### Why use this resource?

This problem continues the theme of continued fractions, developing some of the ideas met in Staircase sequences. It provides further opportunity for students to practise manipulating fractions and inequalities, helping them develop a deeper understanding of how to compare fractions and the effect of dividing by a larger or smaller value.

### Key question

- If you increase the denominator of a fraction do you reduce or increase the value of the fraction?

### Possible support

If students are unsure how to start they can be encouraged to try numerical values for \(a\) and \(b\).