What Is Rational Number Class 7 in Hindi | NCERT Maths Guide

Definition of Rational Numbers in Class 7 Mathematics

A rational number is defined as any number that can be written in the form of a fraction:

$$\frac{p}{q}$$

where:

• $p$ and $q$ are integers
• $q \neq 0$

This means rational numbers include fractions like $\frac{3}{4}$, $\frac{-5}{2}$, and also integers like 7 (which can be written as $\frac{7}{1}$).

In Hindi, rational numbers are called परिमेय संख्याएँ. This concept is fundamental in Class 7 NCERT Maths and helps in understanding operations with fractions and decimals.

Properties of Rational Numbers Explained

Rational numbers have several important properties:

• Closure: The sum, difference, and product of two rational numbers is always a rational number.
• Commutative Property: $a + b = b + a$ and $a \times b = b \times a$ for rational numbers.
• Associative Property: $(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$.
• Existence of Additive Inverse: For any rational number $\frac{p}{q}$, its additive inverse is $-\frac{p}{q}$.
• Existence of Multiplicative Inverse: For any rational number $\frac{p}{q}$ (except zero), its multiplicative inverse is $\frac{q}{p}$.

These properties make rational numbers easy to work with in algebra and arithmetic.

Types of Rational Numbers with Examples

Rational numbers can be classified as:

• Positive Rational Numbers: Numbers greater than zero, e.g., $\frac{3}{5}$, 4.
• Negative Rational Numbers: Numbers less than zero, e.g., $-\frac{2}{7}$, $-9$.
• Zero: Zero is also a rational number because it can be written as $\frac{0}{1}$.

Understanding these types helps in solving problems involving rational numbers effectively.

Representation of Rational Numbers on Number Line

One of the key concepts in Class 7 NCERT is representing rational numbers on the number line.

• Every rational number corresponds to a unique point on the number line.
• Positive rational numbers lie to the right of zero.
• Negative rational numbers lie to the left of zero.

Example:

To represent $\frac{3}{4}$ on the number line:

1. Divide the segment between 0 and 1 into 4 equal parts. 2. Count 3 parts to the right of 0. 3. Mark the point at $\frac{3}{4}$.

This visual helps students understand the size and order of rational numbers.

Comparing Rational Numbers: A Simple Method

To compare two rational numbers, follow these steps:

1. Convert both to fractions with the same denominator. 2. Compare their numerators.

Example: Compare $\frac{3}{4}$ and $\frac{5}{6}$.

• Find LCM of denominators 4 and 6, which is 12.
• Convert:
• $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
• $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$

Since $9 < 10$, $\frac{3}{4} < \frac{5}{6}$.

This method is easy and useful for Class 7 students to solve NCERT exercises.

Worked Example: Adding Rational Numbers

Problem: Add $\frac{2}{3}$ and $\frac{4}{5}$.

Solution:

1. Find LCM of denominators 3 and 5, which is 15. 2. Convert fractions:

$$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$$

$$\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$$

3. Add numerators:

$$\frac{10}{15} + \frac{12}{15} = \frac{10 + 12}{15} = \frac{22}{15}$$

4. The answer is an improper fraction, which can be written as a mixed number:

$$\frac{22}{15} = 1 \frac{7}{15}$$

This example demonstrates how to add rational numbers step-by-step.