Question

find ten rational number between
2/5 and 3/4​

Answer 1

☆ Solution ☆

Given :-

• $\frac{2}{5}$ and $\frac{3}{4}$

To Find :-

• Ten rational number.

Step-by-Step-Explaination :-

LCM of 5 and 4 is 20

Now, $\frac{2}{5}$ = $\frac{2}{5}$ × $\frac{2}{5}$ = $\frac{4}{20}$ and

$\frac{3}{4}$ = $\frac{3}{4}$× $\frac{5}{5}$ = $\frac{15}{20}$

Since, there is five integer between 8 and 15.

Therefore, we replace $\frac{2}{5}$ and $\frac{3}{4}$ by equivalent rational number having sufficient large common denominator i.e.,

$\frac{2}{5}$ = $\frac{8}{20}$ × $\frac{8}{8}$ = $\frac{64}{160}$ and

$\frac{3}{4}$ = $\frac{15}{20}$ × $\frac{8}{8}$ = $\frac{120}{160}$

Therefore, integers 65, 66,....................., 119 lie between 64 and 120.

$\frac{65}{160}$ < $\frac{66}{160}$ < $\frac{67}{160}$ < $\frac{68}{160}$ ........ < $\frac{120}{160}$

Therefore, ten rational number between $\frac{2}{5}$ and $\frac{3}{4}$ are

$\frac{65}{160}$ < $\frac{66}{160}$ < $\frac{67}{160}$ < $\frac{68}{160}$ < $\frac{69}{160}$ < $\frac{70}{160}$ < $\frac{71}{160}$ < $\frac{72}{160}$

< $\frac{73}{160}$ < $\frac{74}{160}$ < $\frac{75}{160}$.

( Take any ten rational numbers )

Answer 2

Step-by-step explanation:

l.c.m of 5 and 4 is 20.

$\frac{2 \times 4}{5 \times 4} = \frac{8}{20} \\ \\ \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \\ \\ \\ \\ \\ \frac{8 \times 10}{20 \times 10} = \frac{80}{200} \\ \\ \\ \\ \frac{15 \times 10}{20 \times 10} = \frac{150}{200} \\ \\ \\ \\ \\ \\ ten \: rational \: nos \: are \\ \\ \frac{81}{200} < \frac{82}{200} < \frac{83}{200} < \frac{84}{200} < \frac{85}{200} < \frac{86}{200} < \frac{87}{200} < \frac{88}{200} < \frac{89}{200} < \frac{90}{200}$