Answer :
Step-by-step explanation:
In this problem, we need to find three rational numbers between 7/12 and 7/11.
First rational no :
[tex]c=\dfrac{\dfrac{7}{12}+\dfrac{7}{11}}{2}\\\\c=\dfrac{161}{264}[/tex]
Second rational no :
[tex]d=\dfrac{\dfrac{7}{12}+\dfrac{161}{254}}{2}\\\\d=\dfrac{1855}{3048}[/tex]
Rational number are numbers that can be represented as a fraction of two integers
Three rational numbers between [tex]\frac{7}{12}[/tex] and [tex]\frac{7}{11}[/tex] are: [tex]\frac{21}{34}, \frac{14}{23}, \frac{3}{5}[/tex]
The numbers are given as: [tex]\frac{7}{12}[/tex] and [tex]\frac{7}{11}[/tex]
Rewrite the numbers as:
[tex]\frac{7}{12} = \frac{7}{12} \times \frac 66[/tex]
[tex]\frac{7}{12} = \frac{42}{72}[/tex]
and
[tex]\frac{7}{11} = \frac{7}{11} \times \frac 66[/tex]
[tex]\frac{7}{11} = \frac{42}{66}[/tex]
The rational numbers between them will have the same numerator (i.e. 42), and a denominator between 66 and 72
So, we have:
[tex]x = \frac{42}{68}, \frac{42}{69}, \frac{42}{70}[/tex]
Reduce fractions
[tex]x = \frac{21}{34}, \frac{14}{23}, \frac{3}{5}[/tex]
Hence, three rational numbers between [tex]\frac{7}{12}[/tex] and [tex]\frac{7}{11}[/tex] are: [tex]\frac{21}{34}, \frac{14}{23}, \frac{3}{5}[/tex]
Read more about rational numbers at:
https://brainly.com/question/15815501