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.

- \(\frac { 7 }{ 4 }\)
- \(\frac { -5 }{ 6 }\)

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:

- \(\frac { 2 }{ 3 }\) and \(\frac { 4 }{ 5 }\)
- \(\frac { -3 }{ 2 }\) and \(\frac { 5 }{ 3 }\)
- \(\frac { 1 }{ 4 }\) 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