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