Long Multiplication Calculator
Long multiplication by the column method: one row per digit of the bottom number, the carries written out, and the partial products added at the end.
Product
- Partial products
- 28,950 + 144,750 = 173,700
| Step | Multiply by | Working, right to left | Partial product |
|---|---|---|---|
| 1 | 6 (ones) | 5 × 6 = 30, write 0 carry 3; 2 × 6 + 3 = 15, write 5 carry 1; 8 × 6 + 1 = 49, write 9 carry 4; 4 × 6 + 4 = 28, write 28 | 28,950 |
| 2 | 3 (tens) | 5 × 3 = 15, write 5 carry 1; 2 × 3 + 1 = 7, write 7; 8 × 3 = 24, write 4 carry 2; 4 × 3 + 2 = 14, write 14; shifted 1 place left | 144,750 |
| Sum | 28,950 + 144,750 | 173,700 |
- Each digit of the bottom number gives one row, shifted one more place left because it is worth ten times the digit before it. The rows add up to the product.
How the Long Multiplication Calculator works
Long multiplication breaks a large product into one-digit multiplications. Write the number with more digits on top, multiply it by each digit of the bottom number from right to left, shift each partial product one more place left, and add the partial products.
Worked example: 4,825 × 36.
Multiply 4,825 by the 6 in the ones place, working right to left. 5 × 6 = 30: write 0, carry 3. 2 × 6 + 3 = 15: write 5, carry 1. 8 × 6 + 1 = 49: write 9, carry 4. 4 × 6 + 4 = 28: write 28. The first partial product is 28,950.
Multiply by the 3 in the tens place. It stands for 30, so its row starts one place to the left, with a 0 in the ones column: 4,825 × 3 = 14,475, written as 144,750.
Add the rows: 28,950 + 144,750 = 173,700.
The shift is the whole method. 36 is 30 + 6, so 4,825 × 36 = 4,825 × 6 + 4,825 × 30, the distributive law written in columns. Each extra digit in the bottom number adds one more row.
Long multiplication with decimals works on the digits alone. Multiply as if there were no decimal points, then count the decimal places in both numbers and give the product that many. For 3.14 × 2.5: 314 × 25 = 7,850, and 2 + 1 = 3 places gives 7.850, or 7.85.
An estimate catches a row in the wrong place. 4,825 × 36 is a little under 5,000 × 40 = 200,000, so an answer near 17,000 or 1,700,000 has a shift wrong.
Long Multiplication Calculator FAQ
Which number goes on top in long multiplication?
Either gives the same product. The number with more digits on top means fewer rows: 4,825 × 36 takes two rows, while 36 × 4,825 takes four.
What do I do with a zero in the bottom number?
Its row is all zeros, so it can be skipped as long as the next row shifts one extra place. For 512 × 304, the rows are 512 × 4 = 2,048 and 512 × 300 = 153,600, which add to 155,648.
How do I multiply negative numbers?
Multiply without the signs, then make the product negative if exactly one number was negative. -4,825 × 36 = -173,700, and -4,825 × -36 = 173,700.
How do I check a long multiplication answer?
Divide the product by one of the numbers and you should get the other: 173,700 ÷ 36 = 4,825. The long division calculator shows that working too.