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

These NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1

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

Question 1.
List five rational numbers between
(i) -1 and 0
(ii) -2 and -1
(iii) \(\frac{-4}{5}\) and \(\frac{-2}{3}\)
(iv) \(\frac{-1}{2}\) and \(\frac{2}{3}\)
Answer:
(i) -1 and 0
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 1
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 2

(ii) -2 and -1
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 3
are the five rational numbers between -2 and -1

(iii) \(\frac{-4}{5}\) and \(\frac{-2}{3}\)
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 01
The five rational numbers are
\(\frac{-47}{60}<\frac{-23}{30}<\frac{-3}{4}<\frac{-11}{15} \text { and } \frac{-43}{60}\)

(iv) \(\frac{-1}{2}\) and \(\frac{2}{3}\)
L. C. M of 2 and 3 is 6
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 4

Question 2.
Write four more rational numbers in each of the following patterns.
(i) \(\frac{-3}{5}, \frac{-6}{10}, \frac{-9}{15}, \frac{-12}{20}\) ………………
(ii) \(\frac{-1}{4}, \frac{-2}{8}, \frac{-3}{12}\) ………………
(iii) \(\frac{-1}{6}, \frac{2}{-12}, \frac{3}{-18}, \frac{4}{-24}\) ………………
(iv) \(\frac{-2}{3}, \frac{2}{-3}, \frac{4}{-6}, \frac{6}{-9}\) ………………
Answer:
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 5
Thus, we observe a pattern in these numbers.
The next four more rational numbers are
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 6
The four required rational numbers are \(\frac{-15}{25}, \frac{-18}{30}, \frac{-21}{35}\) and \(\frac{-24}{40}\)
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 7
Thus, we observe a pattern in these numbers.
Next Four rational numbers are
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 8
The next four required rational numbers are \(\frac{-4}{16}, \frac{-5}{20}, \frac{-6}{24}\) and \(\frac{-7}{28}\)

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 9
Thus, we observe a pattern in these numbers
The next four rational numbers would be
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 10
The required four rational numbers are \(\frac{5}{-30}, \frac{6}{-36} ; \frac{7}{-42}\) and \(\frac{8}{-48}\)

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 11
Thus, we observe a pattern in these numbers
Four more rational numbers would be
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 7
The required four rational numbers are \(\frac{8}{-12}, \frac{10}{-15} ; \frac{12}{-18}\) and \(\frac{14}{-21}\)

Question 3.
Give four rational numbers equivalent to:
(i) \(\frac{-2}{7}\)
(ii) \(\frac{5}{-3}\)
(iii) \(\frac{4}{9}\)
Answer:
(i) Four rational numbers equivalent to
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 13

(ii) Four rational numbers equivalent to
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 14

(iii) Four rational numbers equivalent to
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 15
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 16

Question 4.
Draw the number line and represent the following rational numbers on it:
(i) \(\frac{3}{4}\)
(ii) \(\frac{-5}{8}\)
(iii) \(\frac{-7}{4}\)
(iv) \(\frac{7}{8}\)
Answer:
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 17

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

Question 5.
ThepointsP,Q,RS,T,U,AandBonthe number line are such that, TR = RS = SU
and AP = PQ = QB. Name the rational numbers represented by P, Q, R, and S.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 02
Answer:
Since AP = PQ = QB
Distance between 2 and 3 is divided into 3 equal parts.
Similarly, distance between -2 and -1 is also divided into three equal parts.
P represents the rational number
\(\left(2+\frac{1}{3}\right) \text { i.e. } \frac{7}{3}\)
Q represents the rational number
\(\left(2+\frac{2}{3}\right) \text { i.e. } \frac{8}{3}\)
R represents the rational number
\(\left(-1-\frac{1}{3}\right) \text { i.e. } \frac{-4}{3}\)
S represents the rational number
\(\left(-1-\frac{2}{3}\right) \text { ie } \frac{-5}{3}\)

