NCERT Solutions for Class 8 Maths Chapter 1 - Exercise

The first chapter of the class 8 math syllabus is on Rational Numbers. It is a significant chapter in math that is covered in class 8.  NCERT Class 8 Math Chapter 1 Rational Numbers has 6 major properties that are dealt with in the solutions. The following is a list of the 6 important properties that come under the chapter Rational Numbers. 

• The Closure Property.

• The Commutative Property.

• The Associative Property.

• The Distributive Property.

• The Identity Property.

• The Inverse Property.

Importance of Rational Numbers

Rational numbers help describe various measures and quantities that integers alone cannot describe fully. Rational numbers are mostly used to measure quantities like mass, length, time, and so on. 

Access NCERT Solutions for class 8 Math  Chapter 1 – Rational Numbers

Exercise 1.2

1. Represent these numbers on the number line.

1. $\dfrac{7}{4}$

Ans: Since, $\dfrac{7}{4}$ is approximately equal to $1.75$.

Therefore, $\dfrac{7}{4}$ can be represented on the number line as follows:

2. $-\dfrac{5}{6}$

Ans: Since, $-\dfrac{5}{6}$ is approximately equal to $-0.833$.

Thus, $-\dfrac{5}{6}$ can be represented on the number line as follows:

2.Represent \[\text{-}\dfrac{\text{2}}{\text{11}}\text{,-}\dfrac{\text{5}}{\text{11}}\text{,-}\dfrac{\text{9}}{\text{11}}\] on the number line.

Ans: We can divide the interval between $\text{0}$ and $\text{-1}$ in $\text{11}$ parts to get.

\[\text{-}\dfrac{\text{2}}{\text{11}}\text{,-}\dfrac{\text{5}}{\text{11}}\text{,-}\dfrac{\text{9}}{\text{11}}\] on number line.

Thus, \[\text{-}\dfrac{\text{2}}{\text{11}}\text{,-}\dfrac{\text{5}}{\text{11}}\text{,-}\dfrac{\text{9}}{\text{11}}\] can be represented on the number line as follows:

3. Write five rational numbers which are smaller than \[\text{2}\].

Ans: Since, we have to write five rational numbers which are less than \[\text{2}\] .

Therefore, we can multiply and divide \[\text{2}\] by \[7\].

Now, \[\text{2}\] becomes \[\dfrac{\text{14}}{\text{7}}\].

Thus, five rational numbers which are smaller than \[\text{2}\] are given as:

\[\dfrac{\text{13}}{\text{7}}\text{,}\dfrac{\text{12}}{\text{7}}\text{,}\dfrac{\text{11}}{\text{7}}\text{,}\dfrac{\text{10}}{\text{7}}\text{,}\dfrac{\text{9}}{\text{7}}\].

4. Find ten rational numbers between \[\dfrac{\text{-2}}{\text{5}}\] and \[\dfrac{\text{1}}{\text{2}}\].

Ans: We can make denominator of  \[\dfrac{\text{-2}}{\text{5}}\] and \[\dfrac{\text{1}}{\text{2}}\] same.

Therefore, multiplying and dividing \[\dfrac{\text{-2}}{\text{5}}\] by $\text{4}$ and \[\dfrac{\text{1}}{\text{2}}\] by $\text{10}$.

Thus, now \[\dfrac{\text{-2}}{\text{5}}\] becomes \[\dfrac{\text{-8}}{\text{20}}\]  and  \[\dfrac{\text{1}}{\text{2}}\] becomes \[\dfrac{\text{10}}{\text{20}}\] .

Hence, ten rational numbers between \[\dfrac{\text{-2}}{\text{5}}\] and \[\dfrac{\text{1}}{\text{2}}\] are:

\[\text{-}\dfrac{\text{7}}{\text{20}}\text{,-}\dfrac{\text{6}}{\text{20}}\text{,-}\dfrac{\text{5}}{\text{20}}\text{,-}\dfrac{\text{4}}{\text{20}}\text{,-}\dfrac{\text{3}}{\text{20}}\text{,-}\dfrac{\text{2}}{\text{20}}\text{,-}\dfrac{\text{1}}{\text{20}}\text{,0,}\dfrac{\text{1}}{\text{20}}\text{,}\dfrac{\text{2}}{\text{20}}\].

5. Find five rational numbers between-

1. \[\dfrac{\text{2}}{\text{3}}\] and \[\dfrac{\text{4}}{\text{5}}\]

Ans: We can make denominator of  \[\dfrac{\text{2}}{\text{3}}\] and \[\dfrac{\text{4}}{\text{5}}\] same.

Therefore, multiplying and dividing \[\dfrac{\text{2}}{\text{3}}\] by $\text{15}$ and \[\dfrac{\text{4}}{\text{5}}\] by $9$.

Thus, now \[\dfrac{\text{2}}{\text{3}}\] becomes \[\dfrac{\text{30}}{\text{45}}\]  and  \[\dfrac{\text{4}}{\text{5}}\] becomes \[\dfrac{\text{36}}{\text{45}}\] .

Hence, ten rational numbers between \[\dfrac{\text{2}}{\text{3}}\] and \[\dfrac{\text{4}}{\text{5}}\] are:

\[\dfrac{\text{31}}{\text{45}}\text{,}\dfrac{\text{32}}{\text{45}}\text{,}\dfrac{\text{33}}{\text{45}}\text{,}\dfrac{\text{34}}{\text{45}}\text{,}\dfrac{\text{35}}{\text{45}}\].

2. \[\dfrac{\text{-3}}{\text{2}}\] and \[\dfrac{\text{5}}{\text{3}}\].

Ans: We can make denominator of  \[\text{-}\dfrac{\text{3}}{\text{2}}\] and \[\dfrac{\text{5}}{\text{3}}\] same.

Therefore, multiplying and dividing \[\text{-}\dfrac{\text{3}}{\text{2}}\] by $3$ and \[\dfrac{\text{5}}{\text{3}}\] by $2$.

Thus, now \[\text{-}\dfrac{\text{3}}{\text{2}}\] becomes \[\text{-}\dfrac{\text{9}}{\text{6}}\]  and  \[\dfrac{\text{5}}{\text{3}}\] becomes \[\dfrac{\text{10}}{\text{6}}\] .

Hence, ten rational numbers between \[\text{-}\dfrac{\text{3}}{\text{2}}\] and \[\dfrac{\text{5}}{\text{3}}\] are:

\[\text{-}\dfrac{\text{8}}{\text{6}}\text{,-}\dfrac{\text{7}}{\text{6}}\text{,-1,-}\dfrac{\text{5}}{\text{6}}\text{,-}\dfrac{\text{4}}{\text{6}}\].

3. \[\dfrac{\text{1}}{\text{4}}\] and \[\dfrac{\text{1}}{\text{2}}\]

Ans: We can make denominator of  \[\dfrac{\text{1}}{\text{4}}\] and \[\dfrac{\text{1}}{\text{2}}\] same.

Therefore, multiplying and dividing \[\dfrac{\text{1}}{\text{4}}\] by $8$ and \[\dfrac{\text{1}}{\text{2}}\] by $16$.

Thus, now \[\dfrac{\text{1}}{\text{4}}\] becomes \[\dfrac{\text{8}}{\text{32}}\]  and  \[\dfrac{\text{1}}{\text{2}}\] becomes \[\dfrac{\text{16}}{\text{32}}\] .

Hence, ten rational numbers between \[\dfrac{\text{1}}{\text{4}}\] and \[\dfrac{\text{1}}{\text{2}}\] are:

\[\dfrac{\text{9}}{\text{32}}\text{,}\dfrac{\text{10}}{\text{32}}\text{,}\dfrac{\text{11}}{\text{32}}\text{,}\dfrac{\text{12}}{\text{32}}\text{,}\dfrac{\text{13}}{\text{32}}\].

6. Write five rational numbers greater than \[\text{-2}\].

Ans:

Since, we have to write five rational numbers which are greater than \[\text{-2}\].

Therefore, we can multiply and divide \[\text{-2}\] by \[7\].

Now, \[\text{-2}\] becomes \[\text{-}\dfrac{\text{14}}{\text{7}}\].

Thus, five rational numbers greater than \[\text{-2}\] are given as:

\[\text{-}\dfrac{\text{13}}{\text{7}}\text{,-}\dfrac{\text{12}}{\text{7}}\text{,-}\dfrac{\text{11}}{\text{7}}\text{,-}\dfrac{\text{10}}{\text{7}}\text{,-}\dfrac{\text{9}}{\text{7}}\].

7. Find ten rational numbers between \[\dfrac{\text{3}}{\text{5}}\] and \[\dfrac{\text{3}}{\text{4}}\].

Ans: We can make denominator of  \[\dfrac{\text{3}}{\text{5}}\] and \[\dfrac{\text{3}}{\text{4}}\] same.

Therefore, multiplying and dividing \[\dfrac{\text{3}}{\text{5}}\] by $16$ and \[\dfrac{\text{3}}{\text{4}}\] by $20$.

Thus, now \[\dfrac{\text{3}}{\text{5}}\] becomes \[\dfrac{\text{48}}{\text{80}}\]  and  \[\dfrac{\text{3}}{\text{4}}\] becomes \[\dfrac{\text{60}}{\text{80}}\] .

Hence, ten rational numbers between \[\dfrac{\text{3}}{\text{5}}\] and \[\dfrac{\text{3}}{\text{4}}\] are:

\[\dfrac{\text{49}}{\text{80}}\text{,}\dfrac{\text{50}}{\text{80}}\text{,}\dfrac{\text{51}}{\text{80}}\text{,}\dfrac{\text{52}}{\text{80}}\text{,}\dfrac{\text{53}}{\text{80}}\text{,}\dfrac{\text{54}}{\text{80}}\text{,}\dfrac{\text{55}}{\text{80}}\text{,}\dfrac{\text{56}}{\text{80}}\text{,}\dfrac{\text{57}}{\text{80}}\text{,}\dfrac{\text{58}}{\text{80}}\].

What do you learn from Chapter 1 Rational Numbers Exercise 1.2?

• Summary 

Rational numbers are indeed an important part of the CBSE Class 8 Maths curriculum. To be precise, in the problems associated with Class 8 Chapter 1, ex 1.2 you will have to deal with the properties of rational numbers. CBSE Class 8 Math Chapter 1 exercise 1.2 teaches students about the closure property, commutative property, associative and distributive property of rational numbers.

• What Kind of Questions Can You Expect?

For those familiar with integers and fractions, rational numbers may seem relatively easy. However, once you delve deep into the fundamental theorems and concepts, the complexity of the problems in the exercise becomes obvious; and, this is where Class 8 Maths NCERT Solutions Chapter 1 exercise 1.2 can be helpful. To ensure a clear understanding of these properties, and translate your understanding into problem-solving skills, you can seek assistance from Vedantu’s free PDF download of Class 8 Maths exercise 1.2 solutions.

Class 8 Math Chapter 1 Exercise 1.2 Solutions

NCERT Exercise 1.2 of Class 8 Math Chapter 1, introduces us to the primary problem patterns you will encounter from the chapter on rational numbers. Finding solutions to all problems in exercise 1.2 Class 8 Math, is easier said than done, on your own. So, if you wish to strengthen your foundation in solving problems involving rational numbers, visit Vedantu’s website to download the free PDF of NCERT Maths Class 8 exercise 1.2.

Download NCERT Math class 8 to help you to revise the complete syllabus and score more marks in your examinations.

NCERT Solutions for Class 8 Math Chapter 1 Other Exercises

Along with this, students can also view additional study materials provided by Vedantu, for Class 8 Maths

• Revision Notes for Class 8 Maths

• CBSE Class 8 Math Syllabus

Benefits of Vedantu NCERT Math Class 8 Chapter 1 Exercise 1.2?

You will find the answer to a lot of doubts you face in the math NCERT solutions Class 8 chapter 1 exercise 1.2. NCERT Class 8 Math, ex. 1.2. require you to find given rational numbers on a number line, find a sequence of rational numbers smaller than the given one, find rational number sequences occurring between two given rational numbers, and the likes. To guarantee full score when you attempt these in your Class 8 Math paper, you can refer to the Vedantu Class 8 Math Chapter 1.2 PDF solutions. 

The PDF download is portable and is carried anywhere and perused for reference. The simplistic breakdown of the solution into easy-to-grasp steps, by Vedantu’s tutors, helps students clarify doubts easily. Conquer class 8 Math chapter 1 exercise 1.2, with Vedantu, today!