NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Exercise 1.2

Exercise 1.2 of Class 8 Maths Chapter 1 teaches the basic properties of rational numbers. The exercise focuses on learning how the operations of addition and multiplication interact with rational numbers. These concepts are valid for getting a good score in exams and they also lay the foundation for mathematics in higher education.

This NCERT Solutions in this exercise is aligned with the latest NCERT syllabus prescribed by CBSE. The solutions are provided in a step by step manner for better conceptual understanding. Regular practice of these solutions makes you better at solving rational number problems and understanding number systems better. 

1.0Download NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Exercise 1.2: Free PDF

Exercise 1.2 shows the rules that rational numbers follow when we add or multiply them. The free PDF of NCERT Solutions for Class 8 Maths Chapter 1 is available for download below:

2.0Key Concepts in Exercise 1.2 of Class 8 Maths Chapter 1

This exercise mainly explains the properties that rational numbers follow when used in operations. Some of the key concepts covered in this chapter are:

• Closure property of rational numbers under addition and multiplication
• Commutative property for addition and multiplication
• Associative property of rational numbers
• Existence of additive and multiplicative identities
• Use of examples to test these properties
• Simple proofs using number operations

3.0NCERT Class 8 Maths Chapter 1: Other Exercises

4.0NCERT Class 8 Maths Chapter 1 Exercise 1.2: Detailed Solutions

• Represent these numbers on the number line. (i) $\frac{7}{4}$ (ii) $\frac{-5}{6}$ Sol. (i) For $7/4$, we make 7 markings of distance 1 / 4 each on the right of zero and starting from 0 . The seventh marking is 7/4.
  
  The point $P$ represents the rational number $\frac{7}{4}$. (ii) For $\frac{-5}{6}$, we make 5 markings of distance $\frac{1}{6}$ each on the left of zero and starting from 0 . The fifth marking is $\frac{-5}{6}$. The point $P$ represents the rational number $\frac{-5}{6}$.
  
• Represent $\frac{-2}{11},\frac{-5}{11},\frac{-9}{11}$ on the number line. Sol. For, $\frac{-2}{11},\frac{-5}{11},\frac{-9}{11}$ we make 11 markings of distance $\frac{1}{11}$ each on the left of zero and starting from 0 . The second marking is $\frac{-2}{11}$. The point B represents the rational number $\frac{-2}{11}$.
  
  The fifth marking is $\frac{-5}{11}$. The point E represents the rational number $\frac{-5}{11}$. The ninth marking is $\frac{-9}{11}$. The point I represents the rational number $\frac{-9}{11}$.
• Write five rational numbers, which are smaller than 2. Sol. Five rational numbers less than 2 may be taken $1,\frac{1}{2},0,-1,-\frac{1}{2}$ There can be many more such rational numbers.
• Find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$. Sol. Converting the given rational numbers with the same denominators. $\frac{-2}{5}=\frac{-2\times 4}{5\times 4}=\frac{-8}{20}$ and, $\frac{1}{2}=\frac{1\times 10}{2\times 10}=\frac{10}{20}$ We know that $-8<-7<-6\dots <10$ $\Rightarrow \frac{-8}{20}<\frac{-7}{20}<\frac{-6}{20}<\dots <\frac{10}{20}$ Thus, we have the following ten rational number between $\frac{-2}{5}$ and $\frac{1}{2}$ : $\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0,\frac{1}{20}\text{ and }\frac{2}{20}$
• Find five rational numbers between (i) $\frac{2}{3}$ and $\frac{4}{5}$ (ii) $\frac{-3}{2}$ and $\frac{5}{3}$ (iii) $\frac{1}{4}$ and $\frac{1}{2}$ Sol. (i) Converting the given rational numbers with the same denominators $\frac{2}{3}=\frac{2\times 5}{3\times 5}=\frac{10}{15}$ and, $\frac{4}{5}=\frac{4\times 3}{5\times 3}=\frac{12}{15}$ also, $\frac{2}{3}=\frac{10}{15}=\frac{10\times 4}{15\times 4}=\frac{40}{60}$ and, $\frac{4}{5}=\frac{12}{15}=\frac{12\times 4}{15\times 4}=\frac{48}{60}$ We know that $40<41<42<43<44<45<46<47<48$ $\Rightarrow \frac{40}{60}<\frac{41}{60}<\frac{42}{60}<\dots <\frac{47}{60}<\frac{48}{60}$ Thus, we have the following five rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ $\frac{41}{60},\frac{42}{60},\frac{43}{60},\frac{44}{60}$ and $\frac{45}{60}$. Note: We may take any five numbers given above from $\frac{41}{60}$ to $\frac{47}{60}$. (ii) Converting the given rational numbers with the same denominators $\frac{-3}{2}=\frac{-3\times 3}{2\times 3}=\frac{-9}{6}$ and, $\frac{5}{3}=\frac{5\times 2}{3\times 2}=\frac{10}{6}$ We know that $-9<-8<-7<-6<...<0<1<2<$.... $<8<9<10$ $\Rightarrow \frac{-9}{6}<\frac{-8}{6}<\frac{-7}{6}<\frac{-6}{6}<\dots <\frac{0}{6}<\frac{1}{6}<\frac{2}{6}<\dots$ $<\frac{8}{6}<\frac{9}{6}<\frac{10}{6}$. Thus, we have the following five rational numbers between $\frac{-3}{2}$ and $\frac{5}{3}$ : $\frac{-8}{6},\frac{-7}{6},\frac{0}{6},\frac{1}{6}$ and $\frac{2}{6}$ (iii) Converting the given rational numbers with the same denominators $\frac{1}{4}=\frac{1}{4}\times \frac{6}{6}=\frac{6}{24}$ and $\frac{1}{2}=\frac{1}{2}\times \frac{12}{12}=\frac{12}{24}$ We know that $6<7<8<9<10<11<12$ Thus, we have the following five rational numbers between $\frac{6}{24}$ and $\frac{12}{24}$. $\frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24},\frac{11}{24}$.
• Write five rational numbers greater than $-2$. Sol. Five rational numbers greater than - 2 may be taken as $-\frac{3}{2},-1,\frac{-1}{2},0,\frac{1}{2}$. There can be many more such rational numbers.
• Find ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$. Sol. Converting the given rational numbers with the same denominators $\frac{3}{5}=\frac{3\times 20}{5\times 20}=\frac{60}{100}\text{ and }\frac{3}{4}=\frac{3\times 25}{4\times 25}=\frac{75}{100}$ We know that $60<61<62<63<$... $<72<73<74<75$ $\Rightarrow \frac{60}{100}<\frac{61}{100}<\frac{62}{100}<\frac{63}{100}<\dots$ $<\frac{72}{100}<\frac{73}{100}<\frac{74}{100}<\frac{75}{100}$. Thus, we have the following ten rational numbers between $\frac{3}{5}$ and $\frac{3}{4}$; $\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100}$, $\frac{69}{100}$ and $\frac{70}{100}$.

5.0Key Features and Benefits of Class 8 Maths Chapter 1 Exercise 1.2

• This exercise describes the main properties of rational numbers in a straightforward way.
• The solutions use simple examples to demonstrate how the properties work in real-world problems.
• They are also aligned with the revised NCERT syllabus currently used in CBSE schools.
• Regular practice enhances accuracy and builds confidence when solving rational number problems.
• Provides a solid foundation for competitive exams like Maths Olympiads and NTSE.
• Solving these can also improve logical thinking and problem solving skills.