Open Middle®
Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to make two equivalent ratios where one of the ratios is a unit rate.
Hint
1. What do we know about a unit rate?
2. Are any numbers off-limits in this problem?
2. Are any numbers off-limits in this problem?
Answer
There are many answers including 68/34 = 2/1 and 78/26 = 3/1. All of them will have a 1 in the denominator of the fraction on the right.
Source: Scott Houston
72/24 =3/1
86/43 = 2/1
70/35 = 2/1
90/45 = 2/1
68/34 = 2/1
72/24=3/1
78/26=3/1
36/18=4/2
I defied Open middle with my answer
Never mind
I’m not a native speaker, so I’m not sure if it counts as a unit rate if the fraction is 4/2, 6/2, 8/2, 6/3, 9/3 or 8/4, which all could be reduced to a fraction that has a 1 in the denominator.
So I’m just gonna list the 7 solutions with a 1 in the denominator first and afterwards the 20 solutions with 4/2, 6/2, 8/2, 6/3, 9/3 or 8/4:
68/34 = 2/1
76/38 = 2/1
78/26 = 3/1
78/39 = 2/1
86/43 = 2/1
87/29 = 3/1
96/48 = 2/1
76/38 = 4/2
78/26 = 9/3
78/39 = 4/2
81/27 = 9/3
82/41 = 6/3
26/13 = 8/4
28/14 = 6/3
32/16 = 8/4
36/18 = 4/2
38/19 = 4/2
48/16 = 9/3
54/18 = 6/2
54/18 = 9/3
54/27 = 6/3
56/14 = 8/2
57/19 = 6/2
58/29 = 6/3
62/31 = 8/4
72/36 = 8/4
76/19 = 8/2