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Rationals Between...

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

There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Circuit Training

Age 14 to 16 Challenge Level:

It is worth spending some time discussing the strategies pupils have adopted.

Another question might be:
What is the ratio of the speeds of the two runners if they are to meet at the start after $1$ lap, $2$ laps, $3$ laps... $n$ laps?.

What is the relationship betweent he ratio of the speeds of the runners and where they meet?