Class 7 Maths Chapter 4 Rational number

--- Chapter 4 – Rational Numbers Rational numbers form a very important part of mathematics. In earlier classes, students have already studied about natural numbers, whole numbers, and integers. Now, in this chapter, the concept of rational numbers is introduced and explained in detail. Definition of Rational Numbers A rational number is any number that can be expressed in the form of p/q, where: p and q are integers, q ≠ 0. For example: are all rational numbers. Thus, rational numbers include fractions, integers, terminating decimals, and recurring decimals. --- Representation on Number Line Just like integers, rational numbers can also be represented on the number line. Each rational number has a unique position on the number line. Positive rational numbers are to the right of zero. Negative rational numbers are to the left of zero. --- Equivalent Rational Numbers Two rational numbers are said to be equivalent if they represent the same value. Example: . By multiplying or dividing both numerator and denominator by the same non-zero number, we can obtain equivalent rational numbers. --- Standard Form of Rational Numbers The standard form of a rational number is obtained when: The denominator is positive. The numerator and denominator have no common factor other than 1. Example: in standard form is . --- Comparison of Rational Numbers To compare rational numbers: 1. Convert them to have the same denominator, or 2. Represent them on the number line. Example: Compare and . LCM of 4 and 8 is 8. . Since , therefore . --- Operations on Rational Numbers This chapter also explains the rules for performing the four basic operations with rational numbers. 1. Addition of Rational Numbers If denominators are the same, add numerators. If denominators are different, take the LCM of denominators. 2. Subtraction of Rational Numbers Similar to addition, but subtract the numerators after making the denominators equal. 3. Multiplication of Rational Numbers Multiply numerators together and denominators together. Example: . 4. Division of Rational Numbers Multiply the first rational number by the reciprocal of the second. Example: . --- Properties of Rational Numbers Rational numbers follow several important properties: 1. Closure Property Addition, subtraction, and multiplication of rational numbers always give another rational number. Division is closed except when dividing by 0. 2. Commutative Property Addition and multiplication are commutative. Subtraction and division are not commutative. 3. Associative Property Addition and multiplication are associative. Subtraction and division are not associative. 4. Distributive Property Multiplication is distributive over addition and subtraction. --- Important Points to Remember Every integer is a rational number (because it can be written as p/1). A rational number can have positive or negative sign. Zero is also a rational number. Between any two rational numbers, there exist infinitely many rational numbers. --- Conclusion The chapter on rational numbers helps students to expand their knowledge of numbers beyond integers and fractions. By understanding rational numbers, their standard form, operations, and properties, students can develop strong mathematical foundations that will help in higher classes, especially in algebra and number theory. ---