Oddiy kasrlar va ular ustida amallar bo‘yicha savol

Birinchi navbatda ichidagi har bir qavsni soddalashtiramiz. 1. $\displaystyle \frac{49}{9}-2=\frac{49}{9}-\frac{18}{9}= \frac{31}{9}$. 2. $1\frac{1}{3}= \frac{4}{3}$, shuning uchun $ \displaystyle 1\frac{1}{3}+\frac{7}{18}= \frac{4}{3}+\frac{7}{18}= \frac{24}{18}+\frac{7}{18}= \frac{31}{18}$. 3. $2\frac{1}{4}= \frac{9}{4}$, $3\frac{3}{4}= \frac{15}{4}$, demak $ \displaystyle 2\frac{1}{4}+3\frac{3}{4}= \frac{9}{4}+\frac{15}{4}= \frac{24}{4}=6$. 4. $3\frac{1}{3}= \frac{10}{3}$, shuning uchun $ \displaystyle 5-3\frac{1}{3}=5-\frac{10}{3}= \frac{15}{3}-\frac{10}{3}= \frac{5}{3}$. Endi ifodaning yuqori qismiga qaraymiz: \[ \frac{\frac{31}{9}}{\frac{31}{18}}= \frac{31}{9}\cdot\frac{18}{31}= \frac{18}{9}=2 . \] Pastki qism esa $6\cdot\frac{5}{3}= \frac{30}{3}=10$. Umumiy ifoda: \[ \frac{2}{10}= \frac{1}{5}. \] Shunday qilib, natija $\displaystyle \frac{1}{5}$, ya'ni variant **D**.