Rational Numbers
\( \mathrm{N} \cdot 27 \)
14. From a \( 62 \frac{1}{2}-\mathrm{m} \)-long rope a piece of length \( 15 \frac{1}{5} \mathrm{~m} \) is cut off. The rest of the rope is divided into 11 equal pleces. Find the length of each equal plece.
1. \( 7 \frac{17}{20} \mathrm{~m} \)
2. \( 18 \frac{19}{20} \mathrm{~kg} \)
ANSWERS
5. ? \( 189 \frac{1}{10} \)
6. \( 110 \frac{1}{2} \mathrm{~km} \)
9. \( 1718 \frac{1}{4} \mathrm{~m}^{2} \)
10. \( 7 \frac{1}{5} \mathrm{~h} \)
3. \( 8 \frac{1}{10} \mathrm{~kg} \)
4. ? \( ? \frac{3}{10} \)
13. \( \frac{36}{5} \)
14. \( 4 \frac{3}{10} \mathrm{~m} \)
7. \( 254 \frac{1}{10} \mathrm{~km} \)
\( 8.17 \frac{16}{25} \mathrm{~m}^{2} \)
11. \( 1 \frac{1}{4} \mathrm{~m} \)
12. \( \frac{105}{4} \)
Representation of Rational Numbers on the Number Line
You are already familiar with the representation of rational numbers on the number line. Let us review what you have learnt in the previous class.
Draw a straight line and take a point \( O \) on the number line. Mark points \( A, B \), \( C, D, E \), etc., at equal distances on the right of the point \( O \).
Also, mark points \( A^{\prime}, B^{\prime}, C^{\prime}, D^{\prime}, E^{\prime} \), etc., at the same equal distances on the left of the point \( O \).
Let the points \( O, A, B, C, D, E \), etc., denote the integers \( 0,1,2,3,4,5 \), etc.. respectively. Similarly, the points \( A^{\prime}, B^{\prime}, C^{\prime}, D^{\prime}, E^{\prime} \), etc., denote the integers \( -1,-2,-3,-4,-5 \), etc., respectively.
Thus, all the integers, which are rational numbers too, can be representec on the number line.
EXAMPLE Represent the rational numbers \( \pm \frac{1}{4}, \pm \frac{1}{2} \) and \( \pm \frac{3}{4} \) on the number line.
Solution Let the points \( O, A \) and \( A^{\prime} \) represent respectively 0,1 and -1 on the number li
\[
\begin{array}{l}
\xrightarrow{\begin{array}{rrrrrrrrrrr}
& \frac{-3}{4} & -\frac{1}{2} & \frac{-1}{4} & 0 & \frac{1}{4} & \frac{1}{2} & \frac{3}{4} & 1 \\
\hline
\end{array}} \\
P Q=Q R=R A=\frac{1}{4} O A . \\
\end{array}
\]
