Too close to call

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

Problem



Arrange these fractions in order, from smallest to largest:

$$\frac{111110}{111111} \qquad \frac{222221}{222223} \qquad \frac{333331}{333334}$$ 

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.