Скачать или смотреть Larry Math Class 120 | Divisibility Rules 3 and 9 Proof

Ever wondered why the shortcut for divisibility by 3 actually works? We all know the rule: if the sum of the digits is divisible by 3, the entire number is too. But in this episode of Larry Math Class, Malcolm takes us beyond the "how" and dives deep into the "why" with a formal mathematical proof!

Using the number 87,654,321 as a case study, Malcolm breaks down the logic of place value. By expanding a large number into powers of 10 and rewriting those powers as a series of 9s plus 1 (for example, 1,000 = 999 + 1), he demonstrates how the "9s" are naturally divisible by 3. This leaves only the individual digits behind to be tested.

Key takeaways from this lesson include:
*Place Value Expansion:* Understanding how to represent numbers using powers of 10.
*The "9s" Method:* Why breaking numbers into (10^n - 1) + 1 is the key to divisibility proofs.
*Common Factors:* How adding two numbers with a common factor of 3 results in a total that is also divisible by 3.
*Universal Application:* Why this same logic applies to testing divisibility by 9.

Whether you are a student looking to sharpen your number theory skills or a math enthusiast who loves a good proof, this video clarifies a fundamental concept in a clear, engaging way. Plus, stay tuned for a special birthday shout-out at the end!

Don't just memorize the rules—master the logic behind them. Hit play and learn how to prove the divisibility rule for 3 and 9 like a pro!