(3/4-1/3)2/3/(1-frac{1{6})div5}*3+frac{frac{frac{2}{3}+frac{1}{2}}{frac{1}{2}-frac{2}{5}}}{2} eching

$$\frac { ( \frac { 3 } { 4 } - \frac { 1 } { 3 } ) \frac { 2 } { 3 } } { ( 1 - \frac { 1 } { 6 } ) \div 5 } \times 3 + \frac { \frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 1 } { 2 } - \frac { 2 } { 5 } } } { 2 }$$

Baholash

$$\frac{65}{6}\approx 10,833333333$$

Yechim qadamlari

4 va 3 ning eng kichik umumiy karralisi 12 ga teng. \frac{3}{4} va \frac{1}{3} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\left(\frac{9}{12}-\frac{4}{12}\right)\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{9}{12} va \frac{4}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{9-4}{12}\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

5 olish uchun 9 dan 4 ni ayirish.

$$\frac{\frac{5}{12}\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{12} ni \frac{2}{3} ga ko‘paytiring.

$$\frac{\frac{5\times 2}{12\times 3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{5\times 2}{12\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{10}{36}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{10}{36} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{5}{18}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

1 ni \frac{6}{6} kasrga o‘giring.

$$\frac{\frac{5}{18}}{\frac{\frac{6}{6}-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{6}{6} va \frac{1}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{5}{18}}{\frac{\frac{6-1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

5 olish uchun 6 dan 1 ni ayirish.

$$\frac{\frac{5}{18}}{\frac{\frac{5}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{\frac{5}{6}}{5} ni yagona kasrga aylantiring.

$$\frac{\frac{5}{18}}{\frac{5}{6\times 5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{\frac{5}{18}}{\frac{1}{6}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{5}{18} ni \frac{1}{6} ga bo'lish \frac{5}{18} ga k'paytirish \frac{1}{6} ga qaytarish.

$$\frac{5}{18}\times 6\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{5}{18}\times 6 ni yagona kasrga aylantiring.

$$\frac{5\times 6}{18}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

30 hosil qilish uchun 5 va 6 ni ko'paytirish.

$$\frac{30}{18}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{30}{18} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

3 va 3 ni qisqartiring.

$$5+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2} ni yagona kasrga aylantiring.

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

3 va 2 ning eng kichik umumiy karralisi 6 ga teng. \frac{2}{3} va \frac{1}{2} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$5+\frac{\frac{4}{6}+\frac{3}{6}}{\left(\frac{1}{2}-\frac{2}{5}\right)\times 2}$$

\frac{4}{6} va \frac{3}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$5+\frac{\frac{4+3}{6}}{\left(\frac{1}{2}-\frac{2}{5}\right)\times 2}$$

7 olish uchun 4 va 3'ni qo'shing.

$$5+\frac{\frac{7}{6}}{\left(\frac{1}{2}-\frac{2}{5}\right)\times 2}$$

2 va 5 ning eng kichik umumiy karralisi 10 ga teng. \frac{1}{2} va \frac{2}{5} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$5+\frac{\frac{7}{6}}{\left(\frac{5}{10}-\frac{4}{10}\right)\times 2}$$

\frac{5}{10} va \frac{4}{10} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$5+\frac{\frac{7}{6}}{\frac{5-4}{10}\times 2}$$

1 olish uchun 5 dan 4 ni ayirish.

$$5+\frac{\frac{7}{6}}{\frac{1}{10}\times 2}$$

\frac{2}{10} hosil qilish uchun \frac{1}{10} va 2 ni ko'paytirish.

$$5+\frac{\frac{7}{6}}{\frac{2}{10}}$$

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

$$5+\frac{\frac{7}{6}}{\frac{1}{5}}$$

\frac{7}{6} ni \frac{1}{5} ga bo'lish \frac{7}{6} ga k'paytirish \frac{1}{5} ga qaytarish.

$$5+\frac{7}{6}\times 5$$

\frac{7}{6}\times 5 ni yagona kasrga aylantiring.

$$5+\frac{7\times 5}{6}$$

35 hosil qilish uchun 7 va 5 ni ko'paytirish.

$$5+\frac{35}{6}$$

5 ni \frac{30}{6} kasrga o‘giring.

$$\frac{30}{6}+\frac{35}{6}$$

\frac{30}{6} va \frac{35}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{30+35}{6}$$

65 olish uchun 30 va 35'ni qo'shing.

$$\frac{65}{6}$$

Omil

$$\frac{5 \cdot 13}{2 \cdot 3} = 10\frac{5}{6} = 10,833333333333334$$