Open Middle®
Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make the biggest/smallest product.
Hint
What numbers should be use to get the biggest product?
Answer
biggest: (8+7)(9-1) smallest: (1-2)(8+9)
Source: Nanette Johnson
Nice exercise in multiplication and flexible thinking, Nanette!
Question: Your answer, smallest: (1-2)(8+9), introduces the possibility of negative numbers. Is that what you intended? If so, I think (1–9)(8+7) is the smallest.
(1–9)(8+7) < (1-2)(8+9)
-48 < -17
If you intended only positive products, then I think that (4–3)(2+1) is the smallest. The 4 and 3 could be replaced by any other consecutive digits between 3 and 9 because their difference will be 1.
My student came up with (9 – 8) (1 + 2) = 3 for the smallest answer and (9 – 1) (7 + 8) = 120
We found out that if negative numbers are allowed. The smallest equation would be (1-9)(8+7) which equals -120 not -48.
(5+5) (6+3)
(9-1)(8+7) and (4 -3)(3+2)
(6+8)(8-5)
(9-4)(5+4
(2-1)(3+6)
(5-4) x (1+2) = 3