GSEB Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.2

Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.2 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.2

Question 1.
Represent these numbers on the number line.

1. $\frac { 7 }{ 4 }$
2. $\frac { -5 }{ 6 }$

Solution:
(i) To represent $\frac { 7 }{ 4 }$ we make 7 markings each at a distance equal to $\frac { 1 }{ 4 }$ on the right of 0.

The 7th point represents the rational number $\frac { 7 }{ 4 }$ as shown in the figure.

The point A $\frac { 7 }{ 4 }$.

(ii) To represent ($\frac { 7 }{ 4 }$) on the nmber Line, we make 5 each at a distance equal to $\frac { 1 }{ 6 }$ on the left of 0. We consider the 5th point as shwn in the figure

The point B represent ($\frac { -5 }{ 6 }$)

Question 2.
Represent $\frac { -2 }{ 11 }$, $\frac { -5 }{ 11 }$, $\frac { -9 }{ 11 }$. on the number line.
Solution:
TO represent $\frac { -2 }{ 11 }$, $\frac { -5 }{ 11 }$ and $\frac { -9 }{ 11 }$ on a number line, we make 11 marking each being equal to distance $\frac { 1 }{ 11 }$ on the left of 0.

• The point A represent $\frac { -2 }{ 11 }$
• The point B represent $\frac { -5 }{ 11 }$
• The point C represent $\frac { -9 }{ 11 }$

Question 3.
Write five rational numbers which are smaller than 2.
Solution:
There can be unlimited rational numbers smaller than 2. Five of them are:
0, -1, $\frac { 1 }{ 2 }$, $\frac { 1 }{ 2 }$, 1

Question 4.
Find ten rational numbers between $\frac { -2 }{ 5 }$ and $\frac { 1 }{ 2 }$
Solution:
To convert $\frac { -2 }{ 5 }$ and $\frac { 1 }{ 2 }$ having the same denominators:
We have $\frac { -2 }{ 5 }$ = $\frac{-2 \times 4}{5 \times 4}$ = $\frac { -8 }{ 20 }$ and $\frac { 1 }{ 2 }$ = $\frac{1 \times 10}{2 \times 10}$ = $\frac { 10 }{ 20 }$
∵ The rational numbers between $\frac { 10 }{ 20 }$ and $\frac { -8 }{ 20 }$ are $\frac { 9 }{ 20 }$, $\frac { 8 }{ 20 }$, $\frac { 7 }{ 20 }$, $\frac { 6 }{ 20 }$, …., $\frac { -6 }{ 20 }$ , $\frac { -7 }{ 20 }$
We can take any 10 of them.
∵ ten rational nnumbers between $\frac { -2 }{ 5 }$ and $\frac { 1 }{ 2 }$ are:

(i) $\frac { 9 }{ 20 }$
(ii) $\frac { 8 }{ 20 }$
(iii) $\frac { 7 }{ 20 }$
(iv) $\frac { 6 }{ 20 }$
(v) $\frac { 5 }{ 20 }$
(vi) $\frac { 4 }{ 20 }$
(vii) $\frac { 3 }{ 20 }$
(viii) $\frac { 2 }{ 20 }$
(ix) $\frac { 1 }{ 20 }$
(x) 0

Question 5.
Find five rational numbers between:

1. $\frac { 2 }{ 3 }$ and $\frac { 4 }{ 5 }$
2. $\frac { -3 }{ 2 }$ and $\frac { 5 }{ 3 }$
3. $\frac { 1 }{ 4 }$ and $\frac { 1 }{ 2 }$

solution:
(i) Coverting $\frac { 2 }{ 3 }$ and $\frac { 4 }{ 5 }$ having same denominators such that difference between the numerators is more than 5.
We have $\frac { 2 }{ 3 }$ = $\frac{2 \times 20}{3 \times 20}$ = $\frac { 40 }{ 60 }$ and $\frac { 4 }{ 5 }$ = $\frac{4 \times 12}{5 \times 12}$ = $\frac { 48 }{ 60 }$
Now, any five rational number between
$\frac{40}{60}\left(=\frac{2}{3}\right)$ and $\frac{48}{60}\left(=\frac{4}{5}\right)$ are: $\frac { 41 }{ 60 }$, $\frac { 42 }{ 60 }$, $\frac { 43 }{ 60 }$ , $\frac { 44 }{ 60 }$, $\frac { 45 }{ 60 }$

(ii) Converting $\frac { -3 }{ 2 }$ and $\frac { 5 }{ 3 }$ with same denominators, we have

∴ Five rational numbers between

(iii) Converting $\frac { 1 }{ 4 }$ and $\frac { 1 }{ 2 }$ to rational numbers with the same denominators, we have

∴ Five rational numbers between $\frac { 1 }{ 4 }$ and $\frac { 1 }{ 2 }$ i.e., $\frac { 8 }{ 32 }$ and $\frac { 16 }{ 32 }$ are: $\frac { 9 }{ 32 }$, $\frac { 10 }{ 32 }$, $\frac { 11 }{ 32 }$, $\frac { 12 }{ 32 }$, $\frac { 13 }{ 32 }$

Question 6.
Write five rational numbers greater than – 2.
Solution:
Five rational numbers greater than – 2 are: $\frac { -3 }{ 2 }$, -1, $\frac { -1 }{ 2 }$, 0, $\frac { 1 }{ 2 }$
Note: There ten rationalnumbers greater than – 2

Question 7.
Find the rational numbers between $\frac { 3 }{ 5 }$ and $\frac { 3 }{ 4 }$.
Solution:
Converting $\frac { 3 }{ 5 }$ and $\frac { 3 }{ 4 }$ such that they between $\frac { 3 }{ 4 }$ and $\frac { 3 }{ 4 }$ such that they have common denominators and their numerators have difference of more than 10, i.each