case study questions class 8 maths chapter 2 pdf

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CBSE Class 8th Maths Value Based Questions PDF Download

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CBSE Class 8th Maths Value Based Questions are the easiest questions which you see in your question paper and the scoring one all student who attempt it surely get they are just little bit difficult and examine your basic knowledge regarding the particular chapter. Maths Value Based Questions for Class 8th are available here at Free of cost. These questions are expected to be asked in the Class 8th board examination. These Maths Value Based Questions are from complete CBSE Syllabus.

CBSE Class 8th Maths Value Based Questions

Most of these Maths Value Based Questions are quite easy and students need only a basic knowledge of the chapter to answer these questions. Download CBSE Maths Value Based Questions for board examinations. These Maths Value Based Questions are prepared by Directorate of Education, Delhi.

CBSE Maths Value Based Questions Class 8th PDF

The purpose of the Maths Value Based Questions is to make students aware of how basic values are needed in the analysis of different situations and how students require to recognize those values in their daily lives. Some questions are subject related. But even if they are not, that one-minute awareness of what we write about value without any specific preparation is a good step indeed.

CBSE Maths Value Based Questions for Class 8th download here in PDF format. The most CBSE Maths Value Based Questions for annual examination are given here for free of cost. The additional questions for practice the Class 8th exam are collected from various sources. It covers questions asked in previous year examinations.

CBSE Maths Value Based Questions for Class 8th Free PDF

Class 8th books have many questions. These questions are regularly asked in exams in one or other way. Practising such most CBSE Maths Value Based Questions certainly help students to obtain good marks in the examinations. 

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NCERT Solutions for Class 8 Maths Free PDF Download

Ncert solutio ns for class 8 maths.

NCERT Solutions for Class 8 Maths will help you to ace the unsolved problems in the maths book prescribed by the CBSE. NCERT Solutions for Class 8 breaks down the solutions into detailed steps to increase your score in exams.

NCERT Solutions are prepared by our team of highly professional, qualified and experienced faculties. These NCERT Solutions for Class 8 Maths helps you to quickly grasp all the concepts and formulas of maths. In case you have a doubt while you are studying NCERT Solutions for Class 8 Maths which we are providing, for this, we have a team of teachers who are just a click away to solve your doubt any time.

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Download NCERT Solutions for Class 8 here.

NCERT Solutions for Class 8 Maths Chapter-wise

• Chapter 1- Rational Numbers
• Chapter 2 – Linear Equations in One Variable
• Chapter 3 – Understanding Quadrilaterals
• Chapter 4 – Practical Geometry
• Chapter 5 – Data Handling
• Chapter 6 – Square and Square Roots
• Chapter 7 – Cube and Cube Roots
• Chapter 8 – Comparing Quantities
• Chapter 9 – Algebraic Expressions and Identities
• Chapter 10 – Visualising Solid Shapes
• Chapter 11- Mensuration
• Chapter 12 – Exponents and Powers
• Chapter 13 – Direct and Inverse Proportions
• Chapter 14 – Factorisation
• Chapter 15 – Introduction to Graphs
• Chapter 16 – Playing with Numbers

CBSE Class 8 Maths Chapter-wise NCERT Solutions

Ncert solutions for class 8 maths chapter 1 – rational numbers.

In this chapter will learn the properties of real numbers, rational numbers, representation of a rational number on number line, additive and multiplicative identity.

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable

In this chapter you will learn the concept of linear equation and methods to solve them, reducing equations to a simpler form and their applications.

NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals

In this chapter, you will learn the basics of a quadrilateral, polygon, kinds of quadrilateral and polygon, the measure of external angle of polygons.

NCERT Solutions for Class 8 Maths Chapter 4 – Practical Geometry

This chapter includes drawing 4 sides in a quadrilateral with 2 adjacent sides, 3 angles, and 1 diagonal area given.

NCERT Solutions for Class 8 Maths Chapter 5 – Data Handling

In this chapter you will learn to organize the data in a systematic method, represent the data in a pictograph, a bar graph, double bar graph, pie chart, and histogram.

NCERT Solutions for Class 8 Maths Chapter 6 – Square and Square Roots

In this chapter, you will learn about the squares of numbers and their properties, various patterns of squares, and square roots of numbers.

NCERT Solutions for Class 8 Maths Chapter 7 – Cube and Cube Roots

In this you will study about cubes of different numbers, cubes of numbers by adding consecutive odd numbers pattern, cube roots of a number, solving cube roots by prime factorization method.

NCERT Solutions for Class 8 Maths Chapter 8 – Comparing Quantities

In this chapter you will compare quantities, increase or decrease of percentage, discount, profit and loss, vat tax, sales tax, computing interest.

NCERT Solutions for Class 8 Maths Chapter 9 – Algebraic Expressions and Identities

In this chapter, you will learn about the algebraic expressions and their types, like and unlike terms, addition and subtraction, multiplication of algebraic expressions, standard identities and their implementation.

NCERT Solutions for Class 8 Maths Chapter 10 – Visualizing Solid Shapes

In this chapter, you will study the cubes, cuboids, cones, cylinders, spheres, hemispheres and their area, triangular pyramids, triangular and square base prisms, application of Euler’s formula.

NCERT Solutions for Class 8 Maths Chapter 11 – Mensuration

In this chapter, you will learn about the perimeter and areas of plane closed figure and surface area, the volume of a solid figure, transform the quantity into other units.

NCERT Solutions for Class 8 Maths Chapter 12 – Exponents and Powers

In this chapter you will study powers with negative exponents, laws of exponents, express the numbers in standard form and comparison of extremely large numbers.

NCERT Solutions for Class 8 Maths Chapter 13 – Direct and Inverse Proportions

In this chapter, you will solve the problems related to direct and inverse proportion and their identification based on relative increase or decrease of a quantity with respect to the first one.

NCERT Solutions for Class 8 Maths Chapter 14 – Factorization

In this chapter, you will learn methods of factorization, division of algebraic expression, error finding in algebraic equations.

