Fractions Less Than One Half

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create as many fractions as possible that are less than one half.


How can you tell if a fraction is less than one half?
What patterns do you notice?
How can you be certain you have all possible solutions?


16 fractions less than one half
1/9, 2/9, 3/9, 4/9, 1/8, 2/8, 3/8, 1/7, 2/7, 3/7, 1/6, 2/6, 1/5, 2/5, 1/4, 1/3

Source: Christine Newell

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  1. I’m curious as to why you are counting equivalent fractions separately in your answer. Since 2/8 = 1/4 and 3/9 = 2/6 = 1/3, I initially found only 13 fractions.

    • Just seeing this. I would count them as separate answers because although they are equivalent, they have a “different number and size of parts” which is language that comes from a 4th grade standard. A question on the equivalent fractions students find would be a great follow-up question, though!

      • yea 4th grade can be a challenge and there is hard questions i’m still kinda stuck on whats something less than 1\2 i wish i did not have to do math the only math i’m really only good at addition subtraction and multiplication

  2. I still wonder what this means lol

  3. Christine Newell is right I am a 4th grader and I dont get these so I just wrote them down

  4. Your answer uses the digits more than 1 time. Are they just meant to be possibilities?

  5. WHAT are THREE fractions that are less than ½?

  6. Nam
    e THREE fractions that are greater than ½?

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