What is Rational Numbers Class 7: Definition & Examples Explained

Definition of Rational Numbers for Class 7 Students

A rational number is any number that can be written as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. Here, $p$ is called the numerator and $q$ the denominator.

• Examples of rational numbers: $\frac{3}{4}$, $-\frac{5}{2}$, $0$, $7$ (since $7 = \frac{7}{1}$).
• Non-examples: $\sqrt{2}$, $\pi$, as they cannot be expressed as a fraction of two integers.

This definition is fundamental in the Class 7 NCERT Mathematics syllabus and helps students identify and work with rational numbers confidently.

Properties of Rational Numbers Explained

Rational numbers have several important properties that make calculations easier:

1. Closure Property: The sum, difference, and product of two rational numbers is always a rational number. 2. Commutative Property: $a + b = b + a$ and $a \times b = b \times a$ for rational numbers. 3. Associative Property: $(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$. 4. Distributive Property: $a \times (b + c) = a \times b + a \times c$.

These properties help in simplifying expressions and solving problems involving rational numbers.

Types of Rational Numbers: Positive, Negative, and Zero

Rational numbers can be:

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

Understanding these types helps in comparing and ordering rational numbers on the number line.

Decimal Representation of Rational Numbers

Every rational number can be expressed as a decimal, which will be either:

• Terminating Decimal: The decimal ends after a finite number of digits. Example: $\frac{3}{4} = 0.75$.
• Repeating Decimal: The decimal digits repeat infinitely. Example: $\frac{2}{3} = 0.666\ldots$ (where 6 repeats).

This helps students identify rational numbers by their decimal forms and convert between fractions and decimals.

Comparing Rational Numbers: A Simple Guide

To compare two rational numbers, follow these steps:

• Convert both to have the same denominator.
• Compare their numerators.

This method is useful for ordering rational numbers on the number line and solving inequalities.

Worked Example: Adding Rational Numbers

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

Step 1: Find the LCM of denominators 5 and 10, which is 10.

Step 2: Convert $\frac{2}{5}$ to $\frac{4}{10}$.

Step 3: Add $\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$.

Answer: $\frac{7}{10}$.

This example shows how to add rational numbers with different denominators, a key skill in Class 7 NCERT Mathematics.