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# NCERT Solutions for Class 7 Maths Chapter 9 – Rational Numbers

In NCERT Solutions for Class 7 Maths Chapter 9 we will study deeply about Rational Numbers. We have prepared complete solutions to all 2 exercises which carry a total of 14 questions. We will study the properties of Rational Numbers- Addition and Subtraction of Integers, Multiplication and Division of Rational Numbers, Positive and Negative Rational Numbers, etc.

Try these NCERT Solutions for Class 7 Chapter 9 ‘Rational Numbers’, which are based on the official syllabus. Instasolv provides you step-by-step solutions to all the questions available in the exercises. We also provide Chapter-wise Solutions of NCERT Class 7 Maths Book. These answers will help you in understanding even the basic concepts. They will improve your speed of solving any question of any type based on these concepts. Through NCERT Solutions, you also develop great accuracy.

For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. We follow the same sequence as in the book so that it becomes easy to refer and understand. This will help you strengthen your concepts and help you in scoring higher marks in the exams.

## NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers: Exercise Discussion

Chapter 9 consists of 14 questions in total. You can follow our NCERT Solutions for Class 7 Chapter 9 but before you move ahead, we suggest you to go through the important topics discussed below for complete understanding of the concepts.

Introduction

Rational Numbers include integers and fractions. All fractions are Rational Numbers.

Need for Rational Numbers

Some situations are not answered by integers or fractional numbers. For this, the need arises to go beyond the number system. For example distance below the sea level of 750m or ¾ km. If we write -3/4 km, this is neither an integer nor a fraction.

What are Rational Numbers?

A rational number is defined as a number that can be expressed in the form p / q, where p and q are integers and q is not equal to 0.

All fractions and integers can also be written as Rational Numbers.

Equivalent Rational Numbers – This follows the same principle as equivalent fractions. By multiplying the numerator and denominator of a rational number by the same non zero integer, we obtain another rational number equivalent to the given rational number.

Positive and Negative Rational Numbers

Positive Rational Numbers: are those Rational Numbers in which both the numerator and the denominator are either positive or negative

Negative Rational Numbers: are those Rational Numbers where either one of the denominator or numerator is negative. In other words, the numerator is negative and the denominator is positive or the numerator is positive and the denominator is negative.

The number zero is neither a positive nor a negative rational number.

Rational Numbers on a Number Line

We have already studied how to represent integers and fractions on a number line. All integers and fractions are part of Rational Numbers. In addition, one can plot negative Rational Numbers to the left of zero on the number line and positive Rational Numbers to the right of zero on the number line.

Rational Numbers in Standard Form

When the denominator of a rational number is always a positive integer and the only common factor between the numerator and the denominator is one, we call it the standard form of a rational number.

Any rational number which is not in the standard form can be reduced to a standard form. To reduce the rational number to its standard form, we divide its numerator and denominator by their highest common factor ignoring the negative sign, if any.

Comparison of Rational Numbers

• In these types of questions, we can plot or visualize the Rational Numbers on the number line to compare them and know which is bigger or smaller than the other.
• To the left of zero the more we go, the smaller the number gets so to compare two negative Rational Numbers, we can check on the number line and the number which comes further to the left of zero is smaller. Alternatively, we can compare the numbers ignoring their negative sign and then reverse the order.
• A negative rational number will always be lesser or smaller in value than a positive rational number.
• We can also reduce Rational Numbers to their standard form and compare them.

Rational Numbers Between Two Rational Numbers

There are unlimited Rational Numbers between any two Rational Numbers.

Operations on Rational Numbers

While adding Rational Numbers with the same denominators, we add the numerators keeping the denominators the same.

If the denominator is not the same, we first convert the Rational Numbers to equivalent Rational Numbers with the same denominator. The LCM (least common multiple) method can be used for this.

Additive Inverse: The rational number which when added to another rational number results in zero is called the additive inverse of that rational number.

Example: -2/3 is the additive inverse of 2/3 and vice versa.

Subtraction

While subtracting two Rational Numbers, we add the additive inverse of the rational number that is being subtracted, to the other rational number.

Ex. 7/5 – 11/5 can also be written as 7/5 + (-11/5) where -11/5 is the additive inverse of 11/5. The answer will be -4/5

Multiplication

The same method is applied as in fractions, where the numerators or both Rational Numbers are multiplied to give the numerator of the answer and the denominators of both Rational Numbers are multiplied to give the denominator of the answer.

Division

We have already studied the reciprocal of a fraction. The same concept is extended to find the reciprocal of a non-zero rational number.

Ex. reciprocal of -2/3 is -3/2

To divide one rational number by the other non-zero rational number we multiply the rational number by the reciprocal of the other.

## Study Tips for NCERT Class 7 Maths  Chapter 9: Reciprocal Numbers

In order to aim for a high score in Class 7 Maths, you must follow  NCERT Solutions for Class 7 Maths Chapter 9. We also recommend that you first read this chapter of CBSE NCERT textbook for Class 7 Maths, to become familiar with the concepts.

Our subject matter experts have provided above a simple explanation and summary for each part and subpart of Chapter 9- ‘Reciprocal Numbers’. Use them to develop a better understanding.

• If any concept is still not understood, ask the experts on the Instasolv app.
• Do all the exercises, solved examples and self-practice questions on your own.