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Fractions Less Than One Half

Directions: Using the whole numbers 1 through 9 as numerators or denominators, how many fractions can you make that are less than one half?

Hint

Hint

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?

Answer

Answer

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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2 comments

  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!

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