Long Multiplication
Learn long multiplication with step-by-step solutions. Multiply large numbers by hand.
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How to Use
- Enter the first number
- Enter the second number
- Click "Multiply"
- View the traditional long multiplication layout and steps
What is Long Multiplication?
Long multiplication (also called column multiplication) is a method for multiplying large numbers by hand. It breaks down the problem by multiplying by each digit of the second number separately, then adding all the partial products together.
Formula
Long Multiplication Process:
1. Multiply by ones digit, write result
2. Multiply by tens digit, shift one place left
3. Continue for each digit
4. Add all partial products
Examples
- 23 × 45: (23×5=115) + (23×40=920) = 1,035
- 156 × 23: (156×3=468) + (156×20=3,120) = 3,588
FAQ
Why do we shift partial products?
When you multiply by the tens digit, you're actually multiplying by that digit times 10. The shift left represents multiplying by 10. Similarly, hundreds digit means shift two places (×100).
What about multiplication with negative numbers?
Multiply the absolute values first, then apply sign rules: if the numbers have the same sign, the result is positive; if different signs, the result is negative.
Is there a faster method?
For mental math, you can break numbers into easier parts (like 25 × 12 = 25 × 10 + 25 × 2 = 250 + 50 = 300). Lattice multiplication is another visual method some find easier.