Open Middle®
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make two different pairs of fractions that have a quotient of 2/3.
Hint
How can you make multiple fractions with equivalent values? How might you think of this problem as either division or multiplication?
Answer
There are many potential answers including 4/2 ÷ 3/1
Source: Robert Kaplinsky in Open Middle Math
If I understood the problem correctly, I found 3/2 ÷ 9/4 and 2/6 ÷ 4/8
There are 7 unique solutions.
1/2 : 3/4 = 2/3
1/2 : 6/8 = 2/3
1/3 : 4/8 = 2/3
2/1 : 9/3 = 2/3
2/4 : 6/8 = 2/3
3/2 : 9/4 = 2/3
3/4 : 9/8 = 2/3
If a/b : c/d is a solution, then so are a/c : b/d, d/c : b/a and d/b : c/a, quadrupling the number of solutions, for a total of 28 solutions.