###### tags: `MATA02-2022`
# Ungraded problems 8

You are to work on these questions only for the benefit of learning the material. These problems are meant for practice, not an assignment to be handed in.

## 1.
Find the following quotients:
1. $3/5$ mod 11
2. $4/3$ mod 13
3. $3/4$ mod 13
4. $4/3$ mod 17
5. $3/4$ mod 17

## 2.
Consider the expression $\frac{2\times 3}{5}$ mod 17. Evaluate this four ways:

1. Find $\frac{1}{5}$ mod 17, that is, find $x$ so that $5x \equiv 1$ mod 17, and then multiply $x$ by 2 and by 3.
2. Find $\frac{2}{5}$ mod 17, that is, find $x$ so that $5x \equiv 2$ mod 17, and multiply $x$ by 3.
3. Find $\frac{3}{5}$ mod 17, that is, find $x$ so that $5x \equiv 3$ mod 17, and multiply $x$ by 2.
4. Find $\frac{6}{5}$ mod 17, that is, find $x$ so that $5x \equiv 6$ mod 17.

# Selected (partial) solutions
<details>
<summary>Solutions to selected problems (click to expand)</summary>

1.1: 9
1.2: 10
1.3: 4
1.4: 7
1.5: 5

2: 8

</details>