**Introduction of study online rational numbers: **

In mathematics a rational number is any number that can be expressed as the quotient a / b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every
integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q**.** (Source – Wikipedia)

The followings are addition and subtraction operations for rational numbers.

**Addition:**

In the addition of rational numbers the denominator can add with the same and all the numerators can be add with keep same as the denominator.

**Subtraction:**

In the subtraction of rational numbers the denominator can subtract with the same and subtract the two numerators also which keep same as the denominator.

**Study online rational number - Example 1**

**1. Addition: `8 / 7` + `1 / 7` .**

**Solution:**

= `(8 + 1) / 7` (adding the numerator)

= `9 / 7`

**Answer is `9 / 7`**

**Study online rational number - Example 2**

**2. Addition: `2 / 7 + 8 / 9` .**

**Solution:**

The l.c.m. of 7 and 9 is 63

`2 / 7 = (2 * 9) / (7 * 9)`

= `18 / 63`

`8 / 9 = (8 * 7) / (9 * 7)`

= `56 / 63`

`2 / 7 + 8 / 9 = 18 / 63 + 56 / 63`

= `(18 + 56) / 63`

= `74 / 63`

**Study online rational number - Example 3**

**3. Subtraction: `6 / 4` – `2 / 8` .**

**Solution:**

`6 / 4` = `(6 * 2) / (4 * 2)`

= `12 / 8`

So,

= `(12 / 8) - (2 / 8)`

= `(12 - 2) / 8`

= `10 / 8`

The followings are multiplication and division operations for rational numbers.

**Multiplication:**

In this rational number we can multiply the numerator and the denominators of both rational numbers.

**Division:**

In this rational number we can take reciprocal of one rational number and the multiply them. Then we can divide the both the rational number of reciprocal.

**1. Multiplication:` 5 / 7` and `1 / 3` .**

**Solution:**

= `(5 * 1) / (7 * 3)` (by multiply the numerator and denominator)

= `5 / 21`

Answer is `5 / 21`

**2. Multiplication: `7 / 5` and `1 / 3` .**

**Solution:**

= `(7 * 1) / (5 * 3)` (by multiply the numerator and denominator)

= `7 / 15`

Answer is `7 / 15`

**3. Division: `3 / 2` by `3 / 6` .**

**Solution:**

The reciprocal of `3 / 6` is = `6 / 3`

So,

= `(3 / 2) * (6 / 3)`

= `(3 * 6) / (2 * 3)`

= `18 / 6`

The lowest form is 3.