NCERT Solutions for Class 8 Maths Chapter 15 – Introduction to Graphs

In this, you will study the representations of data by a bar graph, histogram, pie chart, line graph, and linear graph, application based on the graph using the dependent & independent variable.

NCERT Solutions for Class 8 Maths Chapter 16: Playing with Numbers

In this chapter, you will deal with numbers in a general form, puzzles related to numbers, divisibility tests.

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Solved Questions For You:

Question 1. For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag. (b) The height of competitors in an athletics meet. (c) The number of cassettes produced by  5  companies. (d) The number of passengers boarding trains from  7 : 0 0  a.m. to  7 : 0 0  p.m. at a station. Give reasons for each.

(a) We can’t use the histogram in this case because we cannot define the class intervals for this data.

(b) We can use histogram here because it will be easy to divide the data into class intervals.

(c) We do not have approximate data we won’t use a histogram. We do not know about the number of cassettes produced by companies.

Question 2. List the outcomes you can see in these experiments.

(a) Possible outcomes would be:  A , B , C , D

Question 3. When a die is thrown, list the outcomes of an event of getting

(i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than  5

Possible outcomes:  1 , 2 , 3 , 4 , 5 , 6 (i) (a) Prime numbers:  2 , 3 , 5 It represents the outcomes of Prime numbers (b) Not a prime number:  1 , 4 , 6 It represents the outcomes of not prime numbers. (ii) (a) A number greater than  5 : Only when  6  comes (b) Number not greater than  5 : Only when outcomes:  1 , 2 , 3 , 4  and  5

Question 4. A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey.

From this pie chart answer the following: (i) If  2 0  people liked classical music, how many young people were surveyed? (ii) Which type of music is liked by the maximum number of people? (iii) If a cassette company were to make  1 0 0 0  CDs, how many of each type would they make?

The light chart represents the maximum number as it is  4 0 % of the total.  ∴  Light music is liked by max. people.

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NCERT Solutions for Class 8

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Exponents and Powers Class 8 Questions

Exponents and powers class 8 questions are provided here with solutions and explanations, to help students understand the basic concepts of exponents and powers. These questions are designed as per the latest CBSE/ICSE curriculum guidelines for class 8. Practising these worksheets will clear their doubts and help them to solve higher-order thinking level questions asked in the examinations.

Also, Check

• Important 2 Marks Questions for CBSE 8th Maths
• Important 3 Marks Questions for CBSE 8th Maths
• Important 4 Marks Questions for CBSE 8th Maths

If x is added n times repeatedly, it simply implies n × x = nx, but if we multiply x, n times repeatedly it means x n . Thus, x n is an exponential form, any number written like this is called exponents. In x n , x is called the base of the exponent and n is called the power

Learn more about exponents and powers .

Exponents and Powers Class 8 Questions with Solutions

Below are the practice questions on exponents and powers for class 8 with detailed solutions.

Question 1: Simplify (27) 2/3 – (81) 1/2 .

(27) 2/3 – (81) 1/2 = (3 3 ) 2/3 – (9 2 ) 1/2

= 3 3 × ⅔ – 9 2 × ½

= 9 – 9 = 0

∴ (27) 2/3 – (81) 1/2 = 0.

Question 2: If 3 x – y = 27 and 3 x + y = 243, then what is the value of x and y?

Given, 3 x – y = 27 = 3 3 and 3 x + y = 243 = 3 5

Comparing the powers on both sides of the exponents, we get

⇒ x – y = 3 ….(i)

x + y = 5 ….(ii)

Adding equations (i) and (ii),

then y = 1.

Question 3: Simplify the following:

\(\begin{array}{l}\frac{3^{-5}\times 5^{-7}\times (-2)^{3}}{3^{4}\times 5^{-2}\times (-2)^{-3}}\end{array} \)

Using the laws of exponents,

\(\begin{array}{l}\frac{3^{-5}\times 5^{-7}\times (-2)^{3}}{3^{4}\times 5^{-2}\times (-2)^{-3}}=3^{(-5-4)}\times 5^{(-7+2)}\times (-2)^{(3+3)}\end{array} \)

= -2 6 /(3 9 × 5 5 ).

Question 4: Determine (8x) x if 9 x + 2 = 240 + 9 x .

9 x + 2 = 240 + 9 x

⇒ 9 x . 9 2 – 9 x = 240

⇒ 9 x (9 2 – 1) = 240

⇒ 9 x × (81 – 1) = 240

⇒ 9 x = 240/80 = 3

⇒ (3 2 ) x = 3

Comparing powers on both the sides,

2x = 1 ⇒ x = ½

∴ (8x) x = (8 × ½) ½ = 4 1/2 = 2.

• Ratio and Proportion
• Scientific Notation
• Algebraic Expressions
• Factorisation

Question 5: Simplify:

(i) 8x 5 y 7 / 12x 9 y 4

(ii) ( –5x 3 /2y –4 ) –3

(i)8x 5 y 7 / 12x 9 y 4 = ⅔ (x 5 – 9 y 7 – 4 ) = 2y 3 /3x 4 .

(ii) ( –5x 3 /2y –4 ) -3 = [( –5) – 3 × (x 3 ) – 3 ] / [2 –3 . (y –4 ) – 3 ]

= { –8 × x –9 }/{125 y 12 }

= –8/125x 9 y 12 .

Question 6: Given, 10 0.48 = x and 10 0.70 = y and x z = y 2 , then find the approximate value of z.

Given, x z = y 2 ⇒ (10 0.48 ) z = (10 0.70 ) 2

⇒ 10 0.48z = 10 1.40 ⇒ 0.48z = 1.40

⇒ z = 140/48 = 2.9 (approx.)

Question 7: If 5 3x + 2 = 25 × 5 (4x – 1) , then find the value of x.

We have, 5 3x + 2 = 25 × 5 (4x – 1)

⇒ 5 3x + 2 = 5 2 × 5 (4x – 1)

⇒ 5 3x + 2 = 5 (2 + 4x – 1)

⇒ 5 3x + 2 = 5 4x + 1

As the bases are equal, comparing powers on both side we get,

3x + 2 = 4x + 1

⇒ 4x – 3x = 2 – 1

Question 8: If 5 x = 3 y = 45 z , then prove that 1/z = 1/x + 2/y.

