 # Adding 3 Fractions to Get 1

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?

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

## Equivalent Expressions with Fractions

Directions: Using the digits 0 to 9 at most one time each and choosing either …

1. • can only use each digit one time

• 1/3 + 1/2 + 1/6

• 1/3+1/3+1/3=1

2. I there only one answer? 1/4+2/8+3/6

3. Is there only one answer? 1/4+2/8+3/6

4. My students also found 4/8 + 3/9 + 1/6

5. • 4/8 + 3/9 + 1/6

6. 1/3 + 1/3 + 1/3 =1

7. 1/3 + 1/3 + 1/3

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

9. Mikayla Malmquist

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

10. 11. 2/8+1/4+3/6

12. 2/8+5/8+1/8

13. 1/4 + 2/8 + 3/6 = 1

14. 15. 1/3+1/3+1/3

16. 17. 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!

18. 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??

19. i got 1/4 + 2/8 + 3/6

20. 21. 1/4+2/8+3/6

22. 1/4+2/8+3/6

23. 1/3, 1/3, 1/3 🙂

24. 3/9, 2/4, 1/6

25. 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

26. Your friend who says I like your cut G way too much

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

27. 1/2 + 2/8 + 1/4 = 1

28. HELP!!!!!!

29. Nicolette Schlachter

4/8 + 3/9 + 1/6

30. 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

31. 32. I need 3 numbers that have 1 as a numerator and all different denominators! HELP!