Open Middle®
Directions: Using the digits 1 to 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 largest product was found by Sandy Pray’s student and is 8 7/1 * 9 6/2 = 180. It beats the former largest product of 9 7/1 * 8 6/2 which was found by Ivy Kong’s students. The current best answer for smallest product 1 3/9 * 2 4/8
Source: Robert Kaplinsky
Hi Robert, my students figured out that the largest product is 9 7/1 * 8 6/2, which is 176. 🙂
Awesome Ivy! That is MUCH larger. I’ll update it and give your students credit.
Our student discovered 8 7/1 * 9 6/2 = 180. Beats 176 by 4 points but even more made a very reserved student feel like queen of the day!
Wow. Thank you so much for sharing that Sandy! There are never enough moments to make students feel that way. I’ll update the answer.
You are donig a good job sandy pray
Parker, Lily, AJ, Kellan, Delaney, Landon, Leighton, Freddy, Caleb from North Carolina came up with 180 by using 8 7/1 x 9 6/2 =
7 8/1 * 9 6/2 = 180 will also give the largest sum
What is the definition of a mixed number? A lot of textbooks define it as consisting of whole number and a PROPER fraction. If this is the way mixed numbers are defined, then the given answers for largest sum should be changed.
Greatest product:
With improper fractions: 7 8/1 * 9 6/2 = 8 7/1 * 9 6/2 = 180
Without improper fractions: 9 4/5 * 8 6/7 = 86.8
Smallest possible product:
With reducible fractions: 2 4/8 * 1 3/9 = 3.3333
With irreducible fractions: 1 3/8 * 2 4/9 = 3.3611
Note that you can always swap the two factors to get the same result another way.
good job