Algebraic Lightning Trick
Multiplying by 11 (Split & Insert Sum)
To multiply any two-digit number by 11, separate the two digits and drop their sum into the space between them. If the sum is 10 or greater, simply carry 1 into the hundreds place.
Mathematical Symmetry & Identity
$$AB \times 11 = A \; | \; (A+B) \; | \; B$$
Visual Mental Pipeline
Step-by-Step Execution Rules
- 1 No carry (A + B < 10): Split the digits A and B, and insert (A + B) in the center. Example: 35 × 11 → 3 _ 5 → 3 + 5 = 8 → 385.
- 2 With carry (A + B >= 10): If the sum has two digits, keep the last digit in the center and add 1 to the first digit. Example: 78 × 11 → 7 + 8 = 15 → (7 + 1) _ 5 _ 8 = 858.
- 3 Why it works: AB × 11 = AB × 10 + AB = 100A + 10(A+B) + B.
Worked Examples & Thought Process
35 × 11
Example 1
Step 1: Split: 3 _ 5
Step 2: Insert 3+5=8 → 385
= 385
52 × 11
Example 2
Step 1: Split: 5 _ 2
Step 2: Insert 5+2=7 → 572
= 572
78 × 11
Example 3
Step 1: 7 + 8 = 15 (carry 1)
Step 2: (7+1) _ 5 _ 8 = 858
= 858
94 × 11
Example 4
Step 1: 9 + 4 = 13 (carry 1)
Step 2: (9+1) _ 3 _ 4 = 1034
= 1034
Ready to Hone Your Speed?
Put this shortcut into practice with 10 procedural, timed questions. Sharpen your reaction time and track your accuracy.