Given, 5 x = 3 y = 45 z

Then, 5 x = 45 z = (5 × 9) z

⇒ 5 x = 5 z × (3 2 ) z

⇒ 5 x = 5 z × 3 2z …(i)

Similarly, 3 y = 5 z × 3 2z …(ii)

Multiplying equation (i) and (ii), we get,

5 x .3 y = (5 z × 3 2z ) 2

⇒ 5 x .3 y = 5 2z . 3 4z

Comparing powers on both sides.

x = 2z and y = 4z

⇒ 2/x = 1/z and 4/y = z

Adding both the equations,

2/z = 2/x + 4/y

⇒ 1/z = 1/x + 2/y.

Question 9: Simplify:

\(\begin{array}{l}\frac{5(81)^{n+1}-3^{4n+5}}{3\times 3^{4n}+(81)^{n}}\end{array} \)

\(\begin{array}{l}\frac{5(81)^{n+1}-3^{4n+5}}{3\times 3^{4n}+(81)^{n}}=\frac{5\times (3^{4})^{n+1}-3^{4n+5}}{3^{1+4n}+(3^{4})^{n}}\end{array} \)

\(\begin{array}{l}=\frac{5.3^{4}-3^{5}}{3+1}=\frac{5\times 81 – 243}{(3+1)} \end{array} \) \(\begin{array}{l} =\frac{405-243}{4}\end{array} \)

Question 10: Evaluate: (21 2 – 15 2 ) 4/3

(21 2 – 15 2 ) 4/3 . = (441 – 225) 4/3 = (216) 4/3

= (∛216) 4 = 6 4 = 1296

Question 11: If (1331) – x = (225) y , where x and y are integers, then find the value of 3xy.

(1331) – x = (225) y

⇒ (11 3 ) –x = (15 2 ) y

⇒ 11 –3x = 15 2y

The above equation is true only for x = y = 0

∴ 3xy = 3 × 0 × 0 = 0.

Question 12: If (243) – x = (729) y = 3 3 , then find the value of 5x + 6y.

Now, (243) –x = 3 3

⇒ (3 5. ) –x = 3 3

Comparing the powers,

–5x = 3 ⇒ x = –⅗

Again, (729) y = 3 3.

⇒ (9 3 ) y = 3 3

⇒ (3 2 ) 3y = 3 3

⇒ 3 6y = 3 3

6y = 3 ⇒ y = ½

∴ 5x + 6y = 5 × ( –3/5) + 6 × ½

= –3 + 3 = 0

Question 13: If 2 = 10 m and 3 = 10 n , then find the value of 0.15.

0.15 = 1.5/10 = 3/(2 × 10) [as 1.5 = 3/2]

= 10 n /(10 m × 10)

= 10 n – m – 1

Question 14: Given, a = 2 x , b = 4 y , c = 8 z and ac = b 2 . Find the relation between x, y and z.

Given, ac = b 2

⇒ 2 x . 8 z = (4 y ) 2

⇒ 2 x . 2 3z = 2 4y

⇒ 2 x + 3z = 2 4y

Comparing the powers on both sides,

x + 3z = 4y.

Question 15: Find the value of [169 –3 / 196 – 8 ] 1/48 .

[169 –3 / 196 – 8 ] 1/48 = [(13 2 ) –3 / (14 2 ) – 8 ] 1/48

= [13 –3 × 2 / 14 – 8 × 2 ] 1/48

= [13 –6 / 14 – 16 ] 1/48

= [14 16 / 13 6 ] 1/48

= (14) 16 × 1/48 / 13 6 × 1/48

= 14 1/3 / 13 ⅛ .

Practice Worksheet

1. Simplify:

(i) [3 6 ÷ 3 4 ] 3

(ii) [(–2) 5 × (3) 5 ] 2 ÷ [12 × 3 7 ]

(iii) [(2 3 × 3 4 ) 3 × (–5) 3 ] ÷ [60 × (–2) 5 ]

2. If (1331) – x = (225) y , where x and y are integers, then find the value of 3 + xy.

3. If (243) – x = (729) y = 27, then find the value of 5x – 6y.

4. (4) ½ × (0.5) 4 is equal to _______.

5. If 2 x = 4 y = 8 z and xyz = 288, then prove that 1/2x + 1/4y + 1/8z = 11/96.

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• CBSE Maths Chapter 1 Rational Numbers Class 8 Extra Questions

Boost Your Performance in CBSE Mathematics Exam Chapter 1 with Class 8 Rational Numbers Important Questions PDF

Class 8 lays down the foundational concepts for mathematics. These concepts are important as many other concepts you will learn in higher classes are based upon these. Obtaining an in-depth understanding of these concepts then becomes fairly important. To help students in this, Rational Numbers Class 8 Extra Questions pdf is prepared by our subject experts at Vedantu. Vedantu is a platform that provides free NCERT Solution and other study materials for students.

These are prepared to keep in mind the examination pattern to help students in scoring well. Also, it provides accurate and reliable study material free of cost to all the students. The list of Class 8 Rational Numbers Important Questions is prepared carefully studying the previous year question paper and examination pattern. You can also download NCERT Maths Class 8 to help you to revise complete syllabus and score more marks in your examinations. Science students who are looking for NCERT Solutions for Class 8 Science will also find the solutions curated by our Master Teachers really helpful. Download important questions for class 8 Maths chapter 1 pdf here.

Chapter 1 Class 8 Rational Numbers Important Questions (Short and Long Answer Questions)

Very Short Answer Questions                                                                                   1 Marks

1. The additive inverse of   $\dfrac{3}{4}$ is ____ 

Ans: Additive inverse of any number is a number that can be added to a number to get $0$.

Hence, the additive inverse of $\dfrac{\text{3}}{\text{4}}$ is $\text{-}\dfrac{\text{3}}{\text{4}}$ .

