### 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?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

# More Twisting and Turning

##### Age 11 to 16Challenge Level

Rachel thought through the problem like this:

For fractions $-\frac{n}{2}$

twist until reaching $\frac{1}{2}$, then turn to get $-2$, and twist twice.

For fractions $\frac{2}{n}$, start by turning once, then repeat as above.

Ved from WBGS in the UK sent in a more general solution:

If the entangled fraction is positive, then rotate,

If it is negative, then twist,

Repeat until the entangled fraction is 0

Ved also wrote a program which takes the numerator and denominator of the tangled ropes as inputs, follows this procedure, and writes a sequence of Ts and Rs to tell you how to untangle the ropes: