# MAT - Paper 2018 - Q6

> Source: https://ollybritton.com/notes/maths/problems/mat/2018/q6/ · Updated: 2021-10-28 · Tags: mat, notes, maths

## 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??
$$
\frac{1}{5} < \frac{3}{13} < \frac{1}{4}
$$

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