Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 1 Rational Numbers Ex 1.1Textbook Exercise Questions and Answers.
PSEB Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1
1. Represent these numbers on the number line:
Question (i).
\frac {7}{4}
Solution:
To represent \frac {7}{4}, make 7 markings each of a distance equal to \frac {1}{4} on the right side of 0. The 7th point represents the rational number \frac {7}{4}.
The point A is \frac {7}{4}.
Question (ii).
\frac {-5}{6}
Solution:
To represent (\frac {-5}{6}) on the number line, make 5 markings each of a distance equal to on the left side of 0. The 5th point represents the rational number (\frac {-5}{6}).
The point B is (\frac {-5}{6})
2. Represent \frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11} on the number line.
Solution:
To represent the given rational numbers on a number line, make 11 markings each being equal to distance \frac {1}{11} on the left of 0.
Here, the point A is (\frac {-2}{11}).
the point B is (\frac {-5}{11}).
the point C is (\frac {-9}{11}).
3. Write five rational numbers which are smaller than 2.
Solution:
There are infinite rational numbers below 2, positive as well as negative.
Five of them are 1, \frac {1}{3}, \frac {1}{4}, 0, – 1.
4. Find ten rational numbers between \frac {-2}{5} and \frac {1}{2}.
Solution:
First, convert \frac {-2}{5} and \frac {1}{2} having the same denominator, such that the difference between the numerators is more than 10.
\frac{-2}{5}=\frac{-2}{5} \times \frac{4}{4}=\frac{-8}{20};
\frac{1}{2}=\frac{1}{2} \times \frac{10}{10}=\frac{10}{20}
∴ The 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}, \ldots, 0, \frac{1}{20}, \ldots, \frac{9}{20} .
(There can be many more such rational numbers.)
5. Find five rational numbers between
Question (i).
\frac {2}{3} and \frac {4}{5}
Solution:
First, convert \frac {2}{3} and \frac {4}{5} having the same denominator, such that the difference between the numerators is more than 5.
\frac{2}{3}=\frac{2}{3} \times \frac{20}{20}=\frac{40}{60};
\frac{4}{5}=\frac{4}{5} \times \frac{12}{12}=\frac{48}{60}
∴ The five rational numbers between \frac {2}{3} and \frac {4}{5} are \frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60}, \frac{46}{60}.
Question (ii).
\frac {-3}{2} and \frac {5}{3}
Solution:
First, convert \frac {-3}{2} and \frac {5}{3} having the same denominator, such that the difference between the numerators is more than 5.
\frac{-3}{2}=\frac{-3}{2} \times \frac{3}{3}=\frac{-9}{6};
\frac{5}{3}=\frac{5}{3} \times \frac{2}{2}=\frac{10}{6}
∴ The five rational numbers between \frac {-3}{2} and \frac {5}{3} are \frac{-8}{6}, \frac{-7}{6}, 0, \frac{7}{6}, \frac{8}{6}.
Question (iii).
\frac {1}{4} and \frac {1}{2}
Solution:
First, convert \frac {1}{4} and \frac {1}{2} having the same denominator, such that the difference between the numerators is more than 5.
\frac{1}{4}=\frac{1}{4} \times \frac{8}{8}=\frac{8}{32};
\frac{1}{2}=\frac{1}{2} \times \frac{16}{16}=\frac{16}{32}
∴ The five rational numbers between \frac {1}{4} and \frac {1}{2} are \frac{10}{32}, \frac{11}{32}, \frac{12}{32}, \frac{13}{32}, \frac{14}{32}.
(There can be many more such rational numbers.)
[Note : You can write rational numbers of your choice.]
6. Write five rational numbers greater than -2.
Solution:
There can be many rational numbers greater than – 2. Five of them are \frac{-3}{2}, \frac{-1}{4}, 0, \frac{1}{2}, \frac{1}{5}.
7. Find ten rational numbers between \frac {3}{5} and \frac {3}{4}.
Solution:
First, convert \frac {3}{5} and \frac {3}{4} having the same denominator, such that the difference between the numerators is more than 10.
\frac{3}{5}=\frac{3}{5} \times \frac{20}{20}=\frac{60}{100};
\frac{3}{4}=\frac{3}{4} \times \frac{25}{25}=\frac{75}{100}
∴ The ten rational numbers between \frac {3}{5} and \frac {3}{4} are \frac{61}{100}, \frac{62}{100}, \frac{63}{100}, \frac{64}{100}, \frac{65}{100}, \frac{66}{100}, \frac{67}{100}, \frac{68}{100},\frac{69}{100}, \frac{70}{100}