Open Middle®
Directions: Using the digits 1-9 at most one time each, fill in the boxes to make the smallest (or largest) product.
Hint
How can we tell whether it would be better to put the larger numbers in the whole number, numerator, or denominator?
Answer
The current best answer for largest product is 8 7/1 * 9. The current best answer for smallest product 2 3/9 * 1
Source: Robert Kaplinsky
In presenting this problem, as an introduction to Fraction Multiplication, I find it hard to justify that the “mixed number” can include an improper fraction like in the sample answer ( 8 7/1)
Sure. Feel free to modify it for your situation.
the answer is 8 7/1 * 2 3/9* 1
If we allow improper fractions as the fractional part of the mixed number, the greatest product is indeed 8 7/1 * 9 and the smallest is 2 3/9 * 1 = 2,3333…
If we don’t allow improper fractions, the greatest product is 8 6/7 * 9 = 79,7142857…, the smallest product is unchanged.