Rationals Between...

What fractions can you find between the square roots of 65 and 67?

Canny Fraction

Weekly Problem 4 - 2012
What fraction of the volume of this can is filled with lemonade?

Circuit Training

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

Stretching Fractions

Stage: 4 Challenge Level:
What is the routine for calculating the result when the fraction is less than or equal to a half ?

What is the routine when the fraction is greater than a half?

Can you express that in algebra?

If $x$ is the fraction value what is the result in terms of $x$ for the two cases above?

For each denominator (bottom number of the fraction) which fractions are equivalent to other fractions with a smaller denominator?

Which fractions form a loop?

Which fractions do not belong to the loop but track into it?