Represent the rational numbersand 2/5, -5/4 and 11/2 on a single number line. Class 9

Represent the rational numbersand 2/5, -5/4 and 11/2 on a single number line. Class 9

Question 1.

Represent the rational numbersand $\frac{2}{3},-\frac{5}{4}$ and $1 \frac{1}{2}$ on a single number line. Class 9

Solution:

i. $\frac{2}{3}$ = 0.66...

It lies between 0 and 1. Divide the interval between 0 and 1 into 3 equal parts and move two parts to the right of 0.

ii. $-\frac{5}{4}$ = -1.25

It lies between -2 and -1. Divide the interval between -2 and - 1 into 4 equal parts and move one part to the left of - 1.

ii. $1 \frac{1}{2}=\frac{3}{2}$

It lies between 1 and 2. Divide the interval between 1 and 2 into 2 equal parts and move one part to the right of 1.

Question 2.

Find three distinct rational numbers that lie strictly between $-\frac{1}{2}$ and $\frac{1}{4}$. Class 9

Solution:

Rational numbers between a and b is $\frac{a+b}{2}$ .

∴ Rational number between $-\frac{1}{2}$ and $\frac{1}{4}$ is

$\frac{-\frac{1}{2}+\frac{1}{4}}{2}=\frac{-\frac{2}{4}+\frac{1}{4}}{2}=\frac{-\frac{1}{4}}{2}=-\frac{1}{8}$

First rational number = $-\frac{1}{8}$

Rational number between $-\frac{1}{2}$ and $-\frac{1}{8}$ is

$\frac{-\frac{1}{2}+\left(-\frac{1}{8}\right)}{2}=\frac{-\frac{4}{8}-\frac{1}{8}}{2}=\frac{-\frac{5}{8}}{2}=-\frac{5}{16}$

Second rational number = $-\frac{5}{16}$

Next, Rational number between $-\frac{1}{8}$ and $\frac{1}{4}$ is

$\frac{-\frac{1}{8}+\frac{1}{4}}{2}=\frac{-\frac{1}{8}+\frac{2}{8}}{2}=\frac{\frac{1}{8}}{2}=\frac{1}{16}$

∴ Third rational number = $\frac{1}{16}$

∴ Three rational numbers between $-\frac{1}{2}$ and $\frac{1}{4}$ are $-\frac{5}{16},-\frac{1}{8}, \frac{1}{16}$