NCERT Exemplar Class 7 Maths Chapter 8 Solutions: Rational Numbers

NCERT Exemplar Class 7 Maths Solutions Chapter 8 ‘Rational Numbers’ have been compiled to assist you to obtain good marks in your school exams. There are 110 questions in different types of exercises in this chapter of NCERT Exemplar Class 7 Maths comprising objective and subjective questions. These exercise questions have been curated to help you in the analysis of the question paper pattern of your school exam.

After having learnt about natural numbers, whole numbers and integers in your previous classes and previous chapters, you will get to revise all the topics besides a detailed introduction to rational numbers. You will also learn about the standard form and reciprocal of rational numbers and performing simple operations on two or more rational numbers such as addition, multiplication, division, and subtraction.

The NCERT maths exemplar solutions for class 7 chapter 8 are given by Instasolv on an easy to access platform where you can get your queries sorted with just a few clicks. The expert faculty of Instasolv aims at working hard with you to clear your concepts at this stage to help you build a strong foundational base for higher classes.

Important Topics in NCERT Exemplar Class 7 Maths Solutions Chapter 8 – Rational Numbers

Introduction to Rational Numbers

  1. The term Rational is derived from the word ‘Ratio’.
  2. If a number can be expressed in the form ofwith the conditions such that q ≠ 0 and p, q are both integer numbers, then the number is known as a rational number.
  3. If we consider, then we term p as the numerator and q as the denominator.
  4. All the integers and many fractions can be considered an element of the set of rational numbers.

Equivalent Rational Numbers 

Equivalent Rational Numbers are very much similar to equivalent fractions. These numbers can be obtained by multiplication of the numerator and the denominator of a given rational number with an equal non-zero integer respectively.

Positive and Negative Rational Numbers

  1. If both the numerator and denominator of a rational numberare positive integers, then the rational number is a positive one.
  2. If either the numerator or the denominator is negative the rational number can be written in the form-and is known as a negative rational number.
  3. 0 is neither a negative nor a positive rational number.
  4. There can be infinite numbers represented on a number line between two numbers.

Standard Form

If we consider a rational numbersuch that q is a positive integer while p and q do not have any common factors other than 1, in that case, we will callthe standard form.

Comparison and Operations of Rational Numbers:

  1. Rational numbers are compared in the same manner as fractions are compared. Firstly, if the denominators are different, we make them equal by taking the LCM of the denominator and multiplying the numerator by the factor of the LCM. Now, we can make a comparison like we compare whole numbers.
  2. If the rational numbers are negative, we repeat the above procedure just that we reverse the sign of comparison in the end.
  3. The operations on rational numbers are performed in the same way as in, fractions and integers keeping in mind the sign of the number.
  4. Additive inverse of a rational number gives zero on adding it with the given rational number.
  5. Multiplying a rational number with its reciprocal gives the result as unity.

Exercise Discussion of NCERT Exemplar Class 7 Maths Exemplar Chapter 8 – Rational Numbers

  1. The nature of NCERT Exemplar questions is broad ranging from multiple-choice objective questions to statement-based subjective questions.
  2. Questions 1-12 are the MCQs to provide you with ample exercise for extensive practice.
  3. You will get to solve fill in the blanks exercises from questions 13 to 46.
  4. 47-66 are true or false and match the column exercises to test your knowledge about the analytical questions of rational numbers.
  5. Questions 67-110 will require you to evaluate various operations on rational numbers, their representation on the number line, etc.

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