To do long multiplication, follow these clear steps:
Steps for Long Multiplication
- Write the numbers in columns
Place the larger number on top and the smaller number below it, aligning the digits by place value (ones under ones, tens under tens, etc.)
- Multiply by the rightmost digit of the bottom number
Multiply this digit by each digit of the top number, starting from the right (ones place) to the left. Write the result below the line, starting from the right. If a product is more than 9, carry over the extra value to the next digit multiplication
- Multiply by the next digit to the left in the bottom number
Move one digit to the left in the bottom number. Multiply this digit by each digit of the top number as before. Write this new row of results below the first, but shift it one place to the left (add a zero or leave a space at the right) to account for place value
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Repeat for all digits in the bottom number
Continue this process for each digit in the bottom number, shifting the starting position one place to the left each time. -
Add all the rows together
Finally, add all the rows of partial products to get the final answer. Carry over digits as needed during addition
Example: Multiply 244 by 121
- Multiply 244 by 1 (ones place): 244
- Multiply 244 by 2 (tens place): 4880 (write shifted one place to the left)
- Multiply 244 by 1 (hundreds place): 24400 (write shifted two places to the left)
- Add all: 244 + 4880 + 24400 = 29524
Additional Tips
- When carrying numbers, add the carried value to the next multiplication result.
- Practice with different sized numbers to build confidence.
- This method is also called the column method and is useful for multiplying large numbers beyond simple multiplication tables
This approach breaks multiplication into manageable parts and then sums them, making it easier to handle large numbers by hand
