$\text{Ta có:}$

$\text{$\dfrac{1}{2}$ = $\dfrac{1 x 4 x 3}{2 x 4 x 3}$ = $\dfrac{12}{24}$}$

$\text{$\dfrac{3}{a}$ = $\dfrac{3 x 1 x 4}{a x 1 x 4}$ = $\dfrac{12}{a x 1 x 4}$}$

$\text{$\dfrac{4}{5}$ = $\dfrac{4 x 3 x 1}{5 x 3 x 1}$ = $\dfrac{12}{15}$}$

$\text{⇒ $\dfrac{12}{24}$ < $\dfrac{12}{a x 1 x 4}$ < $\dfrac{12}{15}$}$

$\text{a x 1 x 4 ∈ {23; 22; 21; 20; 19; 18; 17; 16}}$

$\text{Vì a là số tự nhiên nên a x 1 x 4 ∈ {B(4)}}$

Vậy a x 1 x 4 ∈ {20; 16)

$\text{TH1:}$

$\text{a x 1 x 4 = 20}$

$\text{a = 20 : 4 : 1}$

$\text{a = 5}$

$\text{TH2:}$

$\text{a x 1 x 4 = 16}$

$\text{a = 16 : 4 : 1}$

$\text{a = 4}$

$\text{⇒ a ∈ {4, 5}}$

$\text{Chúc bạn học tốt nha!}$

`@Lynh`

Đáp án :$\textit{a=10}$

Giải thích :

`1/2` = `1.5/2.5` = `5/10`

`4/5` = `4.3/5.2`=`12/10`

⇒ $\textit{a= 10}$