GSEB Solutions Class 7 Maths Chapter 9 Rational Numbers InText Questions

Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 9 Rational Numbers InText Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 9 Rational Numbers InText Questions

Try These (Page 174)

Question 1.
Is the number $\frac { 2 }{ -3 }$ rational? Think about it.
Solution:
Yes, $\frac { 2 }{ -3 }$ is a rational number,
∵ 2 and – 3 are integers and – 3 ≠ 0.

Question 2.
List ten rational numbers.
Solution:
Following are ten rational numbers:
$\frac { 1 }{ 3 }$, $\frac { 2 }{ -3 }$, $\frac { 4 }{ 5 }$, $\frac { 1 }{ -6 }$, $\frac { -3 }{ – 4 }$ 5.8, 2$\frac { 4 }{ 5 }$, 0.93, 18 and 11.07.
Note.
1. ‘0’ can be written as $\frac { 0 }{ 2 }$ or $\frac { 0 }{ 15 }$, etc. Hence, it is a rational number.
2. A natural number can be written as 5 = $\frac { 5 }{ 1 }$ or 108
= $\frac { 108 }{ 1 }$
Hence, it is also a rational number.

Try These (Page 175)

Question 1.
Fill in the boxes:

Solution:

Try These (Page 175)

Question 1.
Is 5 a positive rational number?
Solution:
Yes, 5 or $\frac { 5 }{ 1 }$ is having both its numerator and denominator as positive.
∴ It is a positive rational number.

Question 2.
List five more positive rational numbers.
Solution:
$\frac { 1 }{ 7 }$, $\frac { 3 }{ 8 }$, $\frac { 5 }{ 17 }$, $\frac { 2 }{ 9 }$ and $\frac { 5 }{ 18 }$ are positive rational numbers.

Try These (Page 176)

Question 1.
Is – 8 a negative rational number?
Solution:
Yes, – 8 or $\frac { -8 }{ 1 }$ is a negative rational number, because its numerator is a negative integer.

Question 2.
List five more negative rational numbers.
Solution:
Five negative rational numbers are as follows:
$\frac { – 5 }{ 9 }$, $\frac { -6 }{ 11 }$, $\frac { -3 }{ 13 }$, $\frac { 3 }{ -10 }$ and $\frac { -1 }{ 7 }$

Try These (Page 176)

Question 1.
Which of these are negative rational numbers?
(i) $\frac { -2 }{ 3 }$
(ii) $\frac { 5 }{ 7 }$
(iii) $\frac { 3 }{ -5 }$
(iv) 0
(v) $\frac { 6 }{ 11 }$
(vi) $\frac { -2 }{ -9 }$
Solution:
(i) $\frac { -2 }{ 3 }$ is a negative rational number.
(ii) $\frac { 5 }{ 7 }$ is a positive rational number.
(iii) $\frac { 3 }{ -5 }$ is a negative rational number.
(iv) 0 is neither a positive nor a negative rational number.
(v) $\frac { 6 }{ 11 }$ is a positive rational number.
(vi) $\frac { -2 }{ -9 }$ is a positive rational number.

∴ (i) $\frac { -2 }{ 3 }$ and (ii) $\frac { 3 }{ -5 }$ are negative rational numbers.

Try These (Page 178)

Question 1.
Find the standard form of:
(i) $\frac { -18 }{ 45 }$
(ii) $\frac { -12 }{ 18 }$
Solution:
(i) Since HCF of 18 and 45 is 9.
∴ $\frac { -18 }{ 45 }$ = $\frac { (-18)÷9 }{ 45÷9 }$ = $\frac { -2 }{ 5 }$
Thus, the standard form of is $\frac { -18 }{ 45 }$ is $\frac { -2 }{ 5 }$

(ii) Since, HCF of 12 and 18 is 6.
∴ $\frac { -12 }{ 18 }$ = $\frac { (-12)÷6 }{ 18÷6 }$ = $\frac { -2 }{ 3 }$
Thus, the standard form of $\frac { -12 }{ 18 }$ is $\frac { -2 }{ 3 }$

Try These (Page 181)

Question 1.
Find five rational numbers between $\frac { -5 }{ 7 }$ and $\frac { -3 }{ 8 }$.
Solution:
First we convert the given rational numbers with common denominators.
∵ LCM of 7 and 8 is 56.

