How to Do Long Multiplication

Do you know how to multiply two multiple-digit numbers together? If not, or you would like to brush up your skills in this area, this article takes you through the method step-by-step.

Steps   

  1. Follow this example. Say that you want to multiply 756 and 32. (Note that there is nothing special about these numbers - they are used for demonstration purposes here.) This technique will work for any numbers, however long. Write it out like this:
    Be sure to line up your columns
  2. Start from the right. Multiply all the numbers on the top row by 2. Six times 2 is 12, so write the units figure under the units, and carry the 1:
    6 times 2 is 12
  3. Now multiply the 5 and the 2, which makes 10. Also add on the 1 that is carried from the last stage. This makes 11, so write 1 on the line, and carry the other 1:
    5 times 2 is 10
  4. Multiply seven times the 2. This makes 14. Add on the carried 1, so it makes 15. Don't carry the tens over this time, as there are no more numbers to multiply on this row. Just write the 15 on the line:
    7 times 2 is 14
  5. Move to multiplying the tens now that you've done the units for the number 32. Put a zero in the units column:
    Put a zero
  6. Multiply six times 3. This makes 18. Again, put the 8 on the line, and carry the 1:
    6 times 3 is 18
  7. Multiply 5 times the 3. This makes 15 but you must add on the carried 1, so it equals 16. Write the 6 on the line, and carry the 1:
    5 times 3 is 15, plus the carried 1
  8. Multiply 7 times the 3. This makes 21, plus the carried 1 makes 22. You don't need to carry the 2, as there are no more numbers to multiply on this line:
    7 times 3 is 21, plus the carried 1
  9. Begin adding up. Now you're done with multiplying; you just need to add together 1512 and 22680. Write a plus sign to remind you of this:
    Write a plus sign
  10. Add two plus zero. This makes 2. Write that in the units column:
    2 plus 0 is 2
  11. Add one plus 8. This makes 9. Write that in too:
    1 plus 8 is 9
  12. Add five plus 6. This makes 11. Write the 1 on the line, and carry the 1:
    5 plus 6 is 11
  13. Add one plus 2. Include the carried 1 to make 4. Write that down:
    1 plus 2 plus 1 is 4
  14. Add the final numbers. 2 plus nothing makes 2; write that in:
    2 plus nothing is 2
  15. Check your answer. It should be: 756 x 32 = 24192.


Tips   

  • Practice on short, easy numbers first.
  • For numbers of more than two digits, follow these steps: first multiply the top number by the units, then add a zero and multiply by the tens, then add two zeros and multiply by the hundreds, then add three zeros and multiply by the thousands, and so on. Add up all the numbers at the end.
  • Don't forget to carry your tens along, else it'll all mess up!