Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make as many true statements as possible.
Hint
How can thinking about improper fractions help support your thinking?
Answer
There are many possible answers. Two examples are:
1/2 of 68 = 34
6/3 of 27 = 54
1/2 of 68 = 34
6/3 of 27 = 54
Source: Rochelle Telfer
i dont know what i comment about but at first i was super confused but then i saw 34 plus 34 equals 68 same with the numbers below so you just multiply the number you equal by 2
6/3 of 27=54
6/3 of 27=54
1/2 of 68=34
6/3 of 27 =54
6/3 of 27 =54
4/2 x 18 = 36
1/4 of 8=2
1/2 of 68=34
1/4 of 8=2
Or
6/3 of 27 =54 4/2 x 18 = 36
1/2 of 16 is 8
1/8 of 56 is 7
1/3 of 6 is 2
1/2 Of 8 is 4
6/3 of 27=54
1/2 of 68=34
or
6/3 of 27=54
1/2 of 8 is 4
1/2 of 68 is 34
1/3 of 6 is 2
2/3 of 12 is 8
4/8=1/2
2/4=1/2
5/10=1/2
3/6=1/2
1/4 of 8 = 2
2/3 of 12 = 8
2/3 of 6 = 4
1/4 of 8= 2
1/2 of 6 = 3
1/2 of 8 = 4
9/6 of 18 =27
2/3 of 6= 4
1/2 of 68=34
6/3 of 27=54
why are they giving us the answer?
2/4 of 28=14
1\9 of 81=9
1/2 of 96= 48
1/2 of 43=21.5
½ of 6=3
4/2 of 7=14
1/2=88=44=1/2=22=1/2=11
1/2=22=11
1/2 of 30=15
1/9 of 91 = 9.91
1/4 of 100 is 25
1/3 of 9 is 3
1/2 of 68=34
3/4 of 250 =
6/3 of 27=54
8/10 of 250 = 200
8/10 of 250 = 200
4/8 of 64 is = 32
8/10 of 250 =200
1/2 of 72= 36
6/3 of 27=54
1/2 of 72=36
8/10 of 250=200
1/2 of 68 = 34
6/3 of 27 = 54
Careful about your answers. The equation we are answering has 2 blank digits after the OF and after the =, and 0 (zero) is NOT one of the allowed numbers we can use to complete the equation. Many of the solutions above contain 0’s or do not fill in all the blank boxes…..
1/2 of 72 is 36
2/1 of 34=68
1/2 of 61=30.5
1/2 of 76=38
1/2 of 86=43
1/2 of 96=48
There are 120 correct solutions for this problem. I have included them all here:
1/2*68=34
1/2*76=38
1/2*78=39
1/2*86=43
1/2*96=48
1/3*78=26
1/3*87=29
2/1*34=68
2/1*38=76
2/1*39=78
2/1*43=86
2/1*48=96
2/3*81=54
2/3*84=56
2/4*36=18
2/4*38=19
2/4*76=38
2/4*78=39
2/6*54=18
2/6*57=19
2/7*63=18
2/8*56=14
2/8*76=19
2/9*63=14
3/1*26=78
3/1*29=87
3/2*54=81
3/2*56=84
3/4*68=51
3/4*96=72
3/6*28=14
3/6*54=27
3/6*58=29
3/6*82=41
3/7*42=18
3/7*49=21
3/7*56=24
3/7*98=42
3/8*56=21
3/9*48=16
3/9*54=18
3/9*78=26
3/9*81=27
4/2*18=36
4/2*19=38
4/2*38=76
4/2*39=78
4/3*51=68
4/3*72=96
4/6*27=18
4/6*57=38
4/6*78=52
4/7*28=16
4/7*56=32
