Open Middle®
Directions: Using the digits 0 to 9 at most one time each, place a digit in each box to make a true fraction division sentence.
Hint
Think about the process you think through to divide fractions. How can you move your fractions around so that you can determine the numerator and denominator of the answer?
Answer
There are many possible answers including:
3/5 ÷ 8/9 = 27/40
7/5 ÷ 8/3 = 21/40
8/1 ÷ 6/3 = 45/90
3/5 ÷ 8/9 = 27/40
7/5 ÷ 8/3 = 21/40
8/1 ÷ 6/3 = 45/90
Source: Shanelia Rhome-Shannon and Aiden (Student)
2/6: 5/4=8/30
Okay this maybe a stupid question, but isn’t open middle supposed to have a correct answer? Like 1 correct answer?
no……there are sometimes many even in some cases infinite
I just now listened to Robert’s seminar and he specifically said one answer. He said open ended has many answers. So yes. You are corrrct.
i think it’s 3/5 ÷ 8/9 = 27/40
3/6 divided by 9/7 = 21/54
3/4 divided by 5/6 = 18/20
You could make it have one answer by saying it has to be the greatest or least quotient possible or something like that.
8/1 ÷ 6/3 = 45/90 <— this is not true. 8/1 = 8, and 6/3 = 2, and 8 ÷ 2 = 4. And 4 is not equivalent to 45/90.
There are 13 unique solutions. If a/b : c/d = e/f is a solution, then so are a/c : b/d = e/f and d/c : b/a = e/f and d/c : b/a = e/f, quadrupling the number of solutions. And if a/b : c/d = e/f is a solution, so is b/a : c/d = f/e, so you can double that number again, for a total of 104 solutions.
3/7 : 8/4 = 12/56
2/6 : 7/3 = 14/98
3/7 : 9/8 = 16/42
2/3 : 8/4 = 19/57
3/6 : 9/7 = 21/54
1/3 : 7/9 = 24/56
1/3 : 6/9 = 27/54
1/3 : 4/6 = 29/58
7/3 : 8/9 = 42/16
2/1 : 7/3 = 48/56
9/3 : 7/2 = 48/56
3/6 : 7/8 = 52/91
4/3 : 9/6 = 72/81
Of the 104, the only ones with only proper fractions are these 19:
1/3 : 4/6 = 29/58
1/3 : 6/9 = 27/54
1/3 : 7/9 = 24/56
1/4 : 3/6 = 29/58
1/6 : 3/9 = 27/54
1/7 : 3/9 = 24/56
2/3 : 7/9 = 48/56
2/7 : 1/3 = 48/56
2/7 : 3/9 = 48/56
2/8 : 3/4 = 19/57
2/9 : 1/3 = 56/84
3/6 : 7/8 = 52/91
3/7 : 1/2 = 48/56
3/7 : 6/8 = 52/91
3/9 : 1/2 = 56/84
3/9 : 6/7 = 21/54
3/9 : 7/8 = 16/42
4/9 : 3/6 = 72/81
6/9 : 3/4 = 72/81
There’s no solution where all fractions are in their simplest form.
8/1 divided by 6/3 = 4 not 0.5 get gud fr
I agree 8/1 / 6/3 is really 8/1 * 3/6 which equals 24/6 which is 4
I reckon its 5
5 What 5 over what