2, 3, 4...

Verification:
For n=1: 12(1) + 2 = 14 ✓
14 ÷ 3 = 4 remainder 2 ✓
14 ÷ 4 = 3 remainder 2 ✓

For n=2: 12(2) + 2 = 26 ✓
26 ÷ 3 = 8 remainder 2 ✓
26 ÷ 4 = 6 remainder 2 ✓

LEARNING FEATURES: ✨

Complete NCERT Chapter 5 problem coverage. High-quality Manim animations throughout. Color-coded mathematical expressions. Number lists side by side for comparison. Pattern discovery with visual emphasis. LCM explanation and application. Step-by-step algebraic derivation. Multiple verification examples. Voiceover narration for clarity.

STUDY TIPS: 📝

Work through the problem before watching. Try finding numbers with different remainders. Create your own remainder problems. Write algebraic expressions for various patterns. Verify solutions by substitution. Understand the LCM connection. Practice with different divisors.

WHY THIS MATTERS: 💡

Remainder problems build algebraic thinking. You learn to express patterns mathematically. This foundation is crucial for advanced mathematics like modular arithmetic, cryptography, and computer science algorithms. Understanding how to generalize from examples to formulas is a core mathematical skill!

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