NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.2

NCERT Solutions Class 8 Mathematics 
Chapter – 1 (Rational Numbers) 

The NCERT Solutions in English Language for Class 8 Mathematics Chapter – 1 Rational Numbers Exercise 1.2 has been provided here to help the students in solving the questions from this exercise. 

Chapter 1: Rational Numbers

Exercise – 1.2 

1. Represent these numbers on the number line.
(i) \mathbf{\frac{7}{4}}                             (ii) \mathbf{\frac{-5}{6}}

Solution –

(i) \mathbf{\frac{7}{4}}
NCERT Maths Solutions Class 8
Here, point A represents \frac{7}{4} on the number line.

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

NCERT Maths Solutions Class 8
Here, point B represents \frac{-5}{6} on the number line.

2. Represent \mathbf{\frac{-2}{11}}, \mathbf{\frac{-5}{11}}, \mathbf{\frac{-9}{11}} on a number line.

Solution – We have \frac{-2}{11}, \frac{-5}{11} and \frac{-9}{11}

NCERT Maths Solutions Class 8

Here, point A represents \frac{-2}{11}, point B represents \frac{-5}{11}, point C represents \frac{-9}{11}

3. Write five rational numbers which are smaller than 2.

Solution –  The number 2 can be written as \frac{20}{10}
Hence, we can say that the five rational numbers which are smaller than 2 are:
\frac{19}{10}, \frac{18}{10}, \frac{17}{10}, \frac{16}{10} and \frac{1}{10}

4. Find the rational numbers between \mathbf{\frac{-2}{5}} and \mathbf{\frac{1}{2}}.

Solution –  Let us make the denominators the same, say 50.
\frac{-2}{5}  = \frac{-2\times 4}{5\times 4} = \frac{-8}{20}

\frac{1}{2} = \frac{1\times 10}{2\times 10} = \frac{10}{20}

Ten rational numbers between \frac{-8}{20} and \frac{10}{20}  are

\frac{-7}{20},\frac{-6}{20},\frac{-5}{20},\frac{-4}{20},\frac{-3}{20},\frac{-2}{20},\frac{-1}{20},0, \frac{1}{20}  and \frac{2}{20}

\frac{-7}{20},\frac{-3}{10},\frac{-1}{4},\frac{-1}{5},\frac{-3}{20},\frac{-1}{10},\frac{-1}{20},0, \frac{1}{20}

5. Find five rational numbers between:
(i) \mathbf{\frac{2}{3}} and \mathbf{\frac{4}{5}}

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

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

Solution –

(i) \mathbf{\frac{2}{3}} and \mathbf{\frac{4}{5}}
Let us make the denominators the same, say 60

\frac{2}{3} = \frac{2\times 20}{3\times 20} = \frac{40}{60}

\frac{4}{5} = \frac{4\times 12}{5\times 12} = \frac{48}{60}
Five rational numbers between \frac{40}{60} and \frac{48}{60} are

\frac{41}{60},\frac{42}{60},\frac{43}{60},\frac{44}{60} and \frac{45}{60}

\frac{41}{60}, \frac{7}{10},\frac{43}{60},\frac{11}{15} and \frac{3}{4}

 

(ii) \mathbf{-\frac{3}{2}} and \mathbf{\frac{5}{3}}
Let us make the denominators the same, say 6

-\frac{3}{2} = – \frac{3\times 3}{3\times 2} = – \frac{9}{6}

\frac{5}{3} = \frac{5\times 2}{3\times 2} = \frac{10}{6}

Five rational numbers between – \frac{9}{6} and \frac{10}{6} are
\frac{-7}{6}, \frac{-5}{6}, \frac{-1}{6}, \frac{1}{6} and \frac{5}{6}

(iii) \mathbf{\frac{1}{4}} and \mathbf{\frac{1}{2}}
Let us make the denominators the same, say 24

\frac{1}{4} = \frac{1\times 6}{4\times 6} = \frac{6}{24}

\frac{1}{2} = \frac{1\times 12}{2\times 12} = \frac{12}{24}

Five rational numbers between \frac{6}{24} and \frac{12}{24}

\frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24} and \frac{11}{24}

\frac{7}{24}, \frac{1}{3}, \frac{3}{8}, \frac{5}{12} and \frac{11}{24}

6. Write five rational numbers greater than -2.

Solution –  -2 can be written as – \frac{20}{10}
Hence, we can say that the five rational numbers greater than – 2 are
\frac{-19}{10},\frac{-11}{10}, \frac{-1}{10},\frac{1}{10} and \frac{3}{10}

7. Find ten rational numbers between \mathbf{\frac{3}{5}} and \frac{3}{4}.

Solution –  Let us make the denominators the same, say 80.

\frac{3}{5} = \frac{3\times 16}{5\times 16} = \frac{48}{80}

\frac{3}{4} = \frac{3\times 20}{4\times 20}  = \frac{60}{80}

Ten rational numbers between \frac{48}{80} and \frac{60}{80} are

\frac{49}{80},\frac{50}{80}, \frac{51}{80},\frac{52}{80},\frac{53}{80},\frac{54}{80},\frac{55}{80},\frac{56}{80},\frac{57}{80} and \frac{58}{80}

\frac{49}{80},\frac{5}{8},\frac{51}{80},\frac{13}{20},\frac{53}{80},\frac{27}{40},\frac{11}{16},\frac{7}{10},\frac{57}{80} and \frac{29}{40}

 

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