2. Multiplicative inverse of is $\dfrac{1}{8}$ 

Ans: Multiplicative inverse of any number is a number that can be multiplied to a number to get $1$.

The multiplicative inverse of  $\dfrac{\text{p}}{\text{q}}$   is   $\dfrac{\text{q}}{\text{p}}$ .

Hence, the multiplicative inverse of  $\dfrac{1}{8}$  is  $8$.

3. A Rational number between $3$  and $4$  is ____ 

Ans: The rational number of any number can be calculated as;

$\dfrac{\left( \text{p+q} \right)}{\text{2}}$

Hence, the required rational number is;

$\dfrac{\left( 3+4 \right)}{2}=\dfrac{7}{2}$

Hence,  $\dfrac{7}{2}$ is a rational number between $3$  and $4$.

4. Reciprocal of $-2$  is ___ 

Ans: Reciprocal of any number will be the inverse of that number.

That is, the reciprocal of  $a$ is  $\dfrac{1}{a}$ .

Hence, the reciprocal of $-2$  is $-\dfrac{1}{2}$ .

5. Zero has ____ reciprocal 

Ans: The product of any number with $0$ will be   $0$  and hence, zero has no reciprocal.

6. Reciprocal of a negative number is _______ 

Ans: The product of any negative number with any number will be negative and hence, the reciprocal of a negative number will be negative .

7. Whole numbers start from______ 

Ans: The numbers that start from  $0$, are called whole numbers.

8. There are _____ rational numbers between $3$  and $4$. 

Ans: Infinite rational numbers are between $3$  and   $4$.

9. What are the multiplicative and additive identities of rational numbers?

Ans: 0 and 1 are the additive and multiplicative identity of rational numbers respectively.

10. Write the additive inverse of $\dfrac{19}{-6}$ and $-\dfrac{2}{3}$

Ans: $\dfrac{19}{-6}$ and $-\dfrac{2}{3}$ = $\dfrac{2}{3}$

11. Write the multiplicative inverse of $-\dfrac{13}{19}$ and $-7$

Ans: $-\dfrac{13}{19} = -\dfrac{19}{13}$ and $-7 = -\dfrac{1}{7}$

12. Mention a rational number which has no reciprocal.

Ans: A rational number “0” has no reciprocal or multiplicative inverse.

13. Mention any 4 rational numbers which are less than 5.

Ans: -1, 1, 2, and 3.

Short Answer Questions                                                                                             2 Marks 

14. Sum of two numbers is  $\dfrac{3}{4}$, one of the number is $\dfrac{1}{8}$ .Find the other one.

Ans: Let the other number be $\text{x}$.

The sum of $\text{x}$ and $\dfrac{1}{8}$ is $\dfrac{3}{4}$ .  Therefore, we have

\[\begin{align} & \Rightarrow \text{x}+\dfrac{1}{8}=\dfrac{3}{4} \\ & \Rightarrow \text{x}=\dfrac{3}{4}-\dfrac{1}{8} \\ & \Rightarrow \text{x}=\dfrac{\left( 3\times 2 \right)-1}{8} \\ \end{align}\] Since, $[\text{LCM}=8]$ Therefore, $\begin{align} & \Rightarrow \text{x}=\dfrac{6-1}{8} \\ & \Rightarrow \text{x}=\dfrac{5}{8} \\ \end{align}$

Therefore, the sum of  $\dfrac{5}{8}$ and $\dfrac{1}{8}$ is $\dfrac{3}{4}$.

15. Simplify $\left( \dfrac{-8}{13} \right)+\left( \dfrac{-3}{26} \right)$ 

Ans:  The given dfraction is;

$\dfrac{-8}{13}-\dfrac{3}{26}$

By simplifying above dfraction, we get

$\Rightarrow \dfrac{\left( -8\times 2 \right)-3}{26}$ 

Since, $[\text{LCM}=26]$

$\begin{align} & \Rightarrow \dfrac{-16-3}{26} \\ & \Rightarrow -\dfrac{19}{26} \\ \end{align}$

Therefore, $\left( \dfrac{-8}{13} \right)+\left( \dfrac{-3}{26} \right)=-\dfrac{19}{26}$ .

16. What number to be multiplied with $\dfrac{1}{4}$ so as to get the product as $-\dfrac{5}{16}$ 

Ans: Let the number be $\text{x}$ .

The product can be written as;

$\Rightarrow \dfrac{1}{4}\times \text{x}$ and,

Product of $\text{x}$ and  $\dfrac{1}{4}$ is $-\dfrac{5}{16}$ .

Therefore, we have

\[\begin{align} & \Rightarrow -\dfrac{5}{16}=\dfrac{1}{4}\times \text{x} \\ & \Rightarrow \text{x}=4\times \left( -\dfrac{5}{16} \right) \\ \end{align}\]

Therefore, we get

$\Rightarrow \text{x}=-\dfrac{5}{4}$

Hence, $-\dfrac{5}{4}$ is the number to be multiplied with $\dfrac{1}{4}$ so as to get the product as  $-\dfrac{5}{16}$.

17. Represent $-\dfrac{2}{7}$ on the number line.

Ans: $-\dfrac{2}{7}$ is a rational number.

$-\dfrac{2}{7}$ on a Number Line, can be represented as follows;

18. Divide $\dfrac{1}{2}$by $\left[ \dfrac{-1}{3}+\dfrac{2}{5} \right]$ 

Ans: The given fraction is;

$\left[ \dfrac{-1}{3}+\dfrac{2}{5} \right]$

By simplifying above fraction, we get

\[\begin{align} & \Rightarrow -\dfrac{1}{3}+\dfrac{2}{5} \\ & \Rightarrow \dfrac{\left( -1.5 \right)+\left( 2.3 \right)}{15} \\ \end{align}\]

Since, $[\text{LCM}=15]$ , therefore

\[\begin{align} & \Rightarrow \dfrac{-5+6}{15} \\ & \Rightarrow \dfrac{1}{15} \\ \end{align}\]

On dividing  $\dfrac{1}{2}$ by $\dfrac{1}{15}$ , we get

\[\begin{align} & \Rightarrow \dfrac{1}{2}\div \dfrac{1}{15} \\ & \Rightarrow \dfrac{1}{2}\times \dfrac{15}{1} \\ & \Rightarrow \dfrac{15}{2} \\ \end{align}\]

19. Find three rational number between $-4$and $4$ Represent them on line.

 Ans: The three rational numbers between $-4$  and $4$ are $-2,-1,1$ .

