NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers download the pdf provided below. Our specialist tutors formulate these exercises to help you with your exam preparation to attain good marks in Maths. Students who wish to score good marks in Maths are advised to practice NCERT Solutions for Class 7 Maths.
Chapter 9 – Rational Numbers consists of 2 exercises, and here we provide the NCERT Solutions to all the questions present in these exercises. Given below are some of the concepts present in this chapter.
- Need For Rational Numbers
- What Are Rational Numbers
- Positive And Negative Rational Numbers
- Rationals Numbers On a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Operations On Rational Numbers
- Addition of Rational Numbers
- Subtraction of Rational Numbers
- Multiplication of Rational Numbers
- Division of Rational Numbers
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers
Class 7 Maths Chapter 9 NCERT Solutions –
Students can download and refer to the Class 7 Maths Ch 9 solutions, which have been solved by the greatest teachers in the country. Some of the most challenging problems can be answered in the most basic of ways. It enables students to fully comprehend the strategy. It also allows them to apply what they’ve learned about the subject to other questions on the exam. Students can access and download solutions at any time and from any location.
9.1 The Introduction
Some sorts of numbers are already familiar to students. Natural numbers, whole numbers, and integers are the three types of numbers. Natural numbers start at 1 and go all the way to infinity. Whole numbers are created by adding 0 to natural numbers. When negative numbers are added to the aforementioned collection, you get a set of integers. You were also taught about fractions, which are integers with a numerator and a denominator.
The number system is extended even further in this chapter, and the idea of Rational Numbers is introduced. You’ll also learn about Rational Numbers’ mathematical operations.
9.2 The Need for Rational Numbers
The term “rational numbers” refers to a specific type of number. This is due to the fact that they can be written in fractional form. Rational numbers can be expressed as a ratio of p to q, where p and q are both integers and q is not zero.
Rational numbers are those that are used on a daily basis. Because there are numerous measures of a quantity that cannot be effectively described by integers or natural numbers alone, they are required. Rational Numbers are required to depict these figures.
9.3 What Do You Mean When You Say “Rational Numbers”?
The definition of a rational number is explained in this section of NCERT Class 7 Maths Chapter 9. A rational number is one that can be written as a p/q ratio, where p and q are both integers and q is not zero. A rational number’s numerator and denominator will both be integers. This indicates that 0 can be a rational number because a rational number can be written as 0/5 or 0/100, for example.
Rational Numbers with Equivalents
Different numerators and denominators can be used to write Rational Numbers. The corresponding Rational Numbers can be obtained by multiplying the rational number’s numerator and denominator with the same integer. Make certain the number is not zero. The procedure is the same as for obtaining equivalent fractions.
Hence, If p/q is a rational number, the comparable Rational Numbers are (p/q) (3/3), (p/q) (10/10), and so on.
9.4 Rational Positive and Negative Numbers
- This is a positive rational number if both the numerator and denominator of the rational number have the same sign. All of the Rational Numbers that are positive are greater than 0. This can be expressed as a (p/q) or a (-p/-q).
- And, negative rational Numbers are those with an opposite sign in either the numerator or denominator. Negative Rational Numbers are all negative numbers that are smaller than zero. (-p/q) or (p/-q) are examples of negative rational numbers.
9.5 Rational Numbers on a Number Line:
The pupils are already familiar with using a number line to represent numbers. Positive integers are those that are to the right of zero and have a (+) sign. The negative integers are those that are to the left of zero and have a (–) sign.
Natural numbers can also be thought of as Rational Numbers with a denominator of 1 when written on the number line.
This portion of the CBSE class 7 Maths Rational Numbers solutions discusses how to write a rational number on the number line. Draw a line and find a point with a coordinate of 0 on it. The number line’s starting point is here. This is to the right of zero if the rational integer given is positive. The rational number is shown to the left of zero if it is negative.
So, if you need to mark (-1/2) and (12) on the number line, they should be placed equidistant from 0, with (1/2) placed halfway between 0 and 1 and (-1/2) placed midway between 0 and -1.
Divide the unit into four parts between 0 and 1 and represent 4/5 on the number line.
9.6 Standard Form Rational Numbers
The concept of rational numbers in their standard form is discussed in Rational Numbers Class 7th Maths Chapter 9. If the denominator of a rational number is a positive integer and there are no additional common factors between the numerator and the denominator other than 1, the number is in its standard form.
For example, 1/3 is a rational integer, and the divisor and dividend share only one common factor: 1. This indicates that 1/3 is in its original form.
A rational number in standard form can have a negative value in its numerator but not in its denominator. If a rational number is not in its standard form, it can be lowered to get it there. This is accomplished by lowering the fraction.
9.7 Rational Numbers Comparison
You will learn how to compare two rational numbers in this section of Chapter 9 Class 7 Maths. The following are the steps that must be followed.
- Make sure the denominators of the two rational numbers are both positive.
- Find the LCM of the positive denominators and use the LCM as the common denominator in each of the Rational Numbers.
- Then compare the two Rational Numbers you’ve obtained, with the higher rational number being the one with a larger numerator.
If you need to compare two negative Rational Numbers, ignore their negative sign and reverse the comparison at the conclusion.
When comparing a negative and positive rational number, it is self-evident that the negative rational number is less than the positive rational number.
9.8 Rational Numbers Between Two Rational Numbers
The rational number between two Rational Numbers is 1/2 (m + n) if there are two Rational Numbers and mn.
You return to the integers and their attributes on various operations to insert Rational Numbers between two Rational Numbers. There can be (x – y – 1) integers between two non-consecutive integers. For example, say the two integers are x and y. Between two successive integers, there can’t be any integers. Between two Rational Numbers, an endless number of Rational Numbers can be put. The dense property is the name for this land.
If two rational numbers say ‘a’ and ‘b,’ do not have the same denominator, use the LCM method to convert the denominators of the fractions to the same denominator. This is the rational number between the two numbers if a number can be written between them.
If there are no numbers between the numerators, multiply the numerator and denominator by 10, which will give you the Rational Numbers between them. You can multiply by multiples of 10 to generate more rational numbers, such as 100, 1000, and so on.
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What are the primary themes addressed in Chapter 9 of the NCERT Solutions for Class 7 Maths?
The following are the important points covered in NCERT Solutions for Class 7 Maths Chapter 9:
- The Need for Rational Numbers
- What Do You Mean When You Say “Rational Numbers”?
- Rational Positive And Negative Numbers
- Numbers on a Number Line with Rationals
- Standardized Rational Numbers
- Rational Numbers Comparison
- Use Reasonable Numbers In the Middle of Two Rational Numbers
- Rational Numbers Operations
- Rational Numbers Addition
- Subtraction of Rational Numbers is number ten.
- Rational Number Multiplication
- Rational Numbers Division
