Important Questions for CBSE Class 7 Maths Chapter 8 - Rational Numbers

1 Mark Questions

1. Reduce \[\dfrac{55}{66}\] into the standard form.

Ans: We know that both $55$ and $66$ are divisible by $11$,

$\dfrac{55\div 11} {66\div 11} $

$ =\dfrac{5}{6} $

2. Fill in the blanks.

(a)$\dfrac{5}{6}.....\dfrac{9}{5}$

(b)$\dfrac{3}{4}......\dfrac{1}{2}$

(c)$\dfrac{2}{5}.......\dfrac{3}{4}$

Ans: (a)$\dfrac{5}{6}  < \dfrac{9}{5}$

(b)$\dfrac{3}{4} > \dfrac{1}{2}$

(c)$\dfrac{2}{5} < \dfrac{3}{4}$

3. Find the additive inverse of $-\dfrac{3}{8}$.

Ans: $\dfrac{3}{8}$

4. Reduce the following to the simplest form.

(a)$\dfrac{36}{54}$

(b)\[\dfrac{8}{72}\]

Ans: 

(a) HCF of $36$ and $54$ is $18$.

Dividing both numerator and denominator by $18$,

$\dfrac{36\div 18} {54\div 18} $

$ =\dfrac{2}{3} $

(b) HCF of $8$ and $72$ is $8$.

Dividing both numerator and denominator by $8$,

$\dfrac{8\div 8} {72\div 8} $

$ =\dfrac{1}{9} $ 

5. Write four more numbers in the following pattern $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$,….

Ans: 

$ -\dfrac{1}{2}\times \dfrac{3}{3}=-\dfrac{3}{6} $

$ -\dfrac{1}{2}\times \dfrac{4}{4}=-\dfrac{4}{8} $ 

$ -\dfrac{1}{3}\times \dfrac{3}{3}=-\dfrac{3}{9}  $  

$ -\dfrac{1}{3}\times \dfrac{4}{4}=-\dfrac{4}{12}  $  

Therefore, $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$, $-\dfrac{3}{6}$, $-\dfrac{4}{8}$, $-\dfrac{3}{9}$, $-\dfrac{4}{12}$

6. Do $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ represent the same number?

Ans: $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ 

$-\dfrac{4}{9}=-\dfrac{4\times 4}{9\times 4}=-\dfrac{16}{36}$

Or $-\dfrac{16}{36}=-\dfrac{16\div 4}{36\div 4}=-\dfrac{4}{9}$

Hence, both represent the same number.

7. List five rational numbers between $-4$ and $-3$.

Ans: 

$-4\times \dfrac{6}{6}=\dfrac{-24}{6}$

$-3\times \dfrac{6}{6}=\dfrac{-18}{6}$

The rational numbers are

$-\dfrac{23}{6},-\dfrac{22}{6},-\dfrac{21}{6},-\dfrac{20}{6},-\dfrac{19}{6}$

8. Give four equivalent numbers for \[\dfrac{3}{8}\].

Ans: 

$ \dfrac{3}{8}\times \dfrac{2}{2}=\dfrac{6}{16}  $  

$ \dfrac{3}{8}\times \dfrac{3}{3}=\dfrac{9}{24}  $  

$ \dfrac{3}{8}\times \dfrac{4}{4}=\dfrac{12}{32}  $  

$ \dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}  $  

$ \dfrac{3}{8}\times \dfrac{2}{2}=\dfrac{6}{16}  $  

9. Draw the number line and represent $-\dfrac{7}{3}$ on it.

Ans: This fraction represents two full parts and one part out of 3 equal parts. The negative sign indicates that it is on the negative side of the number line.

Therefore, each space between two integers on the number line must be divided into 3 equal parts.

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10. Rewrite the following rational numbers in the simplest form.

(a)$\dfrac{12}{36}$

(b)$\dfrac{39}{104}$

Ans: 

(a) HCF of $12$ and $36$ is $12$.

