Fast Subtraction
The "All from 9 and the Last from 10" Sutra.
Core Concepts
Subtracting numbers from a "base" like 100, 1000, or 10,000 is usually tricky because of all the borrowing (regrouping). Vedic Math offers a powerful Sutra (formula) called "All from 9 and the Last from 10" (Nikhilam Navatashcaramam Dashatah) that solves this instantly without borrowing.
The Rule
To subtract any number from a power of 10 (like 100, 1000, etc.):
1. Subtract all digits from 9.
2. Subtract the very last digit (the one on the right) from 10.
Solved Examples
Example 1: Subtracting from 1000
Question: Solve 1000 - 357.
• Apply the rule to 357.
• First digit (3): Subtract from 9 → 9 - 3 = 6.
• Middle digit (5): Subtract from 9 → 9 - 5 = 4.
• Last digit (7): Subtract from 10 → 10 - 7 = 3.
• Answer: 643.
Example 2: Subtracting from 100
Question: Solve 100 - 72.
• Apply the rule to 72.
• First digit (7): Subtract from 9 → 9 - 7 = 2.
• Last digit (2): Subtract from 10 → 10 - 2 = 8.
• Answer: 28.
Example 3: Subtracting from 10,000
Question: Solve 10,000 - 1,234.
• 1: 9 - 1 = 8.
• 2: 9 - 2 = 7.
• 3: 9 - 3 = 6.
• 4 (Last): 10 - 4 = 6.
• Answer: 8,766.
Example 4: When the number is smaller
Question: Solve 1000 - 50.
• Treat 50 as 050 to match the zeros in 1000.
• 0: 9 - 0 = 9.
• 5: 9 - 5 = 4.
• 0 (Last non-zero digit rule exception): Actually, for numbers ending in 0, we just copy the 0 at the end and apply the rule to the rest.
• Alternative Method: 100 - 5 = 95, so 1000 - 50 = 950.
• Answer: 950.