4/7*91=52
4/7*98=56
4/8*26=13
4/8*32=16
4/8*62=31
4/8*72=36
4/9*63=28
4/9*81=36
6/2*18=54
6/2*19=57
6/3*14=28
6/3*27=54
6/3*29=58
6/3*41=82
6/4*18=27
6/4*38=57
6/4*52=78
6/8*52=39
6/8*72=54
6/9*27=18
6/9*48=32
6/9*51=34
6/9*57=38
6/9*72=48
6/9*78=52
6/9*81=54
7/2*18=63
7/3*18=42
7/3*21=49
7/3*24=56
7/3*42=98
7/4*16=28
7/4*32=56
7/4*52=91
7/4*56=98
7/8*56=49
7/9*36=28
7/9*81=63
8/2*14=56
8/2*19=76
8/3*21=56
8/4*13=26
8/4*16=32
8/4*31=62
8/4*36=72
8/6*39=52
8/6*54=72
8/7*49=56
8/9*72=64
9/2*14=63
9/3*16=48
9/3*18=54
9/3*26=78
9/3*27=81
9/4*28=63
9/4*36=81
9/6*18=27
9/6*32=48
9/6*34=51
9/6*38=57
9/6*48=72
9/6*52=78
9/6*54=81
9/7*28=36
9/7*63=81
9/8*64=72
1/2 of 68 = 34
6/3 of 27 = 54
1/2 of 68 = 34
1/2 of 42 = 21
3/7 of 21 = 9
6/3 of 27=54
2/4 of 36 =18
1-2 of 68=34
6-3 of 27=54
7/9 of 81=63
Gabrielle St Oran’s College
My fellow genius classmate
I can confirm Bang’s answer. Also, if we allowed the digit 0, there’d be 252 solutions. Adding onto Bang’s answer, if we only allow proper fractions, there are exactly 60 solutions:
1/2 of 68 = 34
1/2 of 76 = 38
1/2 of 78 = 39
1/2 of 86 = 43
1/2 of 96 = 48
1/3 of 78 = 26
1/3 of 87 = 29
2/3 of 81 = 54
2/3 of 84 = 56
2/4 of 36 = 18
2/4 of 38 = 19
2/4 of 76 = 38
2/4 of 78 = 39
2/6 of 54 = 18
2/6 of 57 = 19
2/7 of 63 = 18
2/8 of 56 = 14
2/8 of 76 = 19
2/9 of 63 = 14
3/4 of 68 = 51
3/4 of 96 = 72
3/6 of 28 = 14
3/6 of 54 = 27
3/6 of 58 = 29
3/6 of 82 = 41
3/7 of 42 = 18
3/7 of 49 = 21
3/7 of 56 = 24
3/7 of 98 = 42
3/8 of 56 = 21
3/9 of 48 = 16
3/9 of 54 = 18
3/9 of 78 = 26
3/9 of 81 = 27
4/6 of 27 = 18
4/6 of 57 = 38
4/6 of 78 = 52
4/7 of 28 = 16
4/7 of 56 = 32
4/7 of 91 = 52
4/7 of 98 = 56
4/8 of 26 = 13
4/8 of 32 = 16
4/8 of 62 = 31
4/8 of 72 = 36
4/9 of 63 = 28
4/9 of 81 = 36
6/8 of 52 = 39
6/8 of 72 = 54
6/9 of 27 = 18
6/9 of 48 = 32
6/9 of 51 = 34
6/9 of 57 = 38
6/9 of 72 = 48
6/9 of 78 = 52
6/9 of 81 = 54
7/8 of 56 = 49
7/9 of 36 = 28
7/9 of 81 = 63
8/9 of 72 = 64
Could an extension be to change this up to ask;
_ /_ OFF _ _ = _ _
that is the same but with a misspelled word.
_ _ / _ _ of _ _ _ = _ _ using all numbers 1 to 9 is an extension.
23/46 of 158 = 79 is the only solution I found for this extension.
27/54 of 138 = 69
32/64 of 158 = 79. yeah there are a lot more answers to my extension!
32/64 of 158 = 79. yeah there are a lot more answers to my extension!