Dividing both numerator and denominator by $12$,

$\dfrac{12\div 12}{ 36\div 12}  $  

$ =\dfrac{1}{3}  $  

(b) HCF of $39$ and $104$ is $13$.

Dividing both numerator and denominator by $13$,

$\dfrac{39\div 13}{ 104\div 13} $  

$ =\dfrac{3}{8}  $  

11. Find the value of $\dfrac{4}{14}\div \dfrac{28}{80}$.

Ans: $\dfrac{4}{14}\div \dfrac{28}{80}$

$ =\dfrac{4}{14}\times \dfrac{80}{28}  $  

$ =\dfrac{40}{49}  $  

12. Find the product of $\dfrac{15}{22}\times \dfrac{11}{5}$.

Ans: $\dfrac{15}{22}\times \dfrac{11}{5}$

$ =\dfrac{3}{2}  $  

$ =1\dfrac{1}{2}  $  

13. Find the value of $\dfrac{5}{8}+\dfrac{1}{3}$.

Ans: LCM of $8$ and $3$ is $24$

$\dfrac{5}{8}\times \dfrac{3}{3}=\dfrac{15}{24}  $  

$ \dfrac{1}{3}\times \dfrac{8}{8}=\dfrac{8}{24}  $  

Therefore,

$ \dfrac{15}{24}+\dfrac{8}{24}  $  

$ =\dfrac{5+8}{24}  $  

$ =\dfrac{23}{24}  $  

3 Marks Questions

14. Find the value of 

(a)$\dfrac{3}{4}+\dfrac{1}{2}$

(b)$\dfrac{5}{8}+\dfrac{3}{4}$

Ans: (a) LCM of $4$ and $2$ is $4$

$ \dfrac{3}{4}\times \dfrac{1}{1}=\dfrac{3}{4}  $  

$ \dfrac{1}{2}\times \dfrac{2}{2}=\dfrac{2}{4}  $  

Therefore,

$ \dfrac{3}{4}+\dfrac{2}{4}  $  

$ =\dfrac{3+2}{4}  $  

$ =\dfrac{5}{4}  $  

(b) LCM of $4$ and $8$ is $8$

$ \dfrac{5}{8}\times \dfrac{1}{1}=\dfrac{5}{8}  $  

$ \dfrac{3}{4}\times \dfrac{2}{2}=\dfrac{6}{8}  $  

Therefore,

$ \dfrac{5}{8}+\dfrac{6}{8}  $  

$ =\dfrac{5+6}{8}  $  

$ =\dfrac{11}{8}  $  

$ =1\dfrac{3}{8}  $  

15. Simplify

(a)$\dfrac{2}{5}-\dfrac{1}{2}$

(b)$\dfrac{1}{5}-\dfrac{3}{4}$

Ans: 

(a) LCM of $5$ and $2$ is $10$

$ \dfrac{2}{5}\times \dfrac{2}{2}=\dfrac{4}{10}  $  

$ \dfrac{1}{2}\times \dfrac{5}{5}=\dfrac{5}{10}  $  

Therefore,

$ \dfrac{4}{10}-\dfrac{5}{10}  $  

$ =\dfrac{4-5}{10}  $  

$ =-\dfrac{1}{10}  $  

(b) LCM of $5$ and $4$ is $20$

$ \dfrac{1}{5}\times \dfrac{4}{4}=\dfrac{4}{20}  $  

$ \dfrac{3}{4}\times \dfrac{5}{5}=\dfrac{15}{20}  $  

Therefore,

$ \dfrac{4}{15}-\dfrac{15}{20}  $  

$ =\dfrac{4-15}{20}  $  

$ =-\dfrac{11}{20}  $  

16. Find the product of 

(a) $\dfrac{14}{3}\times \dfrac{21}{63}$

(b) $\dfrac{2}{5}\times \dfrac{8}{9}$

Ans:

