Question

find two rational number between--4/3and1/2
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Answer 1

$\huge{\bf{\underline{\red{Solution :}}}}$

⇒There are two method which help to we find easily Rational Number :

1. Denominator same Method .
2. Divide by 2 and addition method

$\rule{200}2$

We Use the method - 2)

Steps :

1. Add the Given Rational Number
2. Divide the sum by 2
3. Take one of the given rational number and add it to the result obtained in step 2) like again add and divide by 2.
4. Repeat step 3) for finding more Rational Numbers .

Now we follow these steps and Find Rational Numbers :

$\implies \bold{ Formula :- \frac{a + b}{2}}$

First Rational Number Find - :

$\implies \bold{\frac{\frac{-4}{3} + \frac{1}{2} }{2}}$

$\implies \bold{\frac{\frac{-8 + 3}{6} }{2}}$

$\implies \boxed{\bold{\frac{-5}{12}}}$

Second Rational Number Find :

$\implies \bold{\frac{\frac{-5}{12} + \frac{1}{2} }{2}}$

$\implies \bold{\frac{\frac{-10 + 3}{6} }{2}}$

$\implies \boxed{\bold{\frac{-7}{12}}}$

Third Rational Number Find :

$\implies \bold{\frac{\frac{-7}{12} + \frac{1}{2} }{2}}$

$\implies \bold{\frac{\frac{-14 + 3} {6} }{2}}$

$\implies \boxed{\bold{\frac{-11}{12}}}$

$\rule{200}2$

Rational Number :

• A number that can be expressed in the form of p/q where p and q are integers and q ≠ 0 is called Rational Number .
• Every Natural Number is a Rational Number .
• Zero is also a rational Number as we can write in the form of 0/1
• Every integers is a Rational Number .
• Every fraction is Rational Number .

Answer 2

First method :

Make the denominator same :

L. C. M of 3 and 2 is 6

$\frac{ - 4}{3} = \frac{ - 4 \times 2}{3 \times 2} = \frac{ - 8}{6}$

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

Two rational number between -4/3 and 1/2 are :

-4/6 and -5/6

Second method :

By using formula = $\frac{a + b}{2}$

First number :

a = -4/3 and b = 1/2

=> $\frac{ \frac{ - 4}{3} + \frac{1}{2} }{2}$

=> $\frac{ \frac{ - 8 + 3}{6} }{2}$

=> $\frac{ - 5}{12}$

Second number :

a = -5/12 and b = 1/2

=> $\frac{ \frac{ - 5}{12} + \frac{1}{2} }{2}$

=> $\frac{ \frac{ - 5 + 6}{12} }{2}$

=> $\frac{1}{24}$

There can be infinite rational number between any two given rational number.