Mastering digital Sum concepts and shortcuts for competitive examination

Digital Sum: Zero to Hero

The Magic of "Casting Out Nines"

1. Beginner: What is Digital Sum?

Digital sum kisi bhi number ke digits ko tab tak add karne ka process hai jab tak humein ek single digit (1-9) na mil jaye.

Example: Digital sum of 456
4 + 5 + 6 = 15
1 + 5 = 6

Rule of 9: Digital sum nikalte waqt '9' ko '0' maana ja sakta hai. Isse calculation fast ho jati hai.

2. Intermediate: Operations with Digital Sum

• Addition: LHS ka digital sum = RHS ka digital sum.
• Multiplication: Numbers ko multiply karne ke bajaye unke digital sums ko multiply karein.
• Subtraction: Agar result negative aaye, toh usme 9 add kar dein.
  Ex: 2 - 5 = -3. So, -3 + 9 = 6.

3. Advanced: Division & Square Roots

Division mein humein denominator ka digital sum 1 banana hota hai:

• Agar niche 2 ho, toh upar-niche 5 se multiply karein (2x5=10 -> 1).
• Agar niche 8 ho, toh upar-niche 8 se multiply karein (8x8=64 -> 10 -> 1).

Perfect Square Rule: Kisi bhi perfect square ka digital sum hamesha 1, 4, 7, ya 9 hi hota hai.