### 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?