On a number line, the mentioned rational numbers are represented as follows:

20. Define by example of addition 

(a) Associative Property 

Ans: Associative Property can be stated as while addition or multiplication of any two grouped numbers, the interchange of those numbers won’t get affected on resultant addition or multiplication.

$\Rightarrow \text{a+b = b+a}$

The following example shows how the associative property gets used to solve it;

We can solve  $9+7$ by using Associative Property; we get

$\begin{align} & \Rightarrow \left( 7+9 \right)=\left( 9+7 \right) \\ & \Rightarrow 7+9=16 \\ \end{align}$ and

$\Rightarrow 9+7=16$ 

Therefore, according to the property, we can add or multiply regardless of how the numbers are grouped.

Short Answer Questions                                                                                             3 Marks

21. Simplify $\left[ \dfrac{6}{7}+\dfrac{3}{8}-\dfrac{1}{2} \right]\dfrac{4}{3}$    and find its reciprocal. 

Hence, by solving above dfraction, we get

$\Rightarrow \left[ \dfrac{6\times 8+3\times 7-1\times 28}{56} \right]\dfrac{4}{3}$ 

(Since the LCM of $7,8$ and $2$ is $56$ )

\[\begin{align} & \Rightarrow \left[ \dfrac{48+21-28}{56} \right]\times \dfrac{4}{3} \\ & \Rightarrow \dfrac{41}{56}\times \dfrac{4}{3} \\ & \Rightarrow \dfrac{41}{42} \\ \end{align}\]

Reciprocal of $\dfrac{41}{42}$ is 

$\Rightarrow \dfrac{1}{\dfrac{41}{42}}=1\times \dfrac{42}{41}$ 

\[\Rightarrow \dfrac{42}{41}\] 

Hence, reciprocal of  $\left[ \dfrac{6}{7}+\dfrac{3}{8}-\dfrac{1}{2} \right]\dfrac{4}{3}$ is \[\dfrac{42}{41}\] .

22. Find three Rational Number between $3$ and $4$. Represent them on the Number line.

Ans: $3$   can be written as 

\[\begin{align} & \Rightarrow 3\times \dfrac{10}{10} \\ & \Rightarrow \dfrac{30}{10} \\ \end{align}\] $4$ can be written as \[\begin{align} & \Rightarrow 4\times \dfrac{10}{10} \\ & \Rightarrow \dfrac{40}{10} \\ \end{align}\]

Hence, the three Rational Numbers are  $\dfrac{31}{10},\dfrac{32}{10},\dfrac{33}{10}$ .

$\dfrac{31}{10},\dfrac{32}{10},\dfrac{33}{10}$ these numbers can be represented on a Number line, are as follows;

23. Use appropriate property and find $-\dfrac{1}{6}\times \dfrac{4}{7}+\dfrac{1}{2}-\dfrac{3}{7}\times \dfrac{1}{6}$ 

Ans: The given dfraction is;

$-\dfrac{1}{6}\times \dfrac{4}{7}+\dfrac{1}{2}-\dfrac{3}{7}\times \dfrac{1}{6}$ 

By using associative property $\left( \text{a+b = b+a} \right)$ , we can be simplifying the above dfraction as follows;

\[\begin{align} & \Rightarrow -\dfrac{1}{6}\times \dfrac{4}{7}-\dfrac{3}{7}\times \dfrac{1}{6}+\dfrac{1}{2} \\ & \Rightarrow -\dfrac{1}{6}\times \dfrac{4}{7}-\dfrac{1}{6}\times \dfrac{3}{7}+\dfrac{1}{2} \\ & \Rightarrow -\dfrac{1}{6}\left[ \dfrac{4}{7}+\dfrac{3}{7} \right]+\dfrac{1}{2} \\ & \Rightarrow -\dfrac{1}{6}\times \dfrac{7}{7}+\dfrac{1}{2} \\ \end{align}\]

\[\begin{align} & \Rightarrow \dfrac{-1+3}{6} \\ & \Rightarrow \dfrac{2}{6} \\ & \Rightarrow \dfrac{1}{3} \\ \end{align}\]

Hence,  $-\dfrac{1}{6}\times \dfrac{4}{7}+\dfrac{1}{2}-\dfrac{3}{7}\times \dfrac{1}{6}=\dfrac{1}{3}$ .

24. Find the multiplicative inverse of following  

\[\dfrac{1}{6}\] 

Ans: Multiplicative inverse of any number is a number which can be multiplied to a number to get $1$ .

Hence, the multiplicative inverse of  $\dfrac{1}{6}$ is

\[\begin{align} & \Rightarrow \dfrac{1}{6}\times \text{x}=1 \\ & \Rightarrow \text{x}=6 \\ \end{align}\]

Therefore, the multiplicative inverse of  $\dfrac{1}{6}$ is $6$ .

$-\dfrac{3}{8}$  

Hence, the multiplicative inverse of  $\dfrac{-3}{8}$ is

$\begin{align} & \Rightarrow -\dfrac{3}{8}\times \text{x}=1 \\ & \Rightarrow \text{x}=-\dfrac{8}{3} \\ \end{align}$

Therefore, the multiplicative inverse of  $-\dfrac{3}{8}$  is $-\dfrac{8}{3}$.

$\dfrac{4}{19}$ 

Hence, the multiplicative inverse of  $\dfrac{4}{19}$ is

\[\begin{align} & \Rightarrow \dfrac{4}{19}\times \text{x}=1 \\ & \Rightarrow \text{x}=\dfrac{19}{4} \\ \end{align}\]

Therefore, the multiplicative inverse of  $\dfrac{4}{19}$  is $\dfrac{19}{4}$ .

