Long Multiplication (with steps)
Long multiplication is a written method for multiplying large numbers by breaking the problem into single-digit multiplications, then summing the partial products with correct place-value offsets.
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Tip: Round one factor to estimate: 47×36 ≈ 50×36=1,800. Your exact answer should be close to this.
- 1Write the numbers with the larger on top
- 2Multiply the top number by the ones digit of the bottom number
- 3Multiply the top number by the tens digit, shifting left by one place
- 4Continue for each digit of the bottom number
- 5Sum all partial products
47 × 36=1,69247×6=282, 47×30=1410, sum=1692
123 × 45=5,535123×5=615, 123×40=4920
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
References
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