What is Rational Number Class 7 in Hindi: Definition & Examples

Definition of Rational Numbers for Class 7 Students

A rational number is any number that can be written in the form $\frac{p}{q}$, where:

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

For example:

• $\frac{3}{4}$ is rational because 3 and 4 are integers and 4 is not zero.
• $-\frac{5}{2}$ is rational as well.
• Integers like 7 can be written as $\frac{7}{1}$, so they are also rational numbers.

This definition is fundamental in Class 7 NCERT Mathematics and helps students understand various types of numbers beyond whole numbers.

Types of Rational Numbers and Their Properties

Rational numbers can be:

• Positive rational numbers: Both numerator and denominator are positive, e.g., $\frac{2}{3}$.
• Negative rational numbers: Either numerator or denominator is negative, e.g., $-\frac{4}{5}$ or $\frac{4}{-5}$.
• Zero: Zero can be written as $\frac{0}{q}$ where $q \neq 0$.

Properties of rational numbers:

• Closure under addition, subtraction, multiplication, and division (except division by zero).
• The sum or product of two rational numbers is always rational.
• Rational numbers can be represented on the number line.

Understanding these types and properties is crucial for solving problems in Class 7.

How to Identify Rational Numbers: Examples and Non-Examples

To identify rational numbers, check if the number can be expressed as a fraction of two integers with a non-zero denominator.

Examples of rational numbers:

• $\frac{7}{1}$ (integer 7)
• $-\frac{3}{8}$
• $0$ (can be written as $\frac{0}{5}$)
• $0.75$ (since $0.75 = \frac{3}{4}$)

Non-examples:

• $\sqrt{2}$ (cannot be expressed as a fraction of integers)
• $\pi$ (irrational number)
• $0.1010010001...$ (non-repeating, non-terminating decimal)

Comparison Table:

This helps Class 7 students distinguish rational numbers clearly.

Representation of Rational Numbers on the Number Line

Rational numbers can be placed on the number line because they correspond to exact points.

Steps to represent a rational number $\frac{p}{q}$:

1. Locate integer points on the number line. 2. Divide the segment between 0 and 1 into $q$ equal parts. 3. Move $p$ parts from zero towards the right if positive, or left if negative.

Example: Represent $\frac{3}{4}$ on the number line:

• Divide the segment between 0 and 1 into 4 equal parts.
• Move 3 parts to the right from 0.

This visual understanding helps students grasp the size and position of rational numbers relative to integers.

Arithmetic Operations on Rational Numbers with Examples

Class 7 students should practice the four basic 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 $\frac{2}{3}$ and $\frac{3}{4}$:

$$\frac{2}{3} + \frac{3}{4} = \frac{(2 \times 4) + (3 \times 3)}{3 \times 4} = \frac{8 + 9}{12} = \frac{17}{12}$$

This result is an improper fraction and can also be written as $1 \frac{5}{12}$.

Practicing these operations is essential for solving NCERT exercises confidently.

Importance of Rational Numbers in Class 7 NCERT Mathematics

The chapter on Rational Numbers is a key part of the Class 7 NCERT Mathematics syllabus. It lays the foundation for:

• Understanding fractions and decimals more deeply.
• Solving real-life problems involving ratios, proportions, and percentages.
• Preparing for higher classes where rational numbers are used in algebra and geometry.

Students should focus on:

• Grasping the concept rather than memorizing.
• Practicing all NCERT exercises and examples.
• Using diagrams and number line representations to strengthen understanding.

Mastering rational numbers improves problem-solving skills and boosts exam confidence.