Long Answer Questions                                                                       4 or 5 Marks

25. Find three Rational number between $\dfrac{3}{6}$ and $\dfrac{3}{4}$ 

Hence, the mean of two Rational numbers is a Rational number.

For given numbers;

$\dfrac{3}{6}=\dfrac{1}{2}$ and  $\dfrac{3}{4}$ 

Mean can be calculated as;

\[\begin{align} & \Rightarrow \dfrac{\dfrac{1}{2}+\dfrac{3}{4}}{2} \\ & \Rightarrow \dfrac{\dfrac{5}{4}}{2} \\ & \Rightarrow \dfrac{5}{8} \\ \end{align}\]

Since, $\dfrac{1}{2}<\dfrac{5}{8}<\dfrac{3}{4}$ ;

Now Mean of $\dfrac{1}{2}$ and $\dfrac{5}{8}$ 

\[\begin{align} & \Rightarrow \dfrac{\dfrac{1}{2}+\dfrac{5}{8}}{2} \\ & \Rightarrow \dfrac{\dfrac{9}{8}}{2} \\ & \Rightarrow \dfrac{9}{16} \\ \end{align}\]  

Since, \[\dfrac{1}{2}<\dfrac{9}{16}<\dfrac{5}{8}\]

Mean of $\dfrac{5}{8}$ and $\dfrac{3}{4}$ 

\[\begin{align} & \Rightarrow \dfrac{\dfrac{5}{8}+\dfrac{3}{4}}{2} \\ & \Rightarrow \dfrac{5+6}{8\times 2} \\ & \Rightarrow \dfrac{11}{16} \\ \end{align}\]

$\therefore \dfrac{5}{8}<\dfrac{11}{16}<\dfrac{3}{4}$

Hence, $\dfrac{9}{16},\dfrac{5}{8},\dfrac{11}{16}$ are the three rational numbers are between $\dfrac{3}{6}$ and $\dfrac{3}{4}$ .

26.  

Reciprocal of $-\dfrac{1}{2}$ 

Ans: Reciprocals of any number are going to be the inverse of that number.

Hence, the reciprocal of $-\dfrac{1}{2}$ is;

$\dfrac{1}{-\dfrac{1}{2}}=-2$

Therefore, Reciprocal of $-\dfrac{1}{2}$ is  $-2$ .

Additive inverse of $\dfrac{4}{9}$

Ans: Additive inverse of any number is a number which can be added to a number to get $0$ .

For the given number, we get

$\Rightarrow \dfrac{4}{9}+x=0$ 

$\Rightarrow $       $x=-\dfrac{4}{9}$

Therefore, an additive inverse of $\dfrac{4}{9}$ is $-\dfrac{4}{9}$ .

Multiplicative inverse of $\left[ \dfrac{1}{6}+\dfrac{4}{9} \right]\times \dfrac{4}{3}$ 

Ans:   Multiplicative inverse of any number is a number which can be multiplied to a number to get $1$ .

For given number, we get

  $\begin{align} & \Rightarrow \left[ \dfrac{1}{6}+\dfrac{4}{9} \right]\times \dfrac{4}{3} \\ & \Rightarrow \dfrac{(1\times 3+2\times 4)}{18}\times \dfrac{4}{3} \\ & \Rightarrow \dfrac{(3+8)}{18}\times \dfrac{4}{3} \\ \end{align}$ Therefore, $\begin{align} & \Rightarrow \dfrac{11}{18}\times \dfrac{4}{3} \\ & \Rightarrow \dfrac{22}{27} \\ \end{align}$

Hence, multiplicative inverse of $\left[ \dfrac{1}{6}+\dfrac{4}{9} \right]\times \dfrac{4}{3}$ is  $\dfrac{27}{22}$ .

27. Match the correct 

(a) Whole number

(b) Natural number 

(c) Integer 

(d) Rational Number

Ans:  The correct pairs are as follows;

(a) (ii) 

(b) (iii) 

(c) (i) 

(d) (iv) 

Whole numbers starts from $0$ .

Natural numbers are positive numbers and starts from $1$.

Integers will be positive, negative or $0$ numbers.

Rational numbers are the dfractional numbers.

Important Questions for Class 8 Rational Numbers Free PDF Download

The pdf contains the list of important questions for class 8 rational numbers. These questions are handpicked by our subject experts as these questions have the highest probability of coming in the examinations. Also, these questions are a great revision tool students can use. Solving these questions will help students in obtaining a better understanding of the type of questions asked in the examinations and how to format their answers correctly.

The chapter Rational Numbers is part of the syllabus for SA-I examinations which is for a total of 40 marks. The weightage of this chapter in the examination is 6 marks and a total of three questions are asked from this chapter- one very short answer type question, one short answer type question and one long answer type question.

Subtopics Covered in Detail in Chapter 1 - Rational Numbers

The subtopics that are covered in the detail in the chapter are:

Properties of Rational Numbers.

Closure property

Commutative property

Associativity property

The role of 0

• The role of 1
• Negative of a number

Distributivity of multiplication over addition for rational numbers

Representation of rational numbers on the Number Line.

Rational numbers between two rational numbers.

Rational numbers are of the type p/q where p and q are integers and q ≠ 0. Simply rational numbers can be defined as fractions that can be represented on the number line. Let us look at the concepts that govern rational numbers.

• Properties of Rational Numbers

The properties we are going to discuss are basic mathematical properties that are applicable on integers as well. Let us discuss the properties one by one:

Closure Property

The result of addition, multiplication and subtraction between any two rational numbers is also a rational number. This property is true for all mathematical properties except division because division by 0 is not defined. So divisions other than 0 are included in the closure property.

