Technique explanation
To multiply any number by 12, use the 'double and add neighbor' rule. Working from right to left, double the current digit and add the digit to its immediate right (the neighbor). Add a leading zero to the number to ensure the first digit is processed correctly.
Method Condition: Specifically for the multiplier 12.
Standard fallback: Conventional long multiplication or the distributive property: (N × 10) + (N × 2).
Worked examples
Example 1: No Carries
Calculate 123 × 12.
- Last digit (3): 3 × 2 + 0 = 6.
- Middle digit (2): 2 × 2 + 3 = 7.
- First digit (1): 1 × 2 + 2 = 4.
- Leading zero: 0 × 2 + 1 = 1.
- Result: 1476.
- Check: 123 × 10 + 123 × 2 = 1230 + 246 = 1476.
Example 2: With Carries
Calculate 789 × 12.
- Last digit (9): 9 × 2 + 0 = 18. Write 8, carry 1.
- Middle digit (8): 8 × 2 + 9 + 1 (carry) = 26. Write 6, carry 2.
- First digit (7): 7 × 2 + 8 + 2 (carry) = 24. Write 4, carry 2.
- Leading zero: 0 × 2 + 7 + 2 (carry) = 9.
- Result: 9468.
- Check: 789 × 10 + 789 × 2 = 7890 + 1578 = 9468.
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