Well-designed AP Board Solutions Class 8 Maths Chapter 1 Rational Numbers Exercise 1.2 offers step-by-step explanations to help students understand problem-solving strategies.

## Rational Numbers Class 8 Exercise 1.2 Solutions – 8th Class Maths 1.2 Exercise Solutions

Question 1.

Represent these numbers on the number line.

(i) \(\frac{7}{4}\)

Answer:

First convert the given into mixed fraction. (If Possible)

\(\frac{7}{4}\) = 1\(\frac{3}{4}\). So this \(\frac{7}{4}\) lies in between 1 and 2 so you have to divide the place into 4 parts from 1 and 2, then third point would be the required.

So \(\frac{7}{4}\) = 1\(\frac{3}{4}\) represent the point (C).

(ii) \(\frac{-5}{6}\)

Answer:

Here (-) symbol shows the points left to ‘zero’.

\(\frac{-5}{6}\) can be written as 0 + \(\frac{-5}{6}\).

So this lies in between 0 and -1; we are divide into 6 equal parts.

Then the fifth point shows \(\frac{-5}{6}\).

The point ‘P’ shows \(\left(\frac{-5}{6}\right)\)

Question 2.

Represent \(\frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11}\) on the number line.

Answer:

Given are left to zero on number line (-Symbol) they lie in between ‘0’ and 1.

Because numerator < denominator.

Now divide into 11 parts. (∵ denominator = 11)

Then 2nd, 5th, 9th points would be the answers.

Question 3.

Write five rational numbers which are smaller than 2.

Answer:

(i) Given = 2

It can be written as \(\frac{20}{10}\), then \(\frac{19}{10}, \frac{18}{10}, \frac{11}{10}, \frac{7}{10}, \frac{3}{10}\) are rationals which are smaller than 2.

(ii) Given = 2

It can be written as \(\frac{16}{8}\) then \(\frac{15}{8}, \frac{14}{8}, \frac{13}{8}, \frac{12}{8}, \frac{11}{8}\), ………….. thus we can write so many.

Question 4.

Find ten rational numbers between \(\frac{-2}{5}\) and \(\frac{1}{2}\).

Answer:

First write the denominators equal in given fractions using L.C.M.

Here \(\frac{-2}{5}, \frac{1}{2}\) ⇒ LCM of 5 and 2 = 10

⇒ \(\frac{(-2) 2,5(1)}{10}=\frac{-4,5}{10}\)

So given fractions \(\frac{-2}{5}\) and \(\frac{1}{2}\) can be written as \(\frac{-4}{10}\) and \(\frac{5}{10}\).

Now, write them as \(\frac{-40}{100}\) and \(\frac{50}{100}\).

So that we can write more rationals between \(\frac{-40}{100}\) and \(\frac{50}{100}\) are \(\frac{-39}{100}, \frac{-38}{100}, \frac{-37}{100}\) …………\(\frac{41}{100}, \frac{42}{100}, \frac{43}{100}\) ……. \(\frac{49}{100}\)

Question 5.

Find five rational numbers between

(i) \(\frac{2}{3}\) and \(\frac{4}{5}\)

Answer:

L.C.M of 3 and 5 = 15

So \(\frac{2}{3}, \frac{4}{5}\) can be written as \(\frac{5(2), 3(4)}{15}=\frac{10,12}{15}\)

So, \(\frac{2}{3}\) and \(\frac{4}{5}\) = \(\frac{10}{15}\) and \(\frac{12}{15}\)

To get more and more we can write

\(\frac{10}{15}\) as \(\frac{100}{150}\) and \(\frac{12}{15}\) as \(\frac{120}{150}\)

So given \(\frac{2}{3}\) and \(\frac{4}{5}\) can be written as

\(\frac{100}{150}, \frac{120}{150}\)

So rational numbers between them are \(\frac{101}{150}, \frac{102}{150}, \frac{105}{150}, \frac{110}{150}\) ………… \(\frac{119}{150}\)

(ii) \(\frac{-3}{2}\) and \(\frac{5}{3}\)

Answer:

L.C.M. of 2 and 3 is 6.

Then \(\frac{-3}{2}, \frac{5}{3}\)can be written as

\(\frac{3(-3), 2(5)}{6}=\frac{-9,10}{6}\)

So \(\frac{-9}{6}, \frac{10}{6}\)

Now, rational numbers in between \(\frac{-9}{6}\) and \(\frac{10}{6}\) are

\(\frac{-8}{6}, \frac{-7}{6} \ldots \ldots . \frac{-1}{6}, \frac{0}{6}, \frac{1}{6} \ldots \ldots \ldots \frac{7}{6}, \frac{8}{6}, \frac{9}{6}\) etc.

(iii) \(\frac{1}{4}\) and \(\frac{1}{2}\)

Answer:

L.C.M. of 4 and 2 = 4; \(\frac{1}{4}\) and \(\frac{1}{2}=\frac{1(1), 2(1)}{4}=\frac{1}{4}, \frac{2}{4}\) now write them with big denominator

\(\frac{1}{4}, \frac{2}{4}\) can be written as

\(\frac{6(1)}{6(4)}, \frac{6(2)}{6(4)}=\frac{6}{24}, \frac{12}{24}\)

Now, rational numbers between

\(\frac{6}{24}, \frac{12}{24}\) are \(\frac{7}{24}, \frac{8}{24}, \frac{9}{24}, \frac{10}{24}, \frac{11}{24}\)

(You can multiply with a number greater than six also)

Question 6.

Write five rational numbers greater than -2.

Answer:

We can write -2 are \(\left(\frac{-20}{10}\right)\)

Then \(\frac{-19}{10}, \frac{-18}{10}, \frac{-17}{10}\), ……….. \(\frac{1}{10}\) are rational numbers greater then -2.

Question 7.

Find ten rational numbers between \(\frac{3}{5}\) and \(\frac{3}{4}\).

Answer:

Choose a common multiple of 5,4. They are 20, 40, 80, ………….

Let us choose 80, then

(∵ we need 10 rationals so choose bigger one)

We can write \(\frac{3}{5}, \frac{3}{4}\) as \(\frac{16(3)}{16(5)}, \frac{20(3)}{20(4)}\) = \(\frac{48}{80}, \frac{60}{80}\)

So, \(\frac{49}{80}, \frac{50}{80}, \frac{51}{80}\) …….. \(\frac{57}{80}, \frac{58}{80}, \frac{59}{80}\) are rationed numbers in between them.