MP Board Class 7th Maths Solutions 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 \(\frac{2}{3}\)
Solution:
(i) Five rational numbers between -1 and 0 are \(\frac{-1}{10}, \frac{-1}{20}, \frac{-1}{30}, \frac{-1}{40}, \frac{-1}{50}\)

(ii) -2 and -1
\(-2=\frac{-12}{6}\) and \(-1=\frac{-6}{6}\)
∴ Five rational numbers between -2 and -1 are \(\frac{-11}{6}, \frac{-10}{6}, \frac{-9}{6}, \frac{-8}{6}, \frac{-7}{6}\).

(iii)
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 36

(iv) \(\frac{1}{2}\) and \(\frac{2}{3}\)
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 1
∴ Five rational numbers between \(\frac{1}{2}\) and \(\frac{2}{3}\)
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 2

Question 2.
Write four more rational numbers in each of the following patterns:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 3
Solution:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 4
Therefore, next four rational numbers in this pattern are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 5
Therefore, next four rational numbers in this pattern are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 6
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 7
Therefore, next four rational numbers in this pattern are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 8
Therefore, next four rational numbers in this pattern are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 9

MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Question 3.
Give four rational numbers equivalent to:
(i) \(\frac{-2}{7}\)
(ii) \(\frac{5}{-3}\)
(iii) \(\frac{4}{9}\)
Solution:
Four rational numbers are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 10
Four rational numbers are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 11
Four rational numbers are
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 12

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) \(\frac{7}{8}\)
Solution:
(i) \(\frac{3}{4}\)
The fraction represents 3 parts out of 4 equal parts. Therefore, each space between two integers on the number line must be divided into 4 equal parts.
∴ \(\frac{3}{4}\) can be represented as
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 13

(ii) \(\frac{-5}{8}\)
The fraction represents 5 parts out of 8 equal parts and negative sign represents that it is on the left side of the number line. Therefore, each space between two integers on the number line must be divided into 8 equal parts.
∴ \(\frac{5}{8}\) can be represented as
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 14

(iii) \(\frac{-7}{4}\) = \(-1 \frac{3}{4}\)
The fraction represents 1 full part and 3 parts out of 4 equal parts and negative sign represents that it is on the left side of the number line. Therefore, each space between two integers on the number line must be divided into 4 equal parts.
∴ \(\frac{-7}{4}\) can be represented as
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 15

(iv) \(\frac{7}{8}\)
The fraction represents 7 parts out of 8 equal parts. Therefore, each space between two integers on the number line must be divided into 8 equal parts.
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 16

MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1

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.
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 17
Solution:
Distance between U and T = 1 unit
It is divided into 3 equal parts.
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 18
Similarly, AB = 1 unit
It is divided into 3 equal parts.
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 19

Question 6.
Which of the following pairs represent the same rational number?
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 20
Solution:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 21
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 22
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 23
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MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Question 7.
Rewrite the following rational numbers in the simplest form:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 25
Solution:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 26

Question 8.
Fill in the boxes with the correct symbol out of >, < and =.
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 27
Solution:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 28
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 29

MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1

Question 9.
Which is greater in each of the following:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 30
Solution:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 31
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 32

Question 10.
Write the following rational numbers in ascending order:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 33
Solution:
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 34
MP Board Class 7th Maths Solutions Chapter 9 Rational Numbers Ex 9.1 35

MP Board Class 7th Maths Solutions