Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make a true statement.

### 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)

2/8 + 1/4 + 3/6 = 1

2/4 + 3/9 + 1/6 = 1 (found by Koharu in Ms. Wilson’s class)

Source: Owen Kaplinsky

1/3+1/3+1/3=1

can only use each digit one time

1/3 + 1/2 + 1/6

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

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

HELP!!!!!!

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!