RBSE Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Question 1.
List five rational numbers between:
(i) - 1 and 0
Answer:
Write -1 and 0 as rational numbers with denominator 6.
-1 × \(\frac{6}{6}=\frac{-6}{6}\) and 0 × \(\frac{6}{6}=\frac{0}{6}\)
Five rational numbers between \(\frac{0}{6}\) and \(\frac{-6}{6}\) are \(\frac{-1}{6}, \frac{-2}{6}, \frac{-3}{6}, \frac{-4}{6}\) and\( \frac{-5}{6}\)

(ii) - 2 and - 1
Answer:
Write - 2 and - 1 as rational numbers with denominator 6.
2 × \(\frac{6}{6}=\frac{-12}{6}\) and -1 × \(\frac{6}{6}=\frac{-6}{6} \)
Five rational numbers between \(\frac{-6}{6}\) and \(\frac{-12}{6}\) are \(\frac{-7}{6}, \frac{-8}{6}, \frac{-9}{6}, \frac{-10}{6} \)and \(\frac{-11}{6}\)

(iii) \(-\frac{4}{5}\) and \(-\frac{2}{3}\)
Answer:
LCM of 5 and 3 = 15
Write \(\frac{-4}{5}\) and \(-\frac{2}{3}\) with denominator 15.
\(\frac{-4}{5} \times \frac{3}{3}=\frac{-12}{15}\) and \(\frac{-2}{3} \times \frac{5}{5}=\frac{-10}{15}\)

 Now multiply \(\frac{-12}{15}\) and \(\frac{-10}{15}\) with\( \frac{10}{10}\) to get 5 rational numbers
\(\frac{-12}{15} \times \frac{10}{10}=\frac{-120}{150}\) and \(\frac{-10}{15} \times \frac{10}{10}=\frac{-100}{150}\)
Five rational numbers between \(\frac{-4}{5}\) and \(\frac{-2}{3}\) are \(\frac{-119}{150}, \frac{-118}{150}, \frac{-117}{150}, \frac{-116}{150}, \frac{-115}{150}\)

(iv) \(-\frac{1}{2}\) and \(\frac{2}{3}\)
Answer:
LCM of 2 and 3 = 6
Write \(-\frac{1}{2}\) and \(\frac{2}{3}\) with denominator 6.
\(\frac{1}{2} \times \frac{3}{3}=\frac{3}{6} \)and \(\frac{2}{3} \times \frac{2}{2}=\frac{4}{6}\)

Multiply \(\frac{3}{6} \)and \(\frac{4}{6}\) with \(\frac{10}{10}\) to get 5 rational numbers.
\(\frac{3}{6} \times \frac{10}{10}=\frac{30}{60}\) and\( \frac{4}{6} \times \frac{10}{10}=\frac{40}{60}\)
Five rational numbers between \(\frac{1}{2}\) and \(\frac{2}{3}\) are \(\frac{31}{60}, \frac{32}{60}, \frac{33}{60}, \frac{34}{60}, \frac{35}{60}\)

Question 2.
Write four more rational numbers in each of the following patterns :
(i) \(\frac{-3}{5}, \frac{-6}{10}, \frac{-9}{15}, \frac{-12}{20}\) ..........................
Answer:
\(\frac{-3}{5}, \frac{-6}{10}, \frac{-9}{15}, \frac{-12}{20}\) ..........................
Next four rational numbers are
\(\frac{-15}{25}, \frac{-18}{30}, \frac{-21}{35}, \frac{-24}{40}\)

(ii) \(\frac{-1}{4}, \frac{-2}{8}, \frac{-3}{12}\) ..............................
Answer:
\(\frac{-1}{4}, \frac{-2}{8}, \frac{-3}{12}\) ..............................
Next four rational numbers are
\(\frac{-4}{16}, \frac{-5}{20}, \frac{-6}{24}, \frac{-7}{28}\)

(iii) \(\frac{-1}{6}, \frac{2}{-12}, \frac{3}{-18}, \frac{4}{-24}\) ..........................
Answer:
\(\frac{-1}{6}, \frac{2}{-12}, \frac{3}{-18}, \frac{4}{-24} \)..........................
Next four rational numbers are
\(\frac{-5}{30}, \frac{-6}{36}, \frac{-7}{42}, \frac{-8}{-48}\)

(iv) \(\frac{-2}{3}, \frac{2}{-3}, \frac{4}{-6}, \frac{6}{-9}\) .............................
Answer:
\(\frac{-2}{3}, \frac{2}{-3}, \frac{4}{-6}, \frac{6}{-9}\) .............................
Next four rational numbers are
\(\frac{8}{-12}, \frac{10}{-15}, \frac{12}{-18}, \frac{14}{-21}\)

Question 3.
Give four rational numbers equivalent to:
(i) \(\frac{-2}{7}\)
Answer:
\(\frac{-2}{7}\)
\(\frac{-2}{7} \times \frac{2}{2}=\frac{-4}{14} ; \frac{-2}{7} \times \frac{3}{3}=\frac{-6}{21}\)
\(\frac{-2}{7} \times \frac{4}{4}=\frac{-8}{28} ; \frac{-2}{7} \times \frac{5}{5}=\frac{-10}{35}\)
Four Rational Numbers equivalent to \(\frac{-2}{7}\) are \(\frac{-4}{14}, \frac{-6}{21}, \frac{-8}{28}, \frac{-10}{35}\)

(ii) \(\frac{5}{-3}\)
Answer:

Four Rational Numbers equivalent to \(\frac{5}{-3}\) are \(\frac{10}{-6}, \frac{15}{9}, \frac{20}{-12}\) and \(\frac{25}{-15}\)

(iii) \(\frac{4}{9}\)
Answer:

Four Rational Numbers equivalent to are \(\frac{8}{18}, \frac{12}{27}, \frac{16}{36}, \frac{20}{45}\)

Question 4.
Draw the number line and represent the following rational numbers on it:
(i) \(\frac{3}{4}\)
Answer:

(ii) \(\frac{-5}{8}\)
Answer:

(iii) \(\frac{-7}{4}\)
Answer:

(iv) \(\frac{7}{8}\)
Answer:

Question 5.
The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP *= PQ = QB. Name the rational numbers represented by P, Q, R and S.

Answer:
Here, AP = PQ = QB, between 2 and 3 there are 3 equal parts and between - 2 and - 1 there are 3 equal parts.
∴ P represents = 2 + \(\frac{1}{3}=\frac{6+1}{3}=\frac{7}{3}\)
= 2\(\frac{1}{3}\)

Q represents = 2 + \(\frac{2}{3}=\frac{6+2}{3}=\frac{8}{3} = 2 \frac{2}{3}\)
R represent = - 1 - \(\frac{1}{3}=\frac{-3-1}{3}=\frac{-4}{3} = -1 \frac{1}{3}\)
S represent = -1 - \(\frac{2}{3}=\frac{-3-2}{3}=\frac{-5}{3} = -1 \frac{2}{3}\)

Question 6.
Which of the following pairs represent the same rational number?
(i) \(\frac{-7}{21}\) and \(\frac{3}{9}\)
Answer:
\(\frac{-7}{21}\) and \(\frac{3}{9}\)
Here, \(\frac{-7}{21}\) is a negative rational number and \(\frac{3}{9}\) is a positive rational number,
∴ \(\frac{-7}{21} \neq \frac{3}{9}\)

(ii) \(\frac{-16}{20}\) and \(\frac{20}{-25}\)
Answer:
\(\frac{-16}{20}\) and \(\frac{20}{-25}\)
\(\frac{-16 \div 4}{20 \div 4}=\frac{-4}{5}=\frac{-4}{5}\) and \(\frac{20 \div 5}{-25 \div 5}=\frac{4}{-5}=-\frac{4}{5}\)
∴ \(\frac{-16}{20}=\frac{20}{-25}\)
Thus, \(\frac{-16}{20}\) and \(\frac{20}{-25}\) represent the same rational numbers.

(iii) \(\frac{-2}{-3}\) and \(\frac{2}{3}\)
Answer:
\(\frac{(-2) \div(-1)}{(-3) \div(-1)}=\frac{2}{3}\)
∴ \(\frac{-2}{-3}=\frac{2}{3}\)
Thus, \(\frac{-2}{-3}\) and \(\frac{2}{3}\) represent the same rational numbers.

(iv) \(\frac{-3}{5}\) and \(\frac{-12}{20}\)
Answer:
\(\frac{-3}{5}=\frac{-3}{5} \times \frac{4}{4}=\frac{-12}{20}\)
∴ \(\frac{-3}{5}=\frac{-12}{20}\)
Thus, \(\frac{-3}{5}\) and \(\frac{-12}{20}\) represent the same rational numbers.

(v) \(\frac{8}{-5}\) and \(\frac{-24}{15}\)
Answer:
\(\frac{8}{-5}=\frac{8}{-5} \times \frac{3}{3}=\frac{24}{-15}=\frac{-24}{15}\)
∴ \(\frac{8}{-5}=\frac{-24}{15}\)
Thus, \(\frac{8}{-5}\) and \(\frac{-24}{15}\) represent the same rational numbers.

