Multi-Digit Multiplication: The Standard Algorithm
The standard algorithm multiplies the top number by each digit of the bottom number, starting with the ones. Each partial product is written on its own row; multiplying by the tens digit means multiplying by a number of tens, so that row ends in 0.
Adding the rows gives the product. The worked example shows every row as it is written on paper.
When is it taught?
- Grade 4 (CCSS 4.NBT.B.5): multiply up to four digits by one digit, and two two-digit numbers.
- Grade 5 (CCSS 5.NBT.B.5): fluently multiply multi-digit whole numbers using the standard algorithm.
Worked example: 247 × 36
247×36
247×36148274108892
Left: the problem. Right: the worked answer with both partial products, as in our answer keys.
Step by step
- 1Multiply by the ones digit: 247 × 6 = 1482.
- 2Multiply by the tens digit: 247 × 30 = 7410. The 0 keeps each digit in its place.
- 3Add the partial products: 8892.
- 4Estimate to check: 200 × 40 = 8000, close to 8892.
Common mistakes
- Forgetting the placeholder 0 on the tens row, which makes the answer far too small.
- Adding carried digits before multiplying instead of after.
- Estimating first (round each number) shows at once whether the answer is the right size.
Printable multiplication practice
- 4-digit × 1-digit multiplicationGrade 4 · CCSS 4.NBT.B.5
- 2-digit × 2-digit multiplicationGrade 4 · CCSS 4.NBT.B.5
- 3-digit × 2-digit multiplicationGrade 5 · CCSS 5.NBT.B.5