Commutative Property

The commutative property is true only for addition and multiplication of rational numbers. For any two rational numbers: Commutative property of addition:  $a + b = b + a$ $\dfrac{2}{5} + \dfrac{3}{5} = \dfrac{3}{5} + \dfrac{2}{5}$ Commutative property of multiplication: $a \times b = b \times a$ $\dfrac{3}{7} \times \dfrac{2}{7} = \dfrac{2}{7} \times \dfrac{3}{7}$

Associative Property

Rational numbers follow the property of association only for addition and multiplication. Let a, b and c be three rational numbers: Associative property for addition: $a + (b + c) = (a + b) + c$ Associative property for multiplication: $a \times (b \times c) = (a \times b) \times c$

Distributive Property

Rational numbers follow distributive property for addition and multiplication only. For any three rational numbers p,q and r. $p \times (q + r) = (p \times q) + (p \times r)$

Identity Property

The additive identity for any rational number is 0 and the multiplicative identity is 1.

Inverse Property

For a given rational number $\dfrac{x}{y}$, Additive inverse: $-\dfrac{x}{y}$ Multiplicative inverse: $\dfrac{y}{x}$

Representation of Rational Numbers on the Number Line

Rational numbers can also be represented on the number line just like other whole numbers or integers. 0 represents the origin. Negative rational numbers are present to the left and the positive rational numbers are located on the right side of the number line.

Representation of a rational number can be categorised into:

Proper Fraction: When the value of the numerator is less than the value of denominator, the fraction is called proper fraction and the value is less than one.

Improper Fraction: In case of the improper fraction, the value of the numerator is greater than the value of the denominator. First, we convert the given fraction into a mixed fraction to get a better picture of where the number exists on the number line.

To represent the rational number we divide the distance between the two whole numbers into the number of subunits denoted by the denominator.

The number can also be represented using the process of successive magnification where we convert the rational number into decimal expansion and represent the decimal places successively.

Rational Number Between Two Rational Numbers

The different methods using which rational numbers between two rational numbers can be found are:

The basic method that is used to find the number between two rational numbers is dividing their sum by 2.

A rational number between 5 and 6 can be calculated by $\dfrac{5 + 6}{2} = \dfrac{11}{2}$ $\dfrac{11}{2}$ is a rational number between 5 and 6.

For numbers with a common denominator, rational numbers between them can be easily found.

Rational numbers between $\dfrac{4}{9}$ and $\dfrac{8}{9} are $\dfrac{5}{9}$, $\dfrac{6}{9}$, $\dfrac{7}{9}$. Rational numbers between $-\dfrac{2}{3}$ and $\dfrac{2}{3}$ are: $-\dfrac{1}{3}, 0, \dfrac{1}{3}$

 In the case of different denominators, the first step is to make the denominators of the fraction similar before finding the rational numbers between them.

To find the rational number between $\dfrac{1}{5}$ and $\dfrac{14}{15}$, make the denominators of both the rational numbers equal. So, $\dfrac{1 \times 3}{5 \times 3} = \dfrac{3}{15}$ The rational numbers between them are $\dfrac{4}{15}, \dfrac{5}{15}, \dfrac{6}{15}, \dfrac{7}{15} …. \dfrac{12}{15}, \dfrac{13}{15}$ etc.

List of Important Class 8 Maths Rational Numbers Important Questions

The pdf class 8 maths chapter 1 important questions contains different types of questions that cover all the sub-topics of the entire chapter. Important questions from each topic are included in the pdf to give the students a clear and logical understanding of the chapter. Some of the important questions that are commonly asked in the examination from this chapter are:

• Find the rational number between $\dfrac{2}{3}$ and $\dfrac{4}{5}$.

Determine the rational numbers lying between $-\dfrac{1}{2}$ and $\dfrac{1}{2}$.

Simplify: $\dfrac{3}{4} + \dfrac{(-5)}{8}$.

Simplify: $-\dfrac{2}{3} - \dfrac{4}{5}$.

Solve: $\dfrac{3}{7} \times \dfrac{5}{6}$.

Solve: $-\dfrac{2}{5} \div \dfrac{3}{4}$.

Determine whether the following numbers are rational or irrational: $\sqrt{16}, \sqrt{5}, -3.25, 0.8888 …$

Find the rational number between 1.5 and 1.6.

Simplify: $-\dfrac{7}{9} + \dfrac{(-4)}{9} - \dfrac{1}{3}$.

Find the value of 'x' if $\dfrac{2}{3} \div x = \dfrac{4}{5}$.

Benefits of Class 8 Maths Rational Numbers Important Questions PDF

Rational numbers are a scoring chapter for students. If students prepare the questions from the pdf, they will be able to answer all the questions that are asked from the chapter. Students can be asked short answer type questions from the properties of rational numbers and long answer type questions from the representation of rational numbers on a number line or a rational number between rational numbers.

The benefits of the pdf containing important questions for class 8 maths chapter 1 are given below:

The pdf is prepared in accordance with the examination guidelines to help students to score well in the examinations.

The list of important questions is prepared by the subject experts who have years of experience in teaching.

The list is prepared after thorough research of previous year question papers and incorporating the revisions in the syllabus.

The pdf also contains solutions students can refer to in case of any doubts.

Practising questions from the pdf will improve the student’s understanding of the concepts and the examination pattern.

Chapterwise Important Questions for Class 8 Maths

Planning your schedule is extremely important if you want to score good marks in the upcoming examinations. To help you in this, the Class 8 Chapterwise Important Questions is given below.

Chapter 2 - Linear Equations in One Variable

Chapter 3 - Understanding Quadrilaterals

Chapter 4 - Practical Geometry

Chapter 5 - Data Handling

Chapter 6 - Squares and Square Roots

Chapter 7 - Cubes and Cube Roots

Chapter 8 - Comparing Quantities

Chapter 9 - Algebraic Expressions and Identities

Chapter 10 - Visualising Solid Shapes

Chapter 11 - Mensuration

Chapter 12 - Exponents and Powers

Chapter 13 - Direct and Inverse Proportions

Chapter 14 - Factorisation

Chapter 15 - Introduction to Graphs

Chapter 16 - Playing with Numbers

Mastering the concepts of rational numbers in CBSE Class 8 Maths is crucial for building a strong foundation in Mathematics. By practicing these important questions, you will gain confidence in solving problems related to rational numbers and improve your overall understanding of the chapter. It will also test your level of understanding of the chapter and highlight your weaker sections. Make sure to revise the concepts and formulas related to rational numbers and attempt additional practice questions to enhance your problem-solving skills further. Download the Class 8 Maths Rational Numbers Important Questions pdf and kickstart your preparations for the examination. Best of luck with your studies! 

