Technique explanation
Teaching Explanation
Multiplying a two-digit number by 11 can be visualized as "opening up" the number to let the sum of its digits sit in the middle. For example, to multiply 42 by 11, you split 4 and 2 and place their sum (6) between them to get 462. If the sum of the digits is 10 or greater, we use a carry rail—a small notation below the hundreds place—to add the extra 1 to the leading digit. This ensures the place value remains correct without complex mental bookkeeping.
Method Conditions
Multiplication of a two-digit integer by 11.
Standard Fallback
Standard long multiplication ($n \times 10 + n \times 1$).
Misconception & Correction
Misconception: Writing the entire sum in the middle (e.g., $75 \times 11 = 7125$).
Correction: Only one digit can occupy the tens place. The tens digit of the sum must carry over to the hundreds place.
Module
Worked examples
Worked Examples
- Calculate $42 \times 11$. Step 1: Split the digits 4 and 2. Step 2: Add them: $4 + 2 = 6$. Step 3: Place 6 in the middle: 462. Verification: $42 \times 10 = 420$; $420 + 42 = 462$.
- Calculate $75 \times 11$. Step 1: Split the digits 7 and 5. Step 2: Add them: $7 + 5 = 12$. Step 3: Place 2 in the middle and carry 1 to the 7: $(7+1) \dots 2 \dots 5 = 825$. Verification: $75 \times 10 = 750$; $750 + 75 = 825$.
Academy Course
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