## Rational Numbers Class 8 Important concepts

In the number system, rational numbers are numbers that can be expressed as a ratio of two integers. They can also be the quotient of the ratio if the rational number is an integer. If the rational number is represented by the ratio \(\frac{p}{q}\), then q must be a non-zero integer. Since the denominator can be 1, every integer is a rational number. In rational numbers class 8 covers all the concepts and the arithmetic operations and properties involved on rational numbers are clearly explained.

## Expression of integers as rational numbers

Any integer n can be expressed as a rational number \(\frac{n}{1}\). This form is known as the canonical form of the integer.

**Irreducible Fractions**

All rational numbers can be expressed as an irreducible fraction \(\frac{x}{y}\) where x and y integers and y is not equal to zero. The canonical form of any rational number is expressed by dividing both the numerator and denominator by their greatest common divisor.

**Equality of Two Rational Numbers**

Two rational numbers \(\frac{x}{y}\) and \(\frac{a}{b}\) are said to be equal if

x=a and y=b,as well as xb=ay.

**Order of a Rational Number**

A rational number \(\frac{a}{b}\) is said to be greater than \(\frac{x}{y}\) if and only if \(ay>bx\)

**Addition and Subtraction of Rational Numbers**

Two rational numbers \(\frac{a}{b}\) and \(\frac{c}{d}\) are added as follows:

\(\frac{a}{b}+\frac{c}{d}\) = \(\frac{ad+bc}{bd}\)Similarly the subtraction is done as \(\frac{ad-bc}{bd}\)

**Multiplication of Rational Numbers**

Two rational numbers \(\frac{a}{b}\) and \(\frac{c}{d}\) can be multiplied as \(\frac{ac}{bd}\).

The rational numbers are in their canonical form, their product will be a reducible fraction.

**Division of Rational Numbers**

Division of rational numbers is carried out by multiplying one of the rational numbers with the reciprocal of the other.

To divide \(\frac{a}{b}\) and \(\frac{c}{d}\), \(\frac{a}{b}\) is multiplied by \(\frac{d}{c}\)

**Inverse Numbers**

All rational numbers have two inverses – additive inverse and multiplicative inverse.

Additive inverse of \(\frac{a}{b}\) is – \(\frac{a}{b}\) and the multiplicative inverse is \(\frac{b}{a}\)

## Rational Numbers Class 8 Questions

Here are some practice questions in rational numbers class 8 will test your understanding of the concepts. All questions are objective type and you need to select the right option.

1. A number \(\frac{a}{b}\) is said to rational number if

- Both a and b are integers
- Both a and b are integers and b is not equal to zero
- Both a and b are integers and a is not equal to zero
- 4 Both a and b are integers and both a and b are not equal to zero

2. Which of the following statements is false?

- Rational numbers are closed under addition
- Rational numbers are closed under subtraction
- Rational numbers are closed under multiplication
- Rational numbers are closed under division

3. The multiplicative inverse of a negative rational number is

- A negative rational number
- A positive rational number
- Zero
- One

4. If a+0 = 0+a = a, which is a rational number, then 0 is called as:

- Additional identity of rational numbers
- Reciprocal of a
- The multiplicative inverse of a
- Additive inverse of a

5. For a rational number \frac{a}{b}, if b is not equal to zero, the reciprocal is:

- \(\frac{a}{b}\)
- \(\frac{b}{a}\)
- Only a
- Only b

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