Question

find rational no. between 3/8 2/5

Answer 1

We have been asked to find rational numbers between $\tt{\dfrac{3}{8}\: and \: \dfrac{2}{5}}$ . For this we will follow the given steps :

• Make the given fractions into like fractions by taking their LCM.
• Multiplying the fractions with a same number with both the numerator and the denominator.
• Then we can easily get many rational numbers between two given ones.

So following the above steps ; we will solve :

$\longrightarrow{\tt{ \dfrac{3}{8} and\: \dfrac{2}{5}}}$

LCM of 8 and 5 :

$\boxed{\begin{array} {c | c } 2 & 8 , 5 \\\cline{1-2} 2 & 4 , 5 \\\cline{1-2} 2 & 2 , 5 \\\cline{1-2} 5 & 1 , 5\\\cline{1-2} & 1 , 1\end{array}}$

So the LCM = 40

$\tt{ \dfrac{3 \times 5}{8 \times 5} = \dfrac{15}{40}}$

$\tt{\dfrac{2 \times 8}{5 \times 8} = \dfrac{16}{40}}$

So the numbers we have got after taking the LCM are :

$\tt{\dfrac{15}{40} and\: \dfrac{16}{40}}$

Now following the second step ; we will multiply both the numerator and denominator of both the rationals with same number. Let's take 10.

$\longrightarrow{\tt{ \dfrac{15 \times 10}{40 \times 10} = \dfrac{150}{400}}}$

$\longrightarrow{\tt{ \dfrac{16 \times 10}{10 \times 10} = \dfrac{160}{400}}}$

So now we can take any rationals between :

$\longrightarrow{\tt{ \dfrac{150}{400} and\: \dfrac{160}{400}}}$

For assumption we can take :

• $\tt{\dfrac{158}{400}}$

• $\tt{\dfrac{159}{400}}$

• $\tt{\dfrac{151}{400}}$

• $\tt{\dfrac{152}{400}}$

• $\tt{\dfrac{153}{400}}$