Common numerators

As long as I’m leveraging Five Triangles posts, here is another recent one worth discussing.

Too often, I think students believe that the only way to compare fractions is to find common denominators.  In this problem, three of the four given denominators are big enough primes that the common denominator approach would result in some painful enough by-hand computations.

But the pattern in the numerators screams for attention.  Why not find some common numerators and compare the fractions that way?  That approach cracks the problem pretty efficiently.

As a bonus, the common numerator approach also shows that the four given fractions are surprisingly close to each other in size.

Keep thinking …

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