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.
Open Middle problems always have an open middle, but they can be both open and closed ended.
Ha that was a good one, good use of the name open middle
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
I reckon your wrong
I reckon that you are incorrect because the answer is 3.14159
I reckon your wrong because I don’t like that answer because it is stupid and nobody’s uses reckon so your answer is wrong the real answer is: I think its five which is correct grammer. also how do you talk to girls your probably walk up to them and say I reckon your beautiful. then they will reject you and you will have no family and you can only afford McDonald’s but you will say I reckon I’ll have the big arch but they will not no what your saying so you will die of hunger all because you use incorrect grammer.
Ambros is wrong, Owen kaplinski Is funny, I’ll give u candy like the Easter bunny