How to Do Long Multiplication

Step-by-Step Guide

1. 1

   Step 1: Write the larger number above the smaller number.

   Let's say you're going to multiply 756 and
   32.
   
   Write 756 above 32, making sure that the ones and tens columns of both numbers line up, so that the 6 from 756 is above the 2 in 32 and the 5 in 756 is above the 3 in 32, and so on.
   
   This will make it easier for you to visualize the long multiplication process.
   
   You will essentially begin by multiplying the 2 in 32 by each of the numbers in 756, and then multiplying the 3 in 32 by each of the numbers in
   756.
   
   But let's not get ahead of ourselves.
2. 2

   Step 2: Multiply the number in the ones place of the bottom number by the number in the ones place of the top number.

   Take the 2 from 32 and multiply it by the 6 in
   756.
   
   The product of 6 times 2 is
   12.
   
   Write the units digit, 2, under the units, and carry the 1 over the
   5.
   
   Basically, you write down whatever number is in the ones digit, and if there is a number in the tens digit, you will have to carry it over the number to the left of the top number you just multiplied.
   
   You'll have a 2 directly below the 6 and the
   2. , Now, multiply 2 times 5 to equal
   10.
   
   Add the 1 you carried over above the 5 to 10 to equal 11, and then write a 1 next to the 2 in the bottom row.
   
   You'll have to carry the extra 1 in the tens place over the
   7. , Now, just multiply 2 by 7 to equal
   14.
   
   Then add the 1 that you carried over to 14 to equal
   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 bottom line. , Now, you'll be multiplying the number in the tens place of 32, 3, by each digit in 756, so draw a zero below the 2 in 1512 before you begin so you are already starting in the tens place.
   
   If you were going to keep going and multiply a number in the hundreds place by the top number, then you'd need to draw two zeroes, and so on. , Now, multiply 3 by 6 to equal
   18.
   
   Again, put the 8 on the line, and carry the 1 over above the
   5. , Multiply 3 times
   5.
   
   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 over above the
   7. , Multiply 3 times 7 to equal
   21.
   
   Add the 1 you carried to equal
   22.
   
   You don't need to carry the 2 in 22, as there are no more numbers to multiply on this line, so you can just write it down next to the
   6. , Now, you'll have to simply add up 1512 and
   22680.
   
   First, add 2 plus 0 to equal
   2.
   
   Write the result in the ones column. , Now, add up 1 and 8 to equal
   9.
   
   Write 9 to the left of the
   2. , The sum of 5 and 6 is
   11.
   
   Write down the 1 in the units place and carry the 1 in the tens place over 1 at the very left of the first product. , Add up 1 plus 2 to equal 3 and then add on the 1 you carried over to equal
   4.
   
   Write it down. , The first number has nothing in the ten thousands place, and the second has 2 there.
   
   So, add 0 plus 2 to equal 2 and write it down.
   
   This gives you 24,192, your final answer. , If you want to double check your work, type in the problem into a calculator to see if you've done it correctly.
   
   You should get 756 times 32 equals 24,192.
   
   You're all done!
3. 3

   Step 3: Multiply the number in the ones place of the bottom number by the number in the tens place of the top number.

4. 4

   Step 4: Multiply the number in the ones place of the bottom number by the number in the hundreds place of the top number.

5. 5

   Step 5: Draw a 0 in the units column below the first product.

6. 6

   Step 6: Multiply the number in the tens place of the bottom number by the number in ones place of the top number.

7. 7

   Step 7: Multiply the number in the tens place of the bottom number by the number in tens place of the top number.

8. 8

   Step 8: Multiply the number in the tens place of the bottom number by the number in hundreds place of the top number.

9. 9

   Step 9: Add the ones digits of both products.

10. 10

    Step 10: Add the tens digits of both products.

11. 11

    Step 11: Add the hundreds digits of both products.

12. 12

    Step 12: Add the thousands digits of both numbers.

13. 13

    Step 13: Add the ten thousands digits of both numbers.

14. 14

    Step 14: Check your answer with a calculator.

Detailed Guide

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