You can Download KSEEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2 Questions and Answers helps you to revise the complete syllabus.
KSEEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.2
Question 1.
Represent these numbers on the number line.
(i) \(\frac{7}{4}\)
(ii) \(\frac{-5}{6}\)
Solution:
Question 2.
Represent \(\frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11}\) on the number line.
Solution:
Question 3.
Write five rational numbers which are smaller than 2.
Solution:
Five rational numbers smaller than 2 are 1, 0, \(\frac{-1}{2}\), -1, -2 (In this way infinite numbers can be written)
Question 4.
Find ten rational numbers between \(\frac{-2}{5}\) and \(\frac{1}{2}\)
Solution:
\(\frac{-2}{5}\) and \(\frac{1}{2}\)
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:
(i) \(\frac{2}{3}=\frac{2}{3} \times \frac{5}{5}=\frac{10}{15}=\frac{30}{45}\)
\(\frac{4}{5}=\frac{4}{5} \times \frac{3}{3}=\frac{12}{15}=\frac{36}{45}\)
So, five rational numbers between \(\frac{30}{45}\) and \(\frac{36}{45}\) are \(\frac{31}{45}, \frac{32}{45}, \frac{33}{45}, \frac{34}{45}, \frac{35}{45}\)
(ii) \(\frac{-3}{2}=\frac{-3 \times 3}{2 \times 3}=\frac{-9}{6}\)
\(\frac{5}{3}=\frac{5}{3} \times \frac{2}{2}=\frac{10}{6}\)
So, five rational numbers between \(\frac{-9}{6}\) and \(\frac{10}{6}\) are \(\frac{-8}{6}, \frac{-7}{6}, \frac{-6}{6}, \frac{1}{6}, \frac{2}{6}, \ldots \frac{9}{6}\) (Any five can be written)
(iii) \(\frac{1}{4}\) and \(\frac{1}{2}\)
\(\frac{1}{4}=\frac{1}{4} \times \frac{2}{2}=\frac{2}{8} \times \frac{5}{5}=\frac{10}{40}\)
\(\frac{1}{2}=\frac{1}{2} \times \frac{4}{4}=\frac{4}{8} \times \frac{5}{5}=\frac{20}{40}\)
So, five rational numbers between \(\frac{10}{40}\) and \(\frac{20}{40}\) are \(\frac{11}{40}, \frac{12}{40}, \frac{13}{40}, \frac{14}{40}, \frac{15}{40} \ldots \ldots \ldots\)
Question 6.
Write five rational numbers greater than -2.
Solution:
Five rational numbers greater than -2 are -1, 0, 1, 2, 3, 4 (or many more)
Question 7.
Find ten rational numbers between \(\frac{3}{5}\) and \(\frac{3}{4}\).
Solution:
\(\frac{3}{5}\) and \(\frac{3}{4}\)
\(\frac{3}{5} \times \frac{4}{4}=\frac{12}{20}=\frac{12}{20} \times \frac{5}{5}=\frac{60}{100}\)
\(\frac{3}{4} \times \frac{5}{5}=\frac{15}{20}=\frac{15}{20} \times \frac{5}{5}=\frac{75}{100}\)
ten rational numbers between \(\frac{60}{100}\) and \(\frac{75}{100}\) are \(\frac{61}{100}, \frac{62}{100}, \frac{63}{100} \ldots \ldots . . \frac{74}{100}\) (Out of these any ten can be taken)