# AP 8th Class Maths 1st Chapter Rational Numbers Exercise 1.2 Solutions

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) $$\frac{7}{4}$$
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) $$\frac{-5}{6}$$
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.
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.
(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 $$\frac{1}{2}$$.
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 $$\frac{4}{5}$$
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 $$\frac{5}{3}$$
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 $$\frac{1}{2}$$
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.
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.
Find ten rational numbers between $$\frac{3}{5}$$ and $$\frac{3}{4}$$.
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.