52/3-31/3div22/3*4/5+2frac{1}{5}div2frac{3}{4} eching

$$5 \frac { 2 } { 3 } - 3 \frac { 1 } { 3 } \div 2 \frac { 2 } { 3 } \times \frac { 4 } { 5 } + 2 \frac { 1 } { 5 } \div 2 \frac { 3 } { 4 }$$

Baholash

$$\frac{82}{15}\approx 5,466666667$$

Yechim qadamlari

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$\frac{15+2}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

17 olish uchun 15 va 2'ni qo'shing.

$$\frac{17}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

\frac{3\times 3+1}{3} ni \frac{2\times 3+2}{3} ga bo'lish \frac{3\times 3+1}{3} ga k'paytirish \frac{2\times 3+2}{3} ga qaytarish.

$$\frac{17}{3}-\frac{\left(3\times 3+1\right)\times 3}{3\left(2\times 3+2\right)}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{17}{3}-\frac{1+3\times 3}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$\frac{17}{3}-\frac{1+9}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

10 olish uchun 1 va 9'ni qo'shing.

$$\frac{17}{3}-\frac{10}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{17}{3}-\frac{10}{2+6}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

8 olish uchun 2 va 6'ni qo'shing.

$$\frac{17}{3}-\frac{10}{8}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

\frac{10}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{17}{3}-\frac{5}{4}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

\frac{5}{4} va uning teskari kasrini \frac{4}{5} ni qisqartiring.

$$\frac{17}{3}-1+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{17}{3}-\frac{3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

\frac{17}{3} va \frac{3}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{17-3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

14 olish uchun 17 dan 3 ni ayirish.

$$\frac{14}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

\frac{2\times 5+1}{5} ni \frac{2\times 4+3}{4} ga bo'lish \frac{2\times 5+1}{5} ga k'paytirish \frac{2\times 4+3}{4} ga qaytarish.

$$\frac{14}{3}+\frac{\left(2\times 5+1\right)\times 4}{5\left(2\times 4+3\right)}$$

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$\frac{14}{3}+\frac{\left(10+1\right)\times 4}{5\left(2\times 4+3\right)}$$

11 olish uchun 10 va 1'ni qo'shing.

$$\frac{14}{3}+\frac{11\times 4}{5\left(2\times 4+3\right)}$$

44 hosil qilish uchun 11 va 4 ni ko'paytirish.

$$\frac{14}{3}+\frac{44}{5\left(2\times 4+3\right)}$$

8 hosil qilish uchun 2 va 4 ni ko'paytirish.

$$\frac{14}{3}+\frac{44}{5\left(8+3\right)}$$

11 olish uchun 8 va 3'ni qo'shing.

$$\frac{14}{3}+\frac{44}{5\times 11}$$

55 hosil qilish uchun 5 va 11 ni ko'paytirish.

$$\frac{14}{3}+\frac{44}{55}$$

\frac{44}{55} ulushini 11 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{14}{3}+\frac{4}{5}$$

3 va 5 ning eng kichik umumiy karralisi 15 ga teng. \frac{14}{3} va \frac{4}{5} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{70}{15}+\frac{12}{15}$$

\frac{70}{15} va \frac{12}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{70+12}{15}$$

82 olish uchun 70 va 12'ni qo'shing.

$$\frac{82}{15}$$

Omil

$$\frac{2 \cdot 41}{3 \cdot 5} = 5\frac{7}{15} = 5,466666666666667$$