How to Multiply Multi-Digit Numbers (Long Multiplication)

Long multiplication breaks one hard problem into easy ones. You multiply by one digit of the bottom number at a time, and then add the results, which are called partial products.

Try it with your own problem ↓

The steps

Write the bigger number on top and the other under it, with the digits lined up on the right.
Multiply the top number by the ones digit of the bottom number, one digit at a time from the right. Carry when a product is 10 or more.
Start a new row. Write a 0 in the ones place as a placeholder, because you are now multiplying by tens.
Multiply the top number by the tens digit and write the result to the left of that 0. Repeat for hundreds, adding one more 0 each row.
Draw a line and add the rows.

A worked example

Work out 47 × 38.

    4 7
  × 3 8
  -----
    3 7 6    (47 × 8)
  1 4 1 0    (47 × 30)
  -------
  1 7 8 6

Ones digit, 8: 7 × 8 = 56. Write 6 and carry 5. Then 4 × 8 = 32, plus the carried 5 is 37. The first row is 376.
Placeholder: start the second row with a 0.
Tens digit, 3: 7 × 3 = 21. Write 1 and carry 2. Then 4 × 3 = 12, plus 2 is 14. With the 0 on the end, the second row is 1,410.
Add the rows: 376 + 1,410 = 1,786.

47 × 38 = 1,786. Check by estimating: 50 × 40 = 2,000, and 1,786 is close.

Try it with your own problem

Open the free The Product Ladder with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 47 x 38Opens The Product Ladder with this example

Or try these

Common mistakes

Forgetting the placeholder zero. Without it, the second row is ten times too small.
Dropping a carry. Write the small carried digit above the next column so you remember to add it.
Adding the carry before multiplying. Multiply first, then add the carry.
Misaligned rows. Keep each column of digits in line when you add.

Questions people ask

Why does the second row start with a zero?

Because the 3 in 38 means 30. Multiplying by 30 is multiplying by 3 and then by 10, and the zero does the times-10.

How do I multiply by a number with a zero in it, like 306?

Put a zero placeholder for the tens row, or write a row of zeros. The hundreds row then starts with two zeros.

How can I check my answer?

Estimate with rounded numbers, or swap the two numbers and multiply again. Both ways must give the same product.

Keep learning

Show The Steps is free, with no accounts or ads, and everything is worked out in your own browser. Start at the home page.