Long Multiplication Calculator
Fast, accurate and free online multiply pisemne tool running directly in your browser.
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Other tools you may find usefulWritten multiplication in bars - step by step
Written multiplication is a way to multiply large numbers without a calculator - you do it "in bars", multiplying the first factor by the successive digits of the second factor and adding the resultingpartial productswith the appropriate shift. This calculator generates a complete bar notation: each partial product, shifts, and final total. Just enter twofactorsand the tool will show you multiplication just like you do it in school.
How to perform written multiplication?
We perform written multiplication by multiplying the first factor successively by each digit of the second factor - from the units digit to the highest order:
- We multiply the first factor bythe units digitof the second factor - this is the first partial product.
- We multiply the first factor bythe tens' digitand write the resultshifted one place to the left.
- We do the same with the hundreds, thousands digits, etc. - we move each subsequent product one place further.
- At the end ofwe addall the partial products - their sum is the result of the multiplication (product).
Written multiplication by a two-digit number
When the second factor is two-digit, the result istwo partial products. We write the first one (the ones digit) normally, the second one (the tens digit) we shift one place to the left - which corresponds to multiplication by 10. For example, in 123 × 45 we multiply 123 × 5 = 615, then 123 × 4 = 492, and shift the second one → 4920. The sum 615 + 4920 =5535.
Example: 123 × 45 step by step
- 123 × 5= 615 (units digit of the second factor).
- 123 × 4= 492; we move one place to the left →4920(tens digit).
- We add partial products: 615 + 4920 =5535.
The result of multiplying 123 × 45 is5535.
Table - examples of written multiplication
| Multiplication | Partial products | Result |
|---|---|---|
| 123 × 45 | 615 + 4920 | 5535 |
| 12 × 34 | 48 + 360 | 408 |
| 1234 × 56 | 7404 + 61700 | 69104 |
| 999 × 99 | 8991 + 89910 | 98901 |
| 7 × 8 | — | 56 |
FAQ
What is a partial product?
The partial productis the result of multiplying the first factor by one digit of the second factor. Each digit of the second factor gives a separate partial product, which we write with a shift depending on the order (ones, tens, hundreds). Finally, we add all the partial products.
Why are partial products shifted?
Because each subsequent digit of the second factor means a higher order. The tens digit is actually the digit × 10, so we shift its product one place to the left; hundreds digit (× 100) - by two places, and so on.
Which factor is better to write at the top?
As a rule, we write the factorwith a larger number of digitsat the top, and the one with a smaller one at the bottom - then fewer partial products are created and the calculation is shorter. The result is the same regardless of the order (multiplication is commutative).
Can you multiply negative numbers in writing?
Yes - the calculator supports negative numbers. We count the bar based on absolute values, and the sign of the result depends on the signs of the factors: two different signs give a negative product, two the same signs give a positive product.
How to check the result of written multiplication?
The easiest way is to divide the product by one of the factors - you should get the second factor. You can also sum the partial products again or use ourwritten divisionto check.