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Multiplying Decimals (Middle School)

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the smallest (or largest) product.



What number does each box represent?



SS found the current smallest product with positive factors: 1.35 * 2.46. Kevin Crowl suggested 9.75 * 8.64 which led to 9.64 * 8.75 which is currently the largest product with positive factors. We are still looking for answers.  If you have one, post it in the comments.

Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both.

Source: Robert Kaplinsky

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  1. 1.35 * 2.46 ?? smallest for both positive??

  2. I think largest both positive is 9.75 * 8.64

    • Thanks Kevin. Challenging, right?! Your solution reminded me how this is similar to another problem. https://www.openmiddle.com/rectangles-maximizing-area/. In this problem, you get the largest area when the side lengths are as close to the same amount as possible. Using that reasoning, I realized that 9.64 * 8.75 is a bit closer together and gives 84.35 as an answer as opposed to 84.24.

      Might still be even larger ones!

      • As I was checking through my students’ work the other day, one of them had also found 9.64*8.75 as the largest possible. I appreciate the confirmation, and my whole class was very excited to hear that one of them had done “better” than me!

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