How to Use Partial Products to Multiply One-Digit Numbers By Multi-digit Numbers

How to multiply using partial products

The method keeps the value of each digit visible. In 123, the 1 means 100 and the 2 means 20. You multiply those values, not just the digits.

1. Write the multi-digit number in expanded form

For 4 × 123, write 123 = 100 + 20 + 3.

2. Multiply each part by the one-digit number

• Hundreds: 4 × 100 = 400
• Tens: 4 × 20 = 80
• Ones: 4 × 3 = 12

The partial products are 400, 80 and 12. Writing 4 × 2 = 8 for the tens would lose the place value: there are two tens, so that part is 80.

3. Add the partial products

400 + 80 + 12 = 492, so 4 × 123 = 492.

This works because multiplication distributes over addition: 4 × (100 + 20 + 3) = (4 × 100) + (4 × 20) + (4 × 3). You have multiplied every part of 123 by 4.

What if the number has a zero?

Try 6 × 204. Expanded form is 200 + 0 + 4, so the partial products are 1,200, 0 and 24. Add them to get 1,224.

You can omit the zero product when adding, but keep the place values: 204 is 200 + 4, not 20 + 4. An estimate helps check the result: 6 × 200 = 1,200, so 1,224 is reasonable.

Try it, then check your work

Use partial products to solve 3 × 142 and 5 × 1,206. Write the expanded form and each partial product before adding.

Keep practicing

Open the free Grade 4 worksheet collection and choose Multiplication. Start with the one-digit-by-multi-digit problems and show partial products on separate paper; the collection also includes other multiplication skills.

For more Grade 4 review, visit the Grade 4 Online Center. This place-value approach fits Grade 4 standard 4.NBT.B.5, which includes multiplying up to four-digit whole numbers by one-digit whole numbers.