Question 6.
Which of the following pairs represent the same rational number?
(i) \(\frac{-7}{21}\) and \(\frac{3}{9}\)
(ii) \(\frac{-16}{20}\) and \(\frac{20}{-25}\)
(iii) \(\frac{-2}{-3}\) and \(\frac{2}{3}\)
(iv) \(\frac{-3}{5}\) and \(\frac{-12}{20}\)
(v) \(\frac{8}{-5}\) and \(\frac{-24}{15}\)
(vi) \(\frac{1}{3}\) and \(\frac{-1}{9}\)
(vii) \(\frac{-5}{-9}\) and \(\frac{5}{-9}\)
Answer:
(i) \(\frac{-7}{21}\) and \(\frac{3}{9}\)
Here \(\frac{-7}{21}\) is a negative rational number and \(\frac{3}{9}\) is a positive rational number.
\(\frac{-7}{21}=\frac{-1}{3} ; \frac{3}{9}=\frac{1}{3} ; \frac{-7}{21} \neq \frac{3}{9}\)
Thus, \(\frac{-7}{21}\) and \(\frac{3}{9}\) does not represent the same rational number.

(ii) \(\frac{-16}{20}\) and \(\frac{20}{-25}\)
We have \(\frac{-16}{20}\)= \(\frac{-4}{5}\)
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 18
Thus, \(\frac{-16}{20}\) and \(\frac{20}{-25}\) represent the same rational number.

(iii) \(\frac{-2}{-3}\) and \(\frac{2}{3}\)
\(\frac{-2}{-3}=\frac{+2}{3} ; \frac{2}{3}=\frac{2}{3}\)
Thus, \(\frac{-2}{-3}\) and \(\frac{2}{3}\) represent the same rational number.

(iv) \(\frac{-3}{5}\) and \(\frac{-12}{20}\)
We have, \(\frac{-3}{5}=\frac{-3}{5} ; \frac{-12}{20}=\frac{-3}{5}\)
So, \(\frac{-3}{5}=\frac{-12}{20}\)
Thus \(\frac{-3}{5}\) and \(\frac{-12}{20}\) represent the same rational number.

(v) \(\frac{8}{-5}\) and \(\frac{-24}{15}\)
We have, \(\frac{8}{-5}=\frac{-8}{5} ; \frac{-24}{15}=\frac{-8}{5}\)
So, \(\frac{8}{-5}\) = \(\frac{-24}{15}\)
Thus \(\frac{8}{-5}\) and \(\frac{-24}{15}\) represent the same rational number.

(vi) \(\frac{1}{3}\) and \(\frac{-1}{9}\)
Here \(\frac{1}{3}\) is positive integer and \(\frac{-1}{9}\) is a negative integer.
∴ \(\frac{1}{3} \neq \frac{-1}{9}\)
Thus \(\frac{1}{3}\) and \(\frac{-1}{9}\) does not represent the same rational number.

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

(vii) \(\frac{-5}{-9}\) and \(\frac{5}{-9}\)
\(\frac{-5}{-9}\) and \(\frac{5}{-9}\) is a positive integer.
and \(\frac{-5}{-9}\) = \(\frac{5}{-9}\) is a negative integer
∴ \(\frac{-5}{-9} \neq \frac{5}{-9}\)
Thus \(\frac{-5}{-9}\) and \(\frac{5}{-9}\) do not represent tha same rational number.

