Partial Products Calculator

Partial Products Calculator

Break multiplication into place-value partial products and review the full sum beside the result.

Last updated: March 2026 | By ForgeCalc Engineering

Partial Products Solver

Place value multiplication

Partial Products

20 × 10 = 200
20 × 3 = 60
4 × 10 = 40
4 × 3 = 12
Final Product
312

Sum of all partial products

What Are Partial Products?

Partial products multiplication breaks each factor into place-value parts, multiplies every part, and then adds the results. It is a useful way to show why the standard algorithm works.

How to Find Partial Products

  1. Break each number into place-value parts.
  2. Multiply each part of the first number by each part of the second.
  3. List all of the partial products.
  4. Add them to get the final product.
24 = 20 + 4

Worked Example

Example: 24 × 13 = 312.

20×10 + 20×3 + 4×10 + 4×3 = 312

Frequently Asked Questions

Does it work for decimals?

Yes, but the place-value breakdown is easiest to read with whole numbers.

Why use this method?

It shows the distributive property and reinforces place value.

Is it the same as the standard algorithm?

It is the same underlying math shown more explicitly.

Does it accept negative numbers?

This version is intended for non-negative integers.

Related Tools