(vi) \(\frac{1}{3}\) and \(\frac{-1}{9}\)
Answer:
Here, \(\frac{1}{3}\) is a positive integer and \(\frac{-1}{9}\) is a negative integer, so \(\frac{1}{3} \neq \frac{-1}{9}\)

(vii) \(\frac{-5}{-9}\) and \(\frac{5}{-9}\)
Answer:
\(\frac{-5}{-9}=\frac{-5 \div(-1)}{-9 \div(-1)}=\frac{5}{9}\)
Here, \(\frac{-5}{-9}\) is a positive integer and \(\frac{5}{-9}\) is a negative integer, so \(\frac{-5}{-9} \neq  \frac{5}{-9}\)

Question 7.
Rewrite the following rational number in the simplest form :
(i) \(\frac{-8}{6}\)
Answer:
\(\frac{-8}{6}\)
∵ HCF of 8 and 6 is 2
∴\( \frac{-8}{6}=\frac{-8 \div 2}{6 \div 2}=\frac{-4}{3}\)
Simplest form of \(\frac{-8}{6}\) is \(\frac{-4}{3}\)

(ii) \(\frac{25}{45}\)
Answer:
\(\frac{25}{45}\)
∵ HCF of 25 and 45 is 5
∴ \(\frac{25}{45}=\frac{25 \div 5}{45 \div 5}=\frac{5}{9}\)
Simplest form of \(\frac{25}{45}\) is \(\frac{5}{9}\)

(iii) \(\frac{-44}{72}\)
Answer:
\(\frac{-44}{72}\)
∵ HCF of 44 and 72 is 4.
∴ \(\frac{-44}{72}=\frac{-44 \div 4}{72 \div 4}=\frac{-11}{18}\)
Simplest form of \(\frac{-44}{72}\) is \(\frac{-11}{18}\)

(iv) \(\frac{-8}{10}\)
Answer:
\(\frac{-8}{10}\)
∵ HCF of 8 and 10 is 2.
∴ \(\frac{-44}{72}=\frac{-44 \div 4}{72 \div 4}=\frac{-11}{18}\)
Simplest form of \(\frac{-44}{72}\) is \(\frac{-11}{18}\)

Question 8.
Fill in the blanks with the correct symbol out of >, < and = :
(i) \(\frac{-5}{7}\) _________ \(\frac{2}{3}\)
Answer:
Since \(\frac{-5}{7}\) is negative rational number and \(\frac{2}{3}\) is a positive rational number.

(ii) \(\frac{-4}{5}\) ___________ \(\frac{-5}{7}\)
Answer:
LCM of 5 and 7 = 35

(iii) \(\frac{-7}{8}\) _________ \(\frac{14}{-16}\)
Answer:
LCM of 8 and 16 = 16

(iv) \(\frac{-8}{5}\) _________ \(\frac{-7}{4}\)
Answer:
LCM of 5 and 4 = 20

(v) \(\frac{1}{-3}\) _________ \(\frac{-1}{4}\)
Answer:
LCM of 3 and 4 = 12

(vi) \(\frac{5}{-11}\) _________ \(\frac{-5}{11}\)
Answer:

(vii) 0 _________ \(\frac{-7}{6}\)
Answer:
Since 0 is greater than every negative number.

Question 9.
Which is greater in each of the following:
(i) \(\frac{2}{3}, \frac{5}{2}\)
Answer:
∴ LCM of 3 and 2 = 6

Thus, \(\frac{5}{2}\) is greater rational number.

(ii) \(\frac{-5}{6}, \frac{-4}{3}\)
Answer:
∴ LCM of 6 and 3 = 6

(iii) \(\frac{-3}{4}, \frac{2}{-3}\)
Answer:
∴ LCM of 4 and 3 = 12

Thus, \(\frac{2}{-3}\) is greater rational number.

(iv) \(\frac{-1}{4}\), \(\frac{1}{4}\)
Answer:
Since a positive rational number is always greater than a negative rational number.
∴ \(\frac{1}{4}>\frac{-1}{4}\)
Thus, \(\frac{1}{4}\) is greater rational number.

(v) -3\(\frac{2}{7}\), -3\(\frac{4}{5}\)
Answer:

Thus, -3\(\frac{2}{7}\) is greater rational number.

Question 10.
Write the following rational numbers in ascending order:
(i) \(\frac{-3}{5}, \frac{-2}{5}, \frac{-1}{5}\)
Answer:
Since (- 3) < (- 2) < (- 1)
∴ \(\frac{-3}{5}<\frac{-2}{5}<\frac{-1}{5}\)
Ascending order of given rational number is \(\frac{-3}{5}<\frac{-2}{5}<\frac{-1}{5}\)

(ii) \(\frac{-1}{3}, \frac{-2}{9}, \frac{-4}{3}\)
Answer:
Since LCM of 3, 9 and 3 is 9.

(iii) \(\frac{-3}{7}, \frac{-3}{2}, \frac{-3}{4}\)
Answer:
∴ LCM of 7, 2 and 4 is 28