# MAT - Paper 2018 - Q6

## Flashcards

### 2021-10-28

If you are told “$m$ is the smallest natural number such that $\frac{1}{m} \le q$”, how could you formalise this mathematically?

\[\frac{1}{m-1} > q\]

What trick comes up a lot in dealing with inequalities?

Coming up with two separate inequalities with a shared term and sticking them together.

What’s a trick for approximating something like $\frac{3}{13}$?

Taking the reciprocal and considering what numbers it is sandwiched between.

If

\[4 < \frac{13}{3} < 5\]
what is

\[\frac{3}{13}\]
between?

\[\frac{1}{5} < \frac{3}{13} < \frac{1}{4}\]