Question

Select the rational numbers which lie between $\frac{3}{4}$ and $\frac{5}{6}$

• A. $\frac{19}{20},\frac{23}{20},\frac{27}{20},\frac{31}{20}$
• B. $\frac{19}{15},\frac{23}{10},\frac{27}{20},\frac{31}{20}$
• C. $\frac{19}{15},\frac{23}{25},\frac{27}{2},\frac{31}{15}$
• D. $\frac{19}{25},\frac{23}{25},\frac{27}{25},\frac{31}{25}$

Answer 1

The correct option is A

$\frac{19}{20},\frac{23}{20},\frac{27}{20},\frac{31}{20}$

We know that $\frac{3}{4}<\frac{5}{6}$

So, let $x=\frac{3}{4}$ and $y=\frac{5}{6}$ and take $n=4$ so that we can find 4 different rational numbers.

We have $d=\frac{y-x}{n+1}=\frac{\frac{5}{6}-\frac{3}{4}}{4+1}=\frac{1}{5}$

So, the numbers are $x+d,x+2d,x+3d,x+4d$

$=\frac{3}{4}+\frac{1}{5},\frac{3}{4}+\frac{2}{5},\frac{3}{4}+\frac{3}{5},\frac{3}{4}+\frac{4}{5}$

$=\frac{19}{20},\frac{23}{20},\frac{27}{20},\frac{31}{20}$