Question

find five rational no. between 1 and 5 with solution

Answer 1

There are two methods to solve the given problem :

• Converting the numbers in form of like fractions
• Using the formula : $\tt{ d = \dfrac{y - x }{n + 1}}$

Conversion in the form of like fraction :

Like fractions are the fractions with same denominators.

Eg : $\tt{ \dfrac{2}{7} and \dfrac{8}{7}}$

We cancel the given problem by converting the given numbers into like fractions. So , multiply both numbers with same numerator and denominator.

Note : The number to be multiplied must be more than the number of rational numbers we have to find between.

So , we will take 10 for instance.

$\longrightarrow{\tt{ \dfrac{1}{1} \times \dfrac{10}{10} \implies \dfrac{10}{10}}}$

$\longrightarrow{\tt{\dfrac{5}{1} \times \dfrac{10}{10} \implies \dfrac{50}{10}}}$

$\longrightarrow{\tt{\dfrac{10}{10} and \dfrac{50}{10}}}$

So , now we can choose any 5 rationals between $\tt{ \dfrac{10}{10} and \dfrac{50}{10}}$

For instance :

$\tt{ \dfrac{11}{10} , \dfrac{23}{10} , \dfrac{30}{10} , \dfrac{38}{10} , \dfrac{49}{10}}$

Using the formula :

$\tt{ \dfrac{y - x}{n + 1}}$

$\tt{ y = 5}$ Y is the highest term.

$\tt{x = 1}$ X is the lowest term.

X must be subtracted from Y .

$\tt{ n = 5}$ N is the number of terms to be found.

N must be added with 1.

So , we will use this formula also :

$\longrightarrow{\tt{\dfrac{5 - 1}{5 + 1}}}$

$\longrightarrow{\tt{ d = \dfrac{4}{6}}}$

So the rationals between 1 and 5 are (x + d) (x + 2d) (x + 3d) (x + 4d) (x + 5d)

When value of (d) is put up as (4/6) :

$\tt{ 1 + \dfrac{4}{6} => \dfrac{10}{6}}$

$\tt{ 1 + \dfrac{2 \times 4}{6} => \dfrac{14}{6}}$

$\tt{ 1 + \dfrac{3 \times 4}{6} => \dfrac{18}{6}}$

$\tt{1 + \dfrac{4 \times 4}{6} => \dfrac{22}{6}}$

$\tt{1 + \dfrac{5 \times 4}{6} => \dfrac{26}{6}}$