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WORKED EXAMPLES

Long multiplication calculator

Enter two numbers to see every partial product, carry and decimal place. Then choose a worksheet for the skill you want to practise.

Opening your own calculation requires the calculator. You can read or print the named example below.

Worked example · 105 × 304

105 × 304 = 31,920

Column multiplication

Digits line up by place value.
First factor105
Second factor×304
ones partial420
tens partial0
hundreds partial+31500
Total31920

Follow the digits

Open a row to see each multiplication and carry.

105 × 4 = 420 ones row
Multiply by 4 before shifting. A dot means no incoming carry.
Rowhundredstensones
Carry in·2·
Factor105
Write420
  1. Multiply the ones digit. 5 × 4 = 20. Write 0 and carry 2.
  2. Multiply the tens digit. 0 × 4 + 2 carried in = 2. Write 2.
  3. Multiply the hundreds digit. 1 × 4 = 4. Write 4.

105 × 4 = 420.

105 × 0 = 0 tens row

The tens digit is 0. Its partial product is 0. Keep this row so the next digit stays in the correct column.

105 × 300 = 31,500 hundreds row
Multiply by 3 before shifting. A dot means no incoming carry.
Rowhundredstensones
Carry in·1·
Factor105
Write315
  1. Multiply the ones digit. 5 × 3 = 15. Write 5 and carry 1.
  2. Multiply the tens digit. 0 × 3 + 1 carried in = 1. Write 1.
  3. Multiply the hundreds digit. 1 × 3 = 3. Write 3.

105 × 3 = 315. Shift the row 2 places left because this digit represents 300.

Add the partial products 31,920

420 + 0 + 31,500 = 31,920.

  1. Ones column · 0 + 0 + 0 = 0. Write 0.
  2. Tens column · 2 + 0 + 0 = 2. Write 2.
  3. Hundreds column · 4 + 0 + 5 = 9. Write 9.
  4. Thousands column · 0 + 0 + 1 = 1. Write 1.
  5. Ten-thousands column · 0 + 0 + 3 = 3. Write 3.

Reopen this Numberleaf example
https://numberleafmath.com/long-multiplication-calculator/?from=print#a=105&b=304

Practise a similar problem

3-digit by 3-digit · zeros in the multiplier

New problems for the same skill · US Letter

Student worksheet ↓Worked answer key ↓Open the lesson →

Why does the hundreds row end in two zeros?

In 105 × 304, the 3 stands for 300. Multiplying 105 by 3 gives 315; multiplying by 300 gives 31,500. The tens digit is zero, so the tens row contributes 0. Add 420 + 0 + 31,500 to get 31,920.

For numbers such as 1.25 × 0.4, first multiply 125 × 4. The two decimal places in 1.25 and the one place in 0.4 give three decimal places in 0.500, which is 0.5.

Build a fresh column worksheet or practise decimal multiplication.