(a) $\dfrac{14}{3}\times \dfrac{21}{63}$

$ =\dfrac{2\times 7}{1\times 9}  $  

$ =\dfrac{14}{9}  $  

$ =1\dfrac{5}{9}  $  

(b) $\dfrac{2}{5}\times \dfrac{8}{9}$

$ =\dfrac{2\times 8}{5\times 9}  $  

$ =\dfrac{16}{45}  $  

17. Find the value of 

(a) $-\dfrac{2}{3}\div \dfrac{3}{4}$

(b) $\dfrac{1}{4}\div \dfrac{5}{8}$

Ans: 

(a) $-\dfrac{2}{3}\div \dfrac{3}{4}$

$ =-\dfrac{2}{3}\times \dfrac{3}{4}  $  

$ =-\dfrac{8}{9}  $  

(b) $\dfrac{1}{4}\div \dfrac{5}{8}$

$ =\dfrac{1}{4}\times \dfrac{8}{5}  $  

$ =\dfrac{2}{5}  $  

18. Insert six rational numbers between  $\dfrac{3}{8}$ and $\dfrac{3}{5}$.

Ans: Convert both the denominators into the same denominator.

$\dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}$

$\dfrac{3}{5}\times \dfrac{8}{8}=\dfrac{24}{40}$

Therefore, 

$\dfrac{16}{24}$ $\dfrac{17}{24}$ $\dfrac{18}{24}$ $\dfrac{19}{24}$ $\dfrac{20}{24}$ $\dfrac{21}{24}$ 

Download Important Questions of Rational Numbers Class 7 With Solutions - Free PDF

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A Quick Overview of Class 7 Maths Chapter 9 Rational Numbers

Rational numbers are numbers that can be represented in the form of a fraction. It is a part of the real number system. A number is said to be in rational form if it has both numerator and denominator. More specifically, the definition of rational number states that any number can be represented in the ratio of p and q, where p and q are integers and the value of q is not equals to zero.

As per the Ancient Greek Mathematician, rational numbers are used to measure almost everything. Here are some real-life examples of rational numbers.

• Taxes are represented in the form of rational numbers.

• Divide pizza or anything among your friends.

• Interest rate on saving accounts, loan, and mortgage are expressed in rational form.

• When you complete half of the portion of your work, you say 50% of ½  of the work is completed.

Let us now understand some of the important terms of Class 7 Maths Chapter 9 Rational Numbers.

What Are Rational Numbers?

A rational number is defined as a number that can be written in the form of p/q, where p and q are integers, and q does not equal to 0. For example, 3/5 is a rational number because p = 3, and q = 5 are integers.

What are Positive and Negative Rational Numbers

Positive rational numbers are numbers whose both and numerators and denominators are positive integers. For example, 3/5 is a positive rational number because both the numerator and denominator of this number are positive.

Negative rational numbers are numbers whose either numerator or denominator are negative integers. For example, -3/5 is a negative rational number as the numerator of this number is negative.

How Rational Numbers can be Expressed in Standard Form?

A Rational p/q is said to be in standard form if its denominator that is q is positive and both numerator and denominator i.e. p and q have no other common divisor other than 1.

How to Obtain Rational Numbers Between Two Rational Numbers

We can obtain a rational number between two rational numbers p and q simply by dividing it by 2.

For Example,

• The rational number between 3/1 and 4/1 is 7/2 as 3/1 + 4/1 = 7/2.

• For a negative and positive rational number like -3/20 and 3/20 is -2/20,-1/20, 0/20, 1/20, etc.

• For determining a rational number between two rational numbers with different denominators, we first determine the equivalent fraction with the same denominator then find the rational number between them. For example, we can determine a rational number between -1/3 and 5/20 by converting -1/3 to (-1/3) x (3/3) = -39. Accordingly, we have -2/9,-1/9, 0/9, 1/9, 2/9, 3/9, 4/9.

