7th Class Mathematics - Semester 2

A Mathematics textbook for Class VII, Semester 2. It is a free distribution by Samagra Shiksha, Government of Andhra Pradesh.

Key Content (Chapter 8: Rational Numbers):

• Need for Rational Numbers (అకరణీయ సంఖ్యల అవసరం): The number system is extended from integers to include numbers like frac-3/4, which is neither an integer nor a fractional number, to represent opposite situations involving fractional values, such as distance below sea level.

• Definition of Rational Numbers (అకరణీయ సంఖ్యలు అంటే ఏమిటి?): A rational number is a number that can be expressed in the form p/q, where p and q are integers and q \ne 0. All fractions and integers are rational numbers.

  • p is the numerator (లవము) and q is the denominator (హారము).

• Equivalent Rational Numbers (సమానమైన అకరణీయ సంఖ్యలు): Multiplying or dividing the numerator and denominator by the same non-zero integer yields an equivalent rational number.

• Positive and Negative Rational Numbers (ధన మరియు ఋణ అకరణీయ సంఖ్యలు):

  • A positive rational number has both numerator and denominator as positive integers or both as negative integers.

  • A negative rational number has the numerator and denominator with opposite signs

  • The number 0 is neither a positive nor a negative rational number.

• Standard Form (ప్రామాణిక రూపం): A rational number is in standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1. To reduce to standard form, divide the numerator and denominator by their HCF.

• Comparison of Rational Numbers (అకరణీయ సంఖ్యల పోలిక):

  • A negative rational number is always less than a positive rational number.

  • To compare two negative rational numbers, compare them ignoring the negative signs and then reverse the order.

• Rational Numbers Between Two Rational Numbers: Unlike integers, where the number of integers between two successive integers is 0, there are an unlimited number of rational numbers between any two different rational numbers.