Multiplying by 11
The Sandwich Method for instant answers.
Core Concepts
Multiplying any two-digit number by 11 is one of the most famous and easiest tricks in Vedic Math. We call it the "Sandwich Method" because you split the number and put the sum in the middle!
The Rule
To multiply a two-digit number by 11:
1. Split the two digits apart.
2. Add them together.
3. Place the sum in the middle.
Solved Examples
Example 1: The Basics
Question: Solve 32 × 11.
• Step 1: Split the digits 3 and 2.
• 3 _ 2
• Step 2: Add them: 3 + 2 = 5.
• Step 3: Put 5 in the middle.
• Answer: 352.
Example 2: Another Simple One
Question: Solve 45 × 11.
• Step 1: Split 4 and 5.
• 4 _ 5
• Step 2: Add them: 4 + 5 = 9.
• Step 3: Put 9 in the middle.
• Answer: 495.
Example 3: What if the sum is 10 or more? (Carry)
Question: Solve 85 × 11.
• Step 1: Split 8 and 5.
• 8 _ 5
• Step 2: Add them: 8 + 5 = 13.
• Step 3: We can't put 13 in one spot! So put the 3 in the middle and carry the 1 to the left.
• (8 + 1) _ 3 _ 5
• 9 _ 3 _ 5
• Answer: 935.
Example 4: Three Digits
Question: Solve 123 × 11.
• For larger numbers, write the first digit, then add pairs from left to right, then write the last digit.
• First: 1
• Middle 1: 1 + 2 = 3
• Middle 2: 2 + 3 = 5
• Last: 3
• Answer: 1353.