How to Add Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by adding the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be added taking the LCM of the two denominators. Then, we find the equivalent rational numbers of the given rational number with this LCM as their denominators. Then, we add two rational numbers.

Example: Let us add (-7/5) + (-2/3)

Step 1: LCM of 5 and 3 is 15.

Step 2: (-7/5) +  -2/3 = [-7(3) + (-2)(5)]/15

Step 3: (-7/5) + (-2/3) = [-21 + (-10)]/15 = [-21 -10]/15 = -31/15

How to Subtract Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by subtracting the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be subtracted by making the values of two denominators the same by finding LCM of denominator values.

Example: Let us add (-7/5) - (-2/3)

Step 1: LCM of 5 and 3 is 15

Step 2: (-7/5) - (-2/3) = [-7(3) - (-2)(5)]/15

Step 3: (-7/5) - (-2/3)  = [-21 - (-10)]/15 = [-21 + 10]/15= -11/15

How to Multiply Two Rational Numbers?

The formula two find multiplication of two rational numbers is given by”

Product of Rational Numbers Formula  = ({Product of numerators}/{Product of denominators})

Example:

Find the product of 6/5 × 4/3

The product of 6/5 × 4/3 = 24/15

The multiplication of a rational number with its reciprocal is always equal to 1.

How to Divide Two Rational Numbers?

The division of two rational numbers is similar to the division of fractions, Here are the steps to find the division of two rational numbers.

Step 1: Find the reciprocal of the divisor value.

Step 2: Find the product of numerator and denominator to obtain the result.

Example:

Find the Value of 6/5 ÷ 9/7

Step 1: The reciprocal of 97is 79

Step 2:  Division of two rational number is

6/5 × 7/9 = 42/45

List of the Topics and Subtopics Covered in Class 7 Maths Chapter 8

• 8.1: Introduction To Rational Numbers

• 8.2: Need for Rational numbers

• 8.3: What are Rational Numbers?

• 8.4: Positive and Negative Rational Numbers

• 8.5: Rational Number on Number Line

• 8.6: Rational Number In Standard Form

• 8.7: Comparison of Rational Numbers

• 8.8: Rational Numbers Between Two Rational Number

• 8.9: Operation on Rational Numbers

• 8.9.1: Addition

• 8.9.2: Subtraction

• 8.9.3: Multiplication

• 8.9.4: Division

To practice the important question on all the topics discussed below, download Important Questions of Rational Numbers Class 7 free pdf now.

How Solving Questions on Rational Number For Class 7 will be Beneficial for Students?

Here are some of the benefits of solving questions on Rational numbers for Class 7.

• Students will be familiarized with the different types of questions, complexity level of questions, and important topics of the chapter to focus on.

• Students will be able to develop time management skills and problem-solving skills.

• Students can analyse the level of their preparation based on the marks obtained. They can also analyse their strength and weakness and accordingly improve them.

• Solving these questions repeatedly will help students to revise the complete chapter thoroughly.

• Solving the questions will also help students to attempt the questions asked in the exam more confidently as they will be habitual to solve different types of questions.

• Candidates are suggested to solve the questions and then cross their answers from the solutions provided. The attempt helps them to gain real-time exam experience.

• Practicing the questions enable students to assess their preparedness and understand the techniques to decode problems asked in the exam.

To explore all the benefits mentioned above, it is recommended to download Questions on Rational for Class 7 free pdf now.

Conclusion

When studying CBSE Class 7 Maths Chapter 8 on Rational Numbers, it's crucial to grasp key concepts. Understanding how to represent fractions, compare them, and perform operations like addition, subtraction, multiplication, and division with rational numbers is fundamental. Additionally, learning to convert fractions into decimals and vice versa is essential. Practice solving word problems and equations involving rational numbers to strengthen your problem-solving skills. Remember to simplify fractions and find the lowest common multiple when needed. By mastering these concepts, you'll be well-prepared to handle rational numbers and their applications in various mathematical problems. Consistent practice and a solid understanding will help you excel in this chapter.