Chapter 1.3, Problem 6LC

To determine

To find: the example of the rational that is not integer.

Answer to Problem 6LC

  $\frac{3}{5},-\frac{2}{7},\frac{4}{3}\mathrm{.........}$

Explanation of Solution

Given:

There are rational numbers which are not integers.

Concept used:

The sets of integers are:

  $z=\left\{\mathrm{.....},-3,-2,-1,0,1,2,3,\mathrm{.....}\right\}$ .

The fraction which are not further divisible are not include in integers.

Calculation:

There are rational numbers which are not integers.

Example:

  $\frac{3}{5},-\frac{2}{7},\frac{4}{3}\mathrm{.........}$

All these are non- integer rational numbers. These numbers do not belong to the set of integers.

  $z=\left\{\mathrm{.....},-3,-2,-1,0,1,2,3,\mathrm{.....}\right\}$ .

All naturals numbers together with $0$ and the negatives of all counting numbers form the set of integers denoted by $z$ .

The numbers of the form $\frac{a}{b}$ where $a\text{ and }b$ are integers and $b\ne 0$ are called rational numbers.

  $Q=\left\{\frac{a}{b};a\in z,b\in z,b\ne 0\right\}$ is the set of rational numbers.

Hence, $\frac{3}{5},-\frac{2}{7},\frac{4}{3}\mathrm{.........}$ .