Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the equation true.
Hint
What digits would be bad choices for the denominators?
What digits would be good choices for the denominators?
What digits would be good choices for the denominators?
Answer
Answers found so far include:
2/8 + 1/4 + 3/6 = 1
2/4 + 3/9 + 1/6 = 1 (found by Koharu in Ms. Wilson’s class)
1/6 + 3/9 + 4/8 = 1
2/8 + 1/4 + 3/6 = 1
2/4 + 3/9 + 1/6 = 1 (found by Koharu in Ms. Wilson’s class)
1/6 + 3/9 + 4/8 = 1
Source: Owen Kaplinsky
1/3+1/3+1/3=1
can only use each digit one time
1/3 + 1/2 + 1/6
correct
1/3+1/3+1/3=1
I there only one answer? 1/4+2/8+3/6
Is there only one answer? 1/4+2/8+3/6
My students also found 4/8 + 3/9 + 1/6
Nice! I’ll add that to the answers.
4/8 + 3/9 + 1/6
1/3 + 1/3 + 1/3 =1
1/3 + 1/3 + 1/3
worng only use 1 once and 3 once from 1-9
2/8 + 1/4 + 3/6 = 1
2/8 + 1/4 + 3/6 = 1
2/8+1/4+3/6
2/8+1/4+3/6
2/8+5/8+1/8
1/4 + 2/8 + 3/6 = 1
3/9+3/9+3/9=1
1/3+1/3+1/3
The answer is 3/6+14+28=1
Hey Owen, this is nearly identical to the task I put up about 3 years ago, do you think we should take mine down or maybe collaborate? Your title is definitely better and I went all the way to 10 just because it provided a few more answers and touched on decimals. Also, I was inspired by the book The Wishing Club, which goes perfectly with these tasks.
This answer does not follow the rules with 1 digit in each box, but definitely answers the question. My student came up with 9/12 + 5/34 + 7/68
Oh! I didn’t realize that this is identical to yours! I think I should take mine down instead, because yours is the first one up. What do you think?
I would definitely leave yours up or we’d lose this great discourse thread!
This answer does not follow the rules with 1 digit in each box, but definitely answers the question. My student came up with 9/12 + 5/34 + 7/68
Gina, you should create that one and post it. It may already be on here already but by putting 1 box for numerator and 2 for each denominator you’ve created a pretty challenging task! I wonder if there is more than one answer?
Amazing!! How could you find the answer?? Just keep trial and errors??
i got 1/4 + 2/8 + 3/6
My answer is 1/4+4/8+4/16.
1/4+2/8+3/6
1/4+2/8+3/6
1/3, 1/3, 1/3 🙂
3/9, 2/4, 1/6
2/5 + 2/5 + 1/5 = 1
Wait no I’ll use
2/8 + 1/4 + 3/6
Because I can only use them once
2/8+1/4+3/6?
1/2 + 2/8 + 1/4 = 1
4/8 + 3/9 + 1/6
My fifth-grade student, Yuel, came up with 3 possibilities:
1/4 + 3/6 + 2/8 = 8/8
1/6 + 2/4 + 3/9 = 6/6
4/8 + 3/9 + 1/6 = 6/6
2/6 + 2/6 + 4/12
I need 3 numbers that have 1 as a numerator and all different denominators! HELP!
1/6 + 4/8 + 3/9 =1
G.D.
3/9 + 2/4 + 1/6 = 1
The unique solutions are
1/4 + 2/8 + 3/6
1/6 + 3/9 + 2/4
1/6 + 3/9 + 4/8
You can swap the numerators or the addends (fractions) around to get 6*6=36 times as many solutions.
Correction: You can swap the addends, but not the numerators, so only 3*6 = 18 solutions.
It is 1/4 1/4 and 1/5
Zane found 4/8 + 1/6 + 3/9 = 1