Tag: rational numbers between two rational numbers

From the options, only $0$ can lie between $\dfrac {-5}{2}$ and $\dfrac {3}{4}.$

Clearly, $0$ and $-1$ cannot lie between $0$ and $-1$. 

When a positive integer is divided by another positive integer will yield a rational number

Required number $=$ $\dfrac{1}{2}\left(\dfrac{1}{5}+\dfrac{1}{3}\right)$

Converting the given fraction in decimal format we get $\frac { 1 }{ 3 } =0.33\quad and\quad \frac { 4 }{ 5 } =0.8$

To get the rational numbers between $\displaystyle\frac{2}{3}$ and $\displaystyle\frac{4}{5}$

Take an LCM of these two numbers: $\displaystyle\frac{10}{15}$ and $\displaystyle\frac{12}{15}$

Multiply numerator and denominator by 4: $\displaystyle\frac{40}{60}$ and $\displaystyle\frac{48}{60}$

All the numbers between $\displaystyle\frac{40}{60}$ and $\displaystyle\frac{48}{60}$ form the answer

Some of these numbers are $\displaystyle\frac{41}{60}$, $\displaystyle\frac{42}{60}$, $\displaystyle\frac{43}{60}$, $\displaystyle\frac{44}{60}$, $\displaystyle\frac{45}{60}$

$\dfrac{1}{3} = 0.3333.....$

Both given rational numbers are negative rational number. So, a rational number between both these rational numbers will be negative. But option B is a positive. So, option B will not lie between the given rational numbers. So, correct answer is option B.

To get the rational numbers between $\displaystyle\frac{1}{4}$ and $\displaystyle\frac{1}{2}$

Take an LCM of these two numbers: $\displaystyle\frac{1}{4}$ and $\displaystyle\frac{2}{4}$

Multiply numerator and denominator by 8: $\displaystyle\frac{8}{32}$ and $\displaystyle\frac{16}{32}$

All the numbers between $\displaystyle\frac{8}{32}$ and $\displaystyle\frac{16}{32}$ form the answer

Some of these numbers are $\displaystyle\frac{9}{32}$, $\displaystyle\frac{10}{32}$, $\displaystyle\frac{11}{32}$, $\displaystyle\frac{12}{32}$, $\displaystyle\frac{13}{32}$