CBSE Class 7 Maths Important Questions 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.

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, 

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

5 Important Formulas of Class 7 Chapter 8 Rational Numbers You Shouldn’t Miss!

Chapter 8, "Rational Numbers," introduces key concepts and formulas that are fundamental in understanding and working with rational numbers. Here are five important formulas from this chapter:

1. Addition of Rational Numbers

To add two rational numbers with the same denominator:

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$

If the denominators are different, first find a common denominator and then add.

2. Subtraction of Rational Numbers

To subtract one rational number from another with the same denominator:

$\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$

For different denominators, find a common denominator before subtracting.

3. Multiplication of Rational Numbers

To multiply two rational numbers, multiply the numerators and denominators:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

4. Division of Rational Numbers

To divide one rational number by another, multiply by the reciprocal of the divisor:

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$

5. Reciprocal of a Rational Number

The reciprocal (or multiplicative inverse) of a rational number $\frac{a}{b}$ is:

$\frac{b}{a}$

where $a$ and $b$ are non-zero.

Benefits of Important Questions for Class 7 Maths Chapter 8 Rational Numbers

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

• Students will be familiarised 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 strengths and weaknesses 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.

• Practising the questions enables 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. Practise 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.

Important Study Materials for Class 7 Maths Chapter 8

CBSE Class 7 Maths Important Questions for All Chapters

Class 7 Maths Important Questions and Answers cover key topics, aiding in thorough preparation and making revision simpler.

Important Study Materials for Class 7 Maths