Question

How many integers are between 5/3 and 30/7?

Answer 1

first off, let's convert the "improper" fractions to mixed,

$\bf \cfrac{5}{3}\implies 1\frac{2}{3}\qquad \qquad \qquad\qquad \qquad \cfrac{30}{7}\implies 4\frac{2}{7}\\\\ -------------------------------\\\\ 1\frac{2}{3}\text{\textemdash\textemdash\textemdash}\boxed{2}\text{\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{3}\text{\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{4}\text{\textemdash\textemdash}4\frac{2}{7}$