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'Comparing Continued Fractions' printed from https://nrich.maths.org/
Why do this problem?
For experience of working with inequalities and with
fractions.
Possible approach
If they can't get started students can try numerical values for $a$
and $b$.
Key question
If you increase the denominator of a fraction do you reduce or
increase the value of the fraction?
Possible support
Try the problem
Not Continued Fractions
Possible extension
See the article
Continued Fractions 1