Thus, the five rational numbers, between $\frac { -5 }{ 7 }$ and $\frac { -3 }{ 8 }$ are:
$\frac { -39 }{ 56 }$, $\frac { -38 }{ 56 }$, $\frac { -37 }{ 56 }$, $\frac { -36 }{ 56 }$, $\frac { -35 }{ 56 }$
or $\frac { -39 }{ 56 }$, $\frac { -19 }{ 28 }$, $\frac { -37 }{ 56 }$, $\frac { -9 }{ 14 }$, $\frac { -5 }{ 8 }$

Try These (Page 185)

Question 1.
Find:
(i) $\frac { -13 }{ 7 }$ + $\frac { 6 }{ 7 }$
(ii) $\frac { 19 }{ 5 }$ + $\frac { -7 }{ 5 }$
Solution:

Question 2.
Find:
(i) $\frac { -3 }{ 7 }$ + $\frac { 2 }{ 3 }$
(ii) $\frac { -5 }{ 6 }$ + $\frac { -3 }{ 11 }$
Solution:
(i) $\frac { -3 }{ 7 }$ + $\frac { 2 }{ 3 }$
∵ LCM of 7 and 3 is 21.
∴ $\frac { -3 }{ 7 }$ = $\frac { (-3)×3 }{ 7×3 }$ = $\frac { -9 }{ 21 }$
and $\frac { 2 }{ 3 }$ = $\frac { 2×7 }{ 3×7 }$ = $\frac { 14 }{ 21 }$
∴ $\frac { -3 }{ 7 }$ + $\frac { 2 }{ 3 }$ = $\frac { -9 }{ 21 }$ + $\frac { 14 }{ 21 }$
= $\frac { -9+14 }{ 21 }$
= $\frac { 5 }{ 21 }$

(ii) $\frac { -5 }{ 6 }$ + $\frac { -3 }{ 11 }$
Since, LCM of 6 and 11 is 66.

Try These (Page 186)

Question 1.
What will be the additive inverse of $\frac { -3 }{ 9 }$? $\frac { -9 }{ 11 }$?$\frac { 5 }{ 7 }$?
Solution:
Additive inverse of $\frac { -3 }{ 9 }$ is $\frac { 3 }{ 9 }$
Additive inverse of $\frac { -9 }{ 11 }$ is $\frac { 9 }{ 11 }$
Additive inverse of $\frac { 5 }{ 7 }$ is $\frac { -5 }{ 7 }$

Try These (Page 187)

Question 1.
Find:
(i) $\frac { 7 }{ 9 }$ – $\frac { 2 }{ 5 }$
(ii) 2$\frac { 1 }{ 5 }$ – $\frac { -1 }{ 3 }$
Solution:

Try These (Page 188)

Question 1.
What will be
(i) $\frac { -3 }{ 5 }$ x 7?
(ii) $\frac { -6 }{ 5 }$ x (-2)?
Solution:
(i) $\frac { -3 }{ 5 }$ x 7 = $\frac { (-3)×7 }{ 5 }$ = $\frac { -21 }{ 5 }$
(ii) $\frac { -6 }{ 5 }$ x (-2) = $\frac { -6×(-2) }{ 5 }$ = $\frac { 12 }{ 5 }$

Note:
We multiply two rational numbers in the following way:
(i) Multiply the numerators of the rational numbers.
(ii) Multiply the denominators of the rational numbers.
(iii) Then product =
For example:

Try These (Page 188)

Question 1.
Find:
(i) $\frac { -3 }{ 4 }$ x $\frac { 1 }{ 7 }$
(ii) $\frac { 2 }{ 3 }$ x $\frac { -5 }{ 9 }$
Solution:

Try These (Page 189)

Question 1.
What will be the reciprocal of $\frac { -6 }{ 11 }$ and $\frac { -8 }{ 5 }$?
Solution:
(i) Reciprocal of $\frac { -6 }{ 11 }$ is $\frac { 11 }{ -6 }$
(ii) Reciprocal of $\frac { -8 }{ 5 }$ is $\frac { -5 }{ 8 }$.
To divide one rational number by the other rational number, we multiply the rational number by the reciprocal of the other. For example,

Try These (Page 190)

Question 1.
Find:
(i) $\frac { 2 }{ 3 }$ x $\frac { -7 }{ 8 }$
(ii) $\frac { -6 }{ 7 }$ x $\frac { 5 }{ 7 }$
Solution: