Question

find five rational numbers between 1/2and 6/7

Answer 1

Rational numbers are those numbers which are in the form of $\dfrac{m}{n}$, where m and n are integers and where n ≠ 0 because n is the denominator and the denominator cannot be 0. Example : $\dfrac{8}{5} , \dfrac{3}{7} , \dfrac{2}{1}$ which is 2.


Now coming to your question :-

Find five rational numbers between $\dfrac{1}{2}$ and $\dfrac{6}{7}$

$\boxed{\boxed{\tt{Solution :- }}}$

We can see that the denominators are not equal and also they do not occur in one table except 1 and the number itself.

So, we will cross multiply the fraction.

$\dfrac{1 * 14}{2 * 14}$ and $\dfrac{6 * 14}{7 * 14}$

➾ $\dfrac{14}{28}$ and $\dfrac{84}{14}$


∴ The five rational numbers between $\dfrac{14}{28}$ and $\dfrac{84}{14}$
are :-

$\dfrac{15}{28}$, $\dfrac{65}{28}$, $\dfrac{50}{28}$, $\dfrac{19}{28}$ and $\dfrac{80}{28}$


$\large{\boxed{\boxed{\tt{Thanks}}}}$

Answer 2

Question :

find five rational numbers between 1/2and 6/7.

Solution :

First of all make their denominators same :

$\frac{1}{2} \times \frac{7}{7} = \frac{7}{14} \\ \\ \frac{6}{7} \times \frac{2}{2} = \frac{12}{14}$

But still we can insert only 4 numbers between them.

So , Multiply both the numbers by 10 (Both Numerator and Denominator) :

$\frac{70}{140} \: and \: \frac{120}{140} \\ \\ five \: rational \: numbers \: = \\ \\ \: \frac{71}{140} \\ \\ \frac{72}{140} \\ \\ \frac{73}{140} \\ \\ \frac{74}{140} \\ \\ \frac{75}{140}$