Question

Find a rational no between -3/7 and 1/2

Answer 1

A number is rational when it can be represented as

$$\frac p q,$$

where p, q are integers. For example, 0 is a rational number because it can be represented as

$$\frac 0 1$$

We can say

$$\frac c d \le \frac a b \le \frac e f$$

only if

$$\begin{cases} bc \le ad \\ af \le be \end{cases}$$

where b, d and f are positive. Otherwise, the denominator and numerator of fractions with negative denominators should be multiplied by -1, thus the denominator becomes positive. For example,

$$\frac {-3} 7 \le \frac 0 1 \le \frac 1 2$$

is true because

$$\begin{cases} -3 \le 0 \\ 0 \le 1 \end{cases}$$