FAQs on CBSE Maths Chapter 1 Rational Numbers Class 8 Extra Questions

1. How are Important Questions for CBSE Class 8 Maths Chapter 1 Rational Numbers useful for students?

Ans: Vedantu’s curated list of important questions for Class 8 Maths Chapter 1 Rational Numbers are extremely useful for students. The study materials provided for free by e-learning platforms like Vedantu provide extra questions for practice and help in scoring well in the subject. At Vedantu, these questions are solved by expert teachers. By referring to the important questions PDF for Class 8 Maths Chapter 1 Rational Numbers, students will be able to practice the chapter effectively. These questions also help in revision during exam time. In case students are not able to solve any of the questions of the chapter, they can refer to the solutions provided by Vedantu.

2. Where can I find Important Questions for Class 8 Maths Chapter 1 Rational Numbers?

Ans: Vedantu, a premier online learning platform, provides a well-prepared set of Important Questions for Class 8 Maths Chapter 1 as well as other chapters. Students can trust Vedantu for such a resource as it offers relevant questions that can be asked in the exams. Vedantu provides a free PDF of Important Questions for Class 8 Maths Chapter 1 Rational Numbers along with answers. These solutions are prepared by subject matter experts. These are extremely helpful in exam preparation and provide effective revision during exams.

3. Why must students solve important questions for Class 8 Maths Chapter 1 Rational Numbers during exam preparation?

Ans: Solving extra questions for Class 8 Maths CBSE chapters is really helpful during exams. The list of important questions for Class 8 Maths Chapter 1 Rational Numbers allows students to have a thorough practice. Students will also get familiar with all types of questions that can be asked in the exam. The important questions are picked by a panel of experts to cover all the important topics of the chapters. The questions are selected after referring to the exam pattern and observing the previous year question papers. Vedantu provides important questions free PDF for CBSE Maths examination of Class 8 Chapter 1 that can be utilized at the time of revision. These are really helpful in scoring well in the paper as it will boost students’ confidence while appearing for the board exam.

4. What are the contents of the Class 8 Maths Chapter 1 Rational Numbers NCERT textbook?

Following are the subtopics of Class 8 Maths Chapter 1 Rational Numbers:

• Introduction
• Commutativity
• Associativity
• The role of zero
• Representation of Rational Numbers on the Number Line.
• Rational Numbers between Two Rational Numbers.

5. Why are NCERT Solutions of Chapter 1 of Class 8 Maths Important?

Ans: NCERT Solutions for Chapter 1 of Class 8 Maths Chapter 1 is important because students can understand the concepts easily by solving the NCERT questions. NCERT questions are also important for their exams. Students will get questions based on a similar pattern in their final exams. NCERT Solutions given on Vedantu can help students to score good marks in maths. They can practice all NCERT questions for Chapter1 to score good marks in the math exam.

6. What are the Important Topics Covered in NCERT Solutions of Chapter 1 of Class 8 Maths?

Ans: Chapter 1 of Class 8 Maths is based on rational numbers. The chapter covers the different topics related to rational numbers such as properties of rational numbers, representing rational numbers on a number line, and how to find a rational number between two rational numbers. Students should practice all questions related to the NCERT Solutions for Chapter 1 of Class 8 Maths to understand all topics.

7. What are the properties of rational numbers? 

Properties of rational numbers includes commutative, associative, additive, and closure properties. Students must understand the different properties of rational numbers to get high marks in Class 8 Maths.

8. What do you mean by associative property of rational numbers according to Chapter 1 of Class 8 Maths?

Ans: The associative property of rational numbers means that if you add three or more rational numbers in any sequence the result will be the same. Rational numbers follow the associative property of addition and multiplication. According to the associative property of multiplication, if you multiply two or more rational numbers in any sequence the result will be the same. Thus, according to this property, students can add or multiply two or more rational numbers in any order to get the right result.

9. What is the closure property of rational numbers according to Chapter 1 of Class 8 Maths?

Ans: The closure property of rational numbers states that if you add, subtract, or multiply two rational numbers you will get a rational number. Rational numbers are not closed for division because if you divide a rational number by zero, you will not get a rational number. Thus, the closure property of rational numbers does not fit for division.

10. What are terminating and non-terminating decimals in rational numbers?

Terminating decimals are rational numbers with decimal representations that end, such as 0.25 or 0.5. Non-terminating decimals are rational numbers with decimal representations that continue indefinitely, either repeating or not repeating in a pattern.

11. Are there any specific techniques for solving problems involving rational numbers?

One useful technique is to convert mixed numbers to improper fractions before performing operations. Additionally, when adding or subtracting fractions, it's helpful to find a common denominator to make calculations easier.

12. What are some real-life examples of rational numbers?

Examples of rational numbers in real life include measurements such as distances, weights, and temperatures, as well as fractions representing parts of a whole, such as $\dfrac{3}{4}$ of a pizza or $\dfrac{2}{5}$ of a liter.

13. How can I practice Class 8 Maths Rational Numbers Important Questions?

You can practice extra questions on rational numbers by downloading additional worksheets or PDFs available online or using textbooks with supplementary exercises. These resources typically provide a variety of problems to reinforce your understanding of the topic.

14. What is the difference between rational and irrational numbers?

Rational numbers can be expressed as fractions, while irrational numbers cannot be expressed as fractions and have non-terminating and non-repeating decimal expansions. For example, $\sqrt{2}$ and $\pi$ are irrational numbers.

15. How can we perform operations on rational numbers?

Operations such as addition, subtraction, multiplication, and division can be performed on rational numbers using rules similar to those for integers. For division, we need to ensure that the divisor is not zero.

Chapterwise Important Questions for CBSE Class 8 Maths

Cbse study materials.