Stage: 5 Challenge Level: 
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
Mathematical reasoning & proof. Continued fractions. Stage 5 - Reviewed 2012. Calculating with fractions. Inequality/inequalities. Odd and even numbers. epsilons. Graphs. Stage 5 - Core Mapping. Manipulating algebraic expressions/formulae.
Published October 2000.
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