Friendly Numbers

Using Complements to calculate faster.

Core Concepts

Friendly Numbers (or Complements) are pairs of numbers that add up to a base number like 10, 100, or 1000. In Vedic Math, knowing these pairs instantly is the key to high-speed calculation.

Complements of 10

These are the pairs that sum to 10. Memorize them!

• 1 + 9
• 2 + 8
• 3 + 7
• 4 + 6
• 5 + 5

Solved Examples

Example 1: Finding the Complement

Question: What is the complement of 3 from 10?

• We need a number that adds to 3 to make 10.

• 10 - 3 = 7.

• Answer: 7.

Example 2: Using Friends for Addition

Question: Add 8 + 5 + 2.

• Step 1: Look for friendly numbers.

• 8 and 2 are friends (they make 10).

• Step 2: Add them first: 8 + 2 = 10.

• Step 3: Add the remaining number: 10 + 5 = 15.

• Answer: 15.

This is much faster than doing 8 + 5 = 13, then 13 + 2 = 15!

Example 3: Completing the Ten

Question: Add 27 + 4.

• Step 1: 27 needs 3 to become the next ten (30).

• Step 2: Take 3 from 4. (4 splits into 3 + 1).

• Step 3: 27 + 3 = 30.

• Step 4: 30 + 1 = 31.

• Answer: 31.

Example 4: Complements of 9

Question: What is the complement of 4 from 9?

• Sometimes we need numbers to add up to 9 (for subtraction tricks).

• 9 - 4 = 5.

• Answer: 5.