Magic Number 11 Trick : 11 ā§° āĻāĻžāĻĻā§āĻā§°ā§ āĻā§āĻŖāĻ¨ āĻā§āĻļāĻ˛
Trick: Magic Number 11 : 11 ā§° āĻāĻžāĻĻā§āĻā§°ā§ āĻā§āĻŖāĻ¨ āĻā§āĻļāĻ˛
The Rule / āĻ¨āĻŋā§āĻŽ
For any 2-digit number ab: Multiply by 11 using this pattern: a (a+b) b (āĻ¯āĻŋāĻā§āĻ¨ā§ ā§¨ āĻ āĻāĻā§° āĻ¸āĻāĻā§āĻ¯āĻž ab āĻ 11 ā§°ā§ āĻā§āĻŖ āĻā§°āĻŋāĻŦāĻ˛ā§: āĻĒā§ā§°āĻĨāĻŽ āĻ āĻāĻ āĻ˛āĻŋāĻāĻž → āĻĻā§āĻ¯āĻŧā§āĻāĻž āĻ āĻāĻ āĻ¯ā§āĻ āĻā§°āĻž → āĻļā§āĻˇ āĻ āĻāĻ āĻ˛āĻŋāĻāĻž)
- Keep the first digit (āĻĒā§ā§°āĻĨāĻŽ āĻ āĻāĻāĻā§ āĻ˛āĻŋāĻāĻž)
- Add the two digits (āĻĻā§āĻ¯āĻŧā§āĻāĻž āĻ āĻāĻ āĻ¯ā§āĻ āĻā§°āĻž)
- Keep the last digit (āĻļā§āĻˇ āĻ āĻāĻāĻā§ āĻ˛āĻŋāĻāĻž)
Formula / āĻ¸ā§āĻ¤ā§ā§° : For number ab: ab × 11 → a (a+b) b
Examples / āĻāĻĻāĻžāĻšā§°āĻŖ
i. 34 × 11 = 3 3+4=7 4 Ans = 374
ii. 52 × 11 = 5 5+2 = 7 2 Ans = 572
iii. 81 × 11 = 8 8+1=9 1 Ans = 891
Carry Method : Carry āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
If the middle sum is 10 or more, carry 1. (āĻ¯āĻĻāĻŋ āĻŽāĻžāĻā§° āĻ¯ā§āĻāĻĢāĻ˛ 10 āĻŦāĻž āĻ¤āĻžāĻ¤āĻā§ āĻĄāĻžāĻā§° āĻšāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§ carry āĻā§°āĻŋāĻŦ āĻ˛āĻžāĻā§āĨ¤)
iv. 57 × 11 = 5 5+7 = 12 7
Write 2 in the middle and carry 1 to 5.
5 + 1 = 6 Ans = 627
v. 68 × 11 = 6 6+8=14 8
Write 4 and carry 1.
6 + 1 = 7
Ans = 748
It Helps : i. Makes multiplication very fast, ii. Improves mental maths
iii. Useful in competitive exams iv. Saves calculation time