Long Multiplication Calculator with Steps
Multiply two numbers the long way: every partial product by place value (ones, tens, hundreds), the column sum, and where the decimal point goes when you multiply decimals.
How it works
a × b = Σ (a × each digit of b × its place value) · decimal places of the product = decimal places of a + decimal places of b
Long (column) multiplication splits the bottom number into its digits. The top number is multiplied by each digit, shifted by that digit’s place value (ones, tens, hundreds…), and the partial products are added. With decimals, multiply as if there were no decimal points and then count the decimal places of both factors to place the point — the standard algorithm taught in primary school (Common Core 5.NBT.5).
Worked example
347 × 28: first 347 × 8 = 2,776 (ones digit), then 347 × 20 = 6,940 (tens digit). Adding the partial products gives 2,776 + 6,940 = 9,716, so the product is 9,716.
Sources: Common Core State Standards — 5.NBT.5 (standard multiplication algorithm) · Khan Academy — Multi-digit multiplication
Frequently asked questions
How do you do long multiplication step by step?
Write the larger number on top. Multiply it by the ones digit of the bottom number, then by the tens digit (writing a 0 placeholder first), then the hundreds digit (two zeros) and so on. Finally add all the rows.
Why do we add a zero on the second line?
Because the second digit is in the tens place: 2 in 28 really means 20. Multiplying by 20 is multiplying by 2 and then by 10, and the trailing zero is that ×10 shift.
How do I multiply decimals with long multiplication?
Ignore the decimal points, multiply the whole numbers, then count the digits after the point in both factors. 3.47 × 2.8 has 2 + 1 = 3 decimal places, so 9716 becomes 9.716.
How can I check a long multiplication answer?
Estimate by rounding (350 × 30 = 10,500 is close to 9,716), reverse it with division (9,716 ÷ 28 = 347), or multiply in the other order — the product is the same.
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This calculator is for educational purposes. Double-check important results before acting on them.