Rational numbers

Compute $-\tfrac34 + \tfrac56$.

A water seller in Kano has $7$ litres of water and fills bottles that hold $\tfrac12$ litre each. How many bottles can she fill? (Compute $7 \div \tfrac12$.)

Compute $\left(-\tfrac56\right) \div \left(-\tfrac{10}{9}\right)$.

Which of these numbers have a reciprocal in $\Q$? (Choose all that apply.)

Which of these fractions have terminating decimal expansions? (Choose all that apply.)

Which fraction equals $0.\overline{36} = 0.363636\ldots$?

How many rational numbers lie strictly between $\tfrac13$ and $\tfrac12$?

In the proof that $\sqrt2$ is irrational we have $a^2 = 2b^2$ and conclude that $a$ is even. Which reason is correct?

Which Lean statement says correctly that between any two different rational numbers there is another?

Write period_length(a, b) for whole numbers $a \ge 0$ and $b > 0$. Do long division: start with the remainder a % b, and at each step replace the remainder r by (10 * r) % b. Remember the step at which each remainder first appears. Return the length of the repeating block of $\tfrac ab$, or 0 if the decimal terminates (that is, if the remainder 0 appears).