NCERT Class 7 Maths Chapter 8 ‘Rational Numbers’: Notes and Solutions (Free PDF)

From our lessons in NCERT Class 6 Maths to Class 7 Maths, we have learned a lot about our numbers. We have started our learning with counting the objects, that began with 1, 2, 3, …and called these the natural numbers. We then involved “0” with these numbers and named as the whole numbers. Later we also studied the integers which are just the negative inverse of the positive natural numbers. Now, in NCERT Class 7 Maths Chapter 8, we will study the Rational Numbers.

In this chapter of Class 7 NCERT Maths, we will study the concept of Rational Numbers along with their properties of addition, subtraction, multiplication, and division. We will cover the easy-to-understand notes of the chapter first and then provide solutions to the exercises of chapter 8, class 7 Maths. Let us now have a look at the NCERT Class 7 Maths Chapter 8 Rational Numbers Notes and Solutions (PDF).

Download NCERT Class 7 Maths Chapter 8 – Rational Numbers Notes and Solutions PDF

NCERT Class 7 Maths Chapter 8 Notes – PDF Available

Check the topic-wise notes for NCERT Maths Class 7 – Chapter 8 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the e𝑥am hall.

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Topic 1: 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 ≠ 0. The rational numbers include integers and fractions.

1. Equivalent Rational Numbers: Such rational numbers that are equal to each other are said to be equivalent to each other. For example,

Thus we must note that 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. This is exactly like obtaining equivalent fractions.

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Topic 2: Positive and Negative Rational Numbers

1. Positive Rational Numbers: The rational number (p/q) in which both numerator and denominator are positive. For example, ⅔, ¾. ⅘ and so on.
2. Negative Rational Numbers: The rational numbers in which either the numerator or the denominator is negative are called negative rational numbers.

Note:-

• The number 0 is neither a positive nor a negative rational number.
• There is an unlimited number of rational numbers between two rational numbers.

Topic 3: Rational Number in Standard Form

A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

• How to convert a rational number into its standard form? To reduce the rational number to its standard form, we divide its numerator and denominator by their HCF ignoring the negative sign, if any (The reason for ignoring the negative sign will be studied in higher classes).

If there is a negative sign in the denominator, divide by ‘– HCF’.

Topic 4: Addition of Rational Numbers

1. While adding rational numbers with the same denominators, we add the numerators keeping the denominators the same.
2. Two rational numbers with different denominators are added by first taking the LCM of the two denominators and then converting both the rational numbers to their equivalent forms having the LCM as the denominator.

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Topic 5: Subtraction of Rational Numbers

While subtracting two rational numbers, we add the additive inverse of the rational number to be subtracted to the other rational number

Topic 6: Multiplication of Rational Numbers

To multiply two rational numbers, we multiply their numerators and denominators separately and write the product as (product of numerators/product of denominators).

Topic 6: Division of Rational Numbers

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

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Download NCERT Class 7 Maths Chapter 8 – Rational Numbers Notes and Solutions PDF

NCERT Solutions of Class 7 Maths Chapter 8: Rational Numbers -Free PDF Available!

Below we have provided solutions for NCERT Class 7 Maths Chapter 8, Rational Numbers. Go through for answers to some important questions.

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E𝑥ercise 8.1 Solutions

Q 1. List 5 rational numbers between -1 and 0.

Solutions. We know that there is an unlimited number of rational numbers between two rational numbers. So, the 5 rational numbers between -1 and 0 are -⅔, -¾, -⅘, -⅚, and -6/7. All these rational numbers are greater than -1 but are lesser than 0.

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Q 2. Write four more rational numbers in the following pattern:

Solutions. From the series of rational numbers given above, we know that the numbers in the numerators are a multiple of 3 and the numbers in the denominators are a multiple of 5.

So, the next four rational numbers in this series would be:

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Q 3. Give four rational numbers equivalent to -2/7.

Solutions. We can obtain equivalent rational numbers to the given one by multiplying it with non-zero numbers. So, the four rational numbers equivalent to -2/7 are:

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E𝑥ercise 8.2 Solutions

Q 1. Find the sum of the following:

Solutions. The solutions for each part are given below.

1. Since the denominator of each rational number is the same, the numerators will be directly added (along with their signs) as:
1. Now, in this case, the denominators are not the same. So, here we will take the LCM of the denominators of both the rational numbers.

The LCM of 19 and 57 is 57. So, the addition result of the given rational numbers will be:

FAQs

Q.1. What are Rational Numbers?

Ans: 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 ≠ 0. The rational numbers include integers and fractions.

Q.2. What are positive and negative rational numbers?

Ans: The rational number (p/q) in which both numerator and denominator are positive. For example, ⅔, ¾. ⅘ and so on.

Q.3. What is the standard form of the rational numbers?

Ans: A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

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This was all about NCERT Class 7 Maths Chapter 8, Rational Numbers in which we studied the rational numbers. Download the NCERT Class 7 Maths Chapter 8 Notes and Solutions PDF to ace your e𝑥am preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.