Multiplication Calculator

Using the Multiplication Calculator

This multiplication calculator with work is a great online tool for teaching multi-digit multiplication. It shows you how the product is generated in real-time, step-by-step, and allows you to highlight the individual multiplication steps used to get the answer. If you need a multiplication calculator that shows work, whether for your homework or for an-class demonstrations, this calculator has you covered!

Multi-digit multiplication is a math skill typically introduced around 4th grade after the basic facts are understood and usually model-based number sense has reinforced the concepts of array construction. When you're ready to understand the multi-digit algorithm, this multiplication calculator can be used as an in-class tool to discuss how partial products tie into these earlier manipulative-based skills.

Parts of a Multiplication Problem

A multiplication problem is composed of three parts

1. A Multiplicand

   This is the first number being multiplied. It also sometimes called more generally a factor.

2. A Multiplier

   This is the second number being multiplied. It too is sometimes called more generally a factor.

3. The Product

   This is the answer to the multiplication problem and it is the result of multiplying the multiplicand by the multipler.

How to Do Multi-Digit Multiplication

The steps for multi-digit multiplication are:

1. Take a Digit from the Multiplier

   Take a digit from the multiplier starting from the left.

2. Multiply by the Multiplicand.

   Multiply the single digit and from the multiplier and the multiplicand to get an intermediate product.

3. Write the Down the Product

   This is perhaps the most complex step. Write down the product from the previous multiplication step, but shift it over beneath the problem so that the ones digit in the immediate product is below the multiplier digit.

4. Repeat Until All Multiplier Digits are Used

   Repeat the steps until all of the digits in the multiplier have been used up, shifting each intermediate product one digit to the left each time.

5. Add the Intermediate Products

   The final product is the sum of all of the intermediate products.

These are same steps the long multiplication calculator uses to show the work for a multiplication problem. In the work, the calculator supplies a zero value in place values where the shift step happens. Many people who work a multi-digit multiplication problem by hand will simply leave a space here for brevity, but offsetting with zeroes helps to avoid calculation errors during the addition step by keeping the place values aligned. If you hover over one of the step products in the multiplication calculator's work area, it will show you the intermediate multiplication calculation used to generate it.

More Resources for Learning Multi-Digit Multiplication

I hope this multiplication calculator is a big help figuring out the steps for longer multi-digit multiplication problems and for understanding the steps in multi-digit multiplication. For more multiplication help, be sure to check out these other resources...

Contemporary multiplication teaching involves a lot more than number manipulation, and this video from Graham Fletcher provides an overview of how to get there. If you're a parent and wondering what for in the good graciousness all those Common Core block model worksheets are trying to get across, this video might help.

Another good discussion of how to do long multiplication calculations, and especially with the 'bring down the zero' step, check out the Ducksters.

If you're looking for an alternative multiplication strategy, the second half of this page at wikiHow shows how to do partion the multipler differently. This is fundamentally the same as the traditional algorithm used by the multiplication calculator on this page, but seeing this approach may help enhance a student's understanding of how place values get adjusted as the steps proceed. I personally find this an easier way to think about multiplication if I'm working two or three digit multiplication mentally...

And of course, one of the most important things you can do is practice! These multi-digit multiplication worksheets are just some of the great resources at DadsWorksheets for learning multiplication. Be sure to also check out the other multiplication worksheets, multiplication tables, and multiplication charts to really get your multiplication facts polished up!

Multiplication Calculator Updates

Date	Description
03/04/2017	Initial version of the multiplication calculator.
04/19/2019	Corrected spelling of 'multiplication' in calculator description.