Open Middle®
Directions: Using each of the digits 0-6 only once, make two equivalent ratios (also known as a proportion).
Hint
Can multiples help us find equivalent fractions?
Answer
Number of Unique Solutions: 6
1: 4/13 = 20/65
2: 4/20 = 13/65
3: 5/10 = 23/46
4: 5/10 = 32/64
5: 5/23 = 10/46
6: 5/32 = 10/64
Source: AnneMarie Untalan
i picked #6 because 5 times 2 =10 and 32 times 2 =64 and together will get 10/64
I came up with 5/10=23/46
ok so you got 23/46 would you mine sharing how you arrived there not for my sake my but for the kids. i don’t is it its an improper ratio
i picked #6 becuse 5 time 1 is 10 and 2 time 32 i think is 64 and therefore come the answer 10 over 65
I also think that Marcus because it perfectly matches.
#6 because if you, multiply 5 x 2 you get 10 and if you multiply 32 x 2 equals 64. So when you put that to gather it equals 10/64
and also Marcus 5 x 1 is not 10 its 5 you made a typo.
5/23=10/46
how did you put this in the fraction??
I like this website it helps me understand it
Yea I also like this website
I thing that it’s 5/32 = 10/64
i did 64 times two equals 128
4/13 = 20/65
3/14 = 6/28
5/10=23/46
Also, because that was on the answer sheet, I’ll do 10/5=46/23.
Don’t forget…..
…..Improper fractions!
4/13=20/65
how do you put them in
how
7/13=14/26
Be careful — can’t use 7’s!
5/10 10/20
5/10 = 32/64
5/23 = 10/46
5/32 = 10/64
how do we write them
8/24 = 19/57 is another solution. So is 9/21 = 36/84
4/8 = 8/16 this is equal bc if u do 4 x 2 it’s –
=‘s 8 then 8 x 2 =16.
4/8 = 8/16 this is equal if you do 4 x 2 it’s = 8s then it’s 8×2=16
I did 4/8=8/16 because 4*2=8 and 8*2=16 which makes 8/16.
I did 4/8=8/16 because 4*2=8 and 8*2=16 which gives you 8/16.
5/23 = 10/46 I make like that
If we allowed digits from 0 to 9, there’d be 350 solutions, out of which only 110 have no leading zeros:
4/10 = 38/95
4/13 = 20/65
4/17 = 20/85
4/20 = 13/65
4/20 = 17/85
4/38 = 10/95
5/10 = 23/46
5/10 = 32/64
5/10 = 34/68
5/10 = 36/72
5/10 = 38/76
5/10 = 39/78
5/10 = 43/86
5/10 = 46/92
5/10 = 48/96
5/12 = 40/96
5/17 = 20/68
5/19 = 20/76
5/20 = 17/68
5/20 = 19/76
5/23 = 10/46
5/32 = 10/64
5/34 = 10/68
5/36 = 10/72
5/38 = 10/76
5/39 = 10/78
5/40 = 12/96
5/43 = 10/86
5/46 = 10/92
5/48 = 10/96
6/10 = 27/45
6/12 = 35/70
6/12 = 39/78
6/12 = 45/90
6/15 = 28/70
6/15 = 32/80
6/17 = 30/85
6/27 = 10/45
6/28 = 15/70
6/30 = 17/85
6/32 = 15/80
6/35 = 12/70
6/39 = 12/78
6/45 = 12/90
7/12 = 35/60
7/14 = 28/56
7/14 = 29/58
7/15 = 28/60
7/15 = 42/90
7/16 = 35/80
7/18 = 35/90
7/28 = 14/56
7/28 = 15/60
7/29 = 14/58
7/35 = 12/60
7/35 = 16/80
7/35 = 18/90
7/42 = 15/90
8/10 = 36/45
8/10 = 76/95
8/12 = 30/45
8/12 = 36/54
8/13 = 40/65
8/14 = 20/35
8/14 = 32/56
8/15 = 32/60
8/16 = 27/54
8/16 = 35/70
8/16 = 45/90
8/19 = 24/57
8/19 = 32/76
8/20 = 14/35
8/24 = 19/57
8/27 = 16/54
8/30 = 12/45
8/32 = 14/56
8/32 = 15/60
8/32 = 19/76
8/35 = 16/70
8/36 = 10/45
8/36 = 12/54
8/40 = 13/65
8/45 = 16/90
8/76 = 10/95
9/12 = 36/48
9/12 = 45/60
9/12 = 63/84
9/13 = 54/78
9/15 = 42/70
9/16 = 27/48
9/16 = 45/80
9/18 = 23/46
9/18 = 27/54
9/18 = 32/64
9/18 = 35/70
9/18 = 36/72
9/21 = 36/84
9/23 = 18/46
9/27 = 16/48
9/27 = 18/54
9/32 = 18/64
9/35 = 18/70
9/36 = 12/48
9/36 = 18/72
9/36 = 21/84
9/42 = 15/70
9/45 = 12/60
9/45 = 16/80
9/54 = 13/78
9/63 = 12/84