Long Multiplication (3-digit × 1-digit)

How to multiply a 3-digit number by a 1-digit number

To multiply a 3-digit number by a single digit, you multiply each digit of the big number by the single digit, working from the ones column to the hundreds, and carry whenever a result is 10 or more. Use the animation above to watch each carry happen for 20 problems, then follow the written method.

The method — step by step

1. Write the 3-digit number on top and the single digit below the ones place, with a × sign.
2. Multiply the ones digit by the single digit. Write the ones digit of the answer; if it is 10 or more, carry the tens to the next column.
3. Multiply the tens digit by the single digit, then add the carry. Write the ones digit, carry the rest.
4. Multiply the hundreds digit, add the carry, and write the result.
5. If the hundreds step produces a carry, that becomes the thousands digit.

Worked example: 347 × 6

Column	Multiply (+ carry)	Write / Carry
Ones	7 × 6 = 42	Write 2, carry 4
Tens	4 × 6 = 24, + 4 = 28	Write 8, carry 2
Hundreds	3 × 6 = 18, + 2 = 20	Write 0, carry 2
Thousands	final carry	Write 2

So 347 × 6 = 2082.

Common mistakes to avoid

• Forgetting to add the carry to the next column's product.
• Multiplying, then adding the carry before multiplying — always multiply the digit first, then add the carry.
• Writing a two-digit result in one column instead of carrying.

Practice problems

Try these in the animation above: 268 × 4, 529 × 7, 736 × 8, 615 × 9, 854 × 3, 789 × 3.

Quick tip

Multiplying by a single digit is just repeated addition done efficiently. The carry is the “tens part” of each small product moving one place to the left, exactly like carrying in addition.