Question 7.
Rewrite the following rational numbers in the simplest form:
(i) \(\frac{-8}{6}\)
(ii) \(\frac{25}{45}\)
(iii) \(\frac{-44}{72}\)
(iv) \(\frac{-8}{10}\)
Answer:
(i) \(\frac{-8}{6}\)
\(\frac{-8}{6}=\frac{-4}{3}\) (Divide both sides by 2)
The simplest form is \(\frac{-4}{3}\)

(ii) \(\frac{25}{45}\)
\(\frac{25}{45}=\frac{5}{9}\) (Divide both sides by 5)
The simplest form is \(\frac{5}{9}\)

(iii) \(\frac{-44}{72}\)
\(\frac{-44}{72}=\frac{-11}{18}\)
Dividing both sides by 4)
The simplest \(\frac{-11}{18}\)

(iv) \(\frac{-8}{10}\)
\(\frac{-8}{10}=\frac{-4}{5}\) (Dividing both sides by 2)
The simplest form is \(\frac{-4}{5}\)

Question 8.
Fill in the boxes with the correct symbol out of > , <, and =
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 19
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 20
Answer:
\(\frac{-7}{6}\) is a negative rational number. 6
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 21

(ii) \(\frac{-4}{5} \text { and } \frac{-5}{7}\)
are negative rational numbers.
L.C.M of 5 and 7 is 35.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 22

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

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 23
are negative rational numbers.
L.C.M of 8 and 16 is 16.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 24

(iv) \(\frac{-8}{5}\) and \(\frac{-7}{4}\) are negative rational numbers.
LCM of 5 and 4 = 20
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 25

(v) \(\frac{1}{-3}\) and \(\frac{-1}{4}\) negative rational numbers.
L.C.M of 3 and 4 is 12.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 26

(vi) \(\frac{5}{-11}\) and \(\frac{-5}{11}\) are negative rational numbers.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 27

(vii) \(\frac{-7}{6}\) is a negative integer since 0 is 6
greater than every negative number.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 28

Question 9.
Which is greater in each of the following?
(i) \(\frac{2}{3}, \frac{5}{2}\)
(ii) \(\frac{-5}{6}, \frac{-4}{3}\)
(iii) \(\frac{-3}{4}, \frac{2}{-3}\)
(iv) \(\frac{-1}{4}, \frac{1}{4}\)
(v) \(-3 \frac{2}{7} ;-3 \frac{4}{5}\)
Answer:
(i) \(\frac{2}{3}, \frac{5}{2}\)
L.C.M of 2 and 3 is 6
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 29
Thus \(\frac{5}{2}\) is greater rational number.

(ii) \(\frac{-5}{6}, \frac{-4}{3}\)
L.C.M of 6 and 3 is 6
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 30
Thus \(\frac{-5}{6}\) is greater rational number.

(iii) \(\frac{-3}{4}, \frac{2}{-3}\)
L.C.M of 4 and 3 is 12
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 31
\(\frac{2}{-3}>\frac{-3}{4}\)
Thus, the rational number \(\frac{2}{-3}\) is greater.

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

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

(v) \(-3 \frac{2}{7} ;-3 \frac{4}{5}\)
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 32
Thus, rational number -3\(\frac{2}{7}\) is greater.

Question 10.
Write the following rational numbers in ascending order.
(i) \(\frac{-3}{5}, \frac{-2}{5}, \frac{-1}{5}\)
(ii) \(\frac{-1}{3}, \frac{-2}{9}, \frac{-4}{3}\)
(iii) \(\frac{-3}{7}, \frac{-3}{2}, \frac{-3}{4}\)
Answer:
(i) \(\frac{-3}{5}, \frac{-2}{5}, \frac{-1}{5}\)
\(-\frac{3}{5}<-\frac{2}{5}<-\frac{1}{5}\)
The ascending order is \(-\frac{3}{5},-\frac{2}{5},-\frac{1}{5}\)

(ii) \(\frac{-1}{3}, \frac{-2}{9}, \frac{-4}{3}\)
L.C.M of 3 and 9 is 9
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 33
Thus, the ascending order is
\(\frac{-4}{3}, \frac{-1}{3}, \frac{-2}{9}\)

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

(iii) \(\frac{-3}{7}, \frac{-3}{2}, \frac{-3}{4}\)
L.C.M of 7, 2 and 4 is 28
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 34

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