Food for thought

Powerful fractions Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Problem

Two fractions are shown below.

$\textrm{Fraction} \ A: \frac{10^a +1}{10^a +2} \qquad \textrm{Fraction} \ B: \frac{10^b + 1}{10^b + 2}$

For what values of $a$ and $b$ will fraction A be greater than fraction B?

How might your thinking change if instead we had these two fractions?

$\textrm{Fraction} \ C: \frac{10^c +1}{10^c -1} \qquad \textrm{Fraction} \ D: \frac{10^d + 1}{10^d -1}$

For what values of $c$ and $d$ will fraction C be greater than fraction D?