These NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Exercise 1.2
Question 1.
Represent these numbers on the number line:
(i) \(\frac{7}{4}\)
(ii) \(\frac{-5}{6}\)
Solution:
(i) \(\frac{7}{4}\)
We make 7 markings at distance of \(\frac{1}{4}\) each on the right of 0 and starting from 0, the seventh marking represents \(\frac{7}{4}\).
(ii) \(\frac{-5}{6}\)
We make 5 markings at distance of \(\frac{1}{6}\) each on the left of ‘0’ and starting from ‘0’, the fifth marking represents \(\frac{-5}{6}\)
Question 2.
Represent \(\frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11}\) on a number line.
Solution:
We make 9 markings at distance of \(\frac{1}{11}\) each on the left of ‘0’ and starting from ‘0’, the second marking represents \(\frac{-2}{11}\); the fifth marking represents \(\frac{-5}{11}\) and the ninth marking represents \(\frac{-9}{11}\).
The point A represents \(\frac{-2}{11}\), the point B represents \(\frac{-5}{11}\) and the point C represents \(\frac{-9}{11}\).
Question 3.
Write five rational numbers which are smaller than 2.
Solution:
There can be infinite rational numbers smaller than 2.
Five rational numbers 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:
Convert \(\frac{-2}{5}\) and \(\frac{1}{2}\) with the same denominators.
\(\frac{1}{2}=\frac{1 \times 5}{2 \times 5}=\frac{5}{10}\)
\(\frac{-2}{5}=\frac{2 \times 2}{5 \times 2}=\frac{-4}{10}\)
To get ten rational numbers, multiply both numerator and denominator by 2
\(\frac{5}{10}=\frac{5 \times 2}{10 \times 2}=\frac{10}{20}\)
\(\frac{-4}{10}=\frac{-4 \times 2}{10 \times 2}=\frac{-8}{20}\)
The rational numbers between \(\frac{10}{20}\) and \(\frac{-8}{20}\) are
\(\frac{9}{20}, \frac{8}{20}, \frac{7}{20}, \frac{6}{20}, \frac{5}{20}, \frac{4}{20}, \frac{3}{20}, \ldots \frac{-6}{20}, \frac{-7}{20}\)
We can take any 10 of them.
Question 5.
Find five rational numbers between
(i) \(\frac{2}{3}\) and \(\frac{4}{5}\)
(ii) \(\frac{-3}{2}\) and \(\frac{5}{3}\)
(iii) \(\frac{1}{4}\) and \(\frac{1}{2}\)
Solution:
Convert \(\frac{2}{3}\) and \(\frac{4}{5}\) with the same denominators
\(\frac{2}{3}=\frac{2 \times 5}{3 \times 5}=\frac{10}{15}\)
\(\frac{4}{5}=\frac{4 \times 3}{5 \times 3}=\frac{12}{15}\)
The difference between the numerators should be more than 5
\(\frac{10}{15}=\frac{10 \times 4}{15 \times 4}=\frac{40}{60}\)
\(\frac{12}{15}=\frac{12 \times 4}{15 \times 4}=\frac{48}{60}\)
Five rational numbers between \(\frac{40}{60}\) and \(\frac{48}{60}\) are
\(\frac{41}{60}, \frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60}\)
(ii) Convert \(\frac{-3}{2}\) and \(\frac{5}{3}\) with the same denominators.
\(\frac{-3}{2}=\frac{-3 \times 3}{2 \times 3}=\frac{-9}{6}\)
\(\frac{5}{3}=\frac{5 \times 2}{3 \times 2}=\frac{10}{6}\)
Five rational numbers between \(\frac{-9}{6}\) and \(\frac{10}{6}\) are \(\frac{9}{6}, \frac{8}{6}, \frac{7}{6}, 0, \frac{-7}{6}\)
(iii) Convert \(\frac{1}{4}\) and \(\frac{1}{2}\) with the same denominators
\(\frac{1}{4}=\frac{1}{4}\)
\(\frac{1}{2}=\frac{1 \times 2}{2 \times 2}=\frac{2}{4}\)
The difference between the numerators should be more than 5
\(\frac{1}{4}=\frac{1 \times 8}{4 \times 8}=\frac{8}{32}\)
\(\frac{2}{4}=\frac{2 \times 8}{4 \times 8}=\frac{16}{32}\)
Five rational numbers between \(\frac{8}{32}\) 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:
There are infinite rational numbers greater than -2.
The numbers are \(\frac{-3}{2},-1, \frac{-1}{2}, 0, \frac{1}{2}\)
Question 7.
Find ten rational numbers between \(\frac{3}{5}\) and \(\frac{3}{4}\).
Solution:
Convert \(\frac{3}{5}\) and \(\frac{3}{4}\) with the same denominators
\(\frac{3}{5}=\frac{3 \times 4}{5 \times 4}=\frac{12}{20}\)
\(\frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}\)
The difference between the numerator should be more than 10.
\(\frac{12}{20}=\frac{12 \times 8}{20 \times 8}=\frac{96}{160}\)
\(\frac{15}{20}=\frac{15 \times 8}{20 \times 8}=\frac{120}{160}\)
Thus, ten rational numbers between
