What is Rational Number Class 8 Answer: Definition & Examples

Definition of Rational Numbers for Class 8 Students

In Class 8 mathematics, a rational number is defined as any number that can be written in the form $\frac{p}{q}$, where:

• $p$ and $q$ are integers (whole numbers, positive or negative)
• $q \neq 0$ (denominator cannot be zero)

For example, $\frac{3}{4}$, $\frac{-5}{2}$, and $0$ (which can be written as $\frac{0}{1}$) are rational numbers.

This definition helps students identify and classify numbers as rational or not. Rational numbers include fractions, integers, and decimals that can be converted into fractions.

Properties and Examples of Rational Numbers

Rational numbers have several important properties:

• Closure: The sum, difference, and product of two rational numbers are always rational.
• Commutative and Associative: Addition and multiplication of rational numbers follow these properties.
• Existence of Additive Inverse: For every rational number $\frac{p}{q}$, there exists $-\frac{p}{q}$.

Examples:

• $\frac{2}{3} + \frac{1}{3} = 1$ (rational)
• $-\frac{4}{5}$ is rational because numerator and denominator are integers
• Integer 7 is rational as $\frac{7}{1}$

Understanding these properties helps solve Class 8 NCERT problems efficiently.

How to Identify Rational Numbers: Comparison with Irrational Numbers

To clearly understand what is rational number class 8 answer, it's helpful to compare rational numbers with irrational numbers.

This comparison clarifies the concept and helps students avoid confusion.

Converting Rational Numbers Between Fractions and Decimals

Rational numbers can be converted from fractions to decimals and vice versa:

• Fraction to Decimal: Divide numerator by denominator.
• Decimal to Fraction: Use place value to write as fraction, then simplify.

Example 1:

Convert $\frac{3}{4}$ to decimal:

$$\frac{3}{4} = 0.75$$

Example 2:

Convert 0.6 to fraction:

0.6 = $\frac{6}{10} = \frac{3}{5}$ after simplification.

This skill is important for Class 8 students to solve NCERT exercises involving rational numbers.

Basic Operations on Rational Numbers with Formulas

Class 8 students must know how to perform operations on rational numbers:

• Addition:

$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$

• Subtraction:

$$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$$

• Multiplication:

$$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$

• Division:

$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$

Worked Example:

Add $\frac{2}{5}$ and $\frac{3}{10}$:

$$\frac{2}{5} + \frac{3}{10} = \frac{2 \times 2}{5 \times 2} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}$$

Mastering these operations is key for NCERT Class 8 exam success.

Importance of Rational Numbers in Class 8 NCERT Mathematics

The chapter on Rational Numbers is crucial for Class 8 students because:

• It forms the basis for understanding algebraic expressions and equations.
• Helps in solving real-life problems involving ratios, proportions, and percentages.
• Builds strong number sense and prepares students for higher classes.

Students should focus on:

• Understanding definitions and properties
• Practicing NCERT textbook exercises
• Using diagrams and examples for clarity

Regular revision and practice ensure confidence in exams.