operatorname{le}(1-2/5)*((1/2+1/3-1/4)*(frac{1}{2}-frac{1}{13})+frac{3}{4}:frac{9}{2}] eching

$$\operatorname { le } ( 1 - \frac { 2 } { 5 } ) \cdot ( ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } ) \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 13 } ) + \frac { 3 } { 4 } : \frac { 9 } { 2 } ]$$

Baholash

$$\frac{129el}{520}$$

Yechim qadamlari

1 ni \frac{5}{5} kasrga o‘giring.

$$le\left(\frac{5}{5}-\frac{2}{5}\right)\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{5}{5} va \frac{2}{5} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$le\times \frac{5-2}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

3 olish uchun 5 dan 2 ni ayirish.

$$le\times \frac{3}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$le\times \frac{3}{5}\left(\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{3}{6} va \frac{2}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$le\times \frac{3}{5}\left(\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

5 olish uchun 3 va 2'ni qo'shing.

$$le\times \frac{3}{5}\left(\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

6 va 4 ning eng kichik umumiy karralisi 12 ga teng. \frac{5}{6} va \frac{1}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$le\times \frac{3}{5}\left(\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{10}{12} va \frac{3}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$le\times \frac{3}{5}\left(\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

7 olish uchun 10 dan 3 ni ayirish.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

2 va 13 ning eng kichik umumiy karralisi 26 ga teng. \frac{1}{2} va \frac{1}{13} ni 26 maxraj bilan kasrlarga aylantirib oling.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{13}{26} va \frac{2}{26} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

11 olish uchun 13 dan 2 ni ayirish.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{11}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{12} ni \frac{11}{26} ga ko‘paytiring.

$$le\times \frac{3}{5}\left(\frac{7\times 11}{12\times 26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{7\times 11}{12\times 26} kasridagi ko‘paytirishlarni bajaring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{3}{4} ni \frac{9}{2} ga bo'lish \frac{3}{4} ga k'paytirish \frac{9}{2} ga qaytarish.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3}{4}\times \frac{2}{9}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{4} ni \frac{2}{9} ga ko‘paytiring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3\times 2}{4\times 9}\right)$$

\frac{3\times 2}{4\times 9} kasridagi ko‘paytirishlarni bajaring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{6}{36}\right)$$

\frac{6}{36} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{1}{6}\right)$$

312 va 6 ning eng kichik umumiy karralisi 312 ga teng. \frac{77}{312} va \frac{1}{6} ni 312 maxraj bilan kasrlarga aylantirib oling.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{52}{312}\right)$$

\frac{77}{312} va \frac{52}{312} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$le\times \frac{3}{5}\times \frac{77+52}{312}$$

129 olish uchun 77 va 52'ni qo'shing.

$$le\times \frac{3}{5}\times \frac{129}{312}$$

\frac{129}{312} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$le\times \frac{3}{5}\times \frac{43}{104}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{5} ni \frac{43}{104} ga ko‘paytiring.

$$le\times \frac{3\times 43}{5\times 104}$$

\frac{3\times 43}{5\times 104} kasridagi ko‘paytirishlarni bajaring.

$$le\times \frac{129}{520}$$

Kengaytirish

$$\frac{129el}{520}$$

Yechim qadamlari

1 ni \frac{5}{5} kasrga o‘giring.

$$le\left(\frac{5}{5}-\frac{2}{5}\right)\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{5}{5} va \frac{2}{5} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$le\times \frac{5-2}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

3 olish uchun 5 dan 2 ni ayirish.

$$le\times \frac{3}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$le\times \frac{3}{5}\left(\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{3}{6} va \frac{2}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$le\times \frac{3}{5}\left(\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

5 olish uchun 3 va 2'ni qo'shing.

$$le\times \frac{3}{5}\left(\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

6 va 4 ning eng kichik umumiy karralisi 12 ga teng. \frac{5}{6} va \frac{1}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$le\times \frac{3}{5}\left(\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{10}{12} va \frac{3}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$le\times \frac{3}{5}\left(\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

7 olish uchun 10 dan 3 ni ayirish.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

2 va 13 ning eng kichik umumiy karralisi 26 ga teng. \frac{1}{2} va \frac{1}{13} ni 26 maxraj bilan kasrlarga aylantirib oling.

$$le\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{13}{26} va \frac{2}{26} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

11 olish uchun 13 dan 2 ni ayirish.

$$le\times \frac{3}{5}\left(\frac{7}{12}\times \frac{11}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{12} ni \frac{11}{26} ga ko‘paytiring.

$$le\times \frac{3}{5}\left(\frac{7\times 11}{12\times 26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{7\times 11}{12\times 26} kasridagi ko‘paytirishlarni bajaring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

\frac{3}{4} ni \frac{9}{2} ga bo'lish \frac{3}{4} ga k'paytirish \frac{9}{2} ga qaytarish.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3}{4}\times \frac{2}{9}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{4} ni \frac{2}{9} ga ko‘paytiring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{3\times 2}{4\times 9}\right)$$

\frac{3\times 2}{4\times 9} kasridagi ko‘paytirishlarni bajaring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{6}{36}\right)$$

\frac{6}{36} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{1}{6}\right)$$

312 va 6 ning eng kichik umumiy karralisi 312 ga teng. \frac{77}{312} va \frac{1}{6} ni 312 maxraj bilan kasrlarga aylantirib oling.

$$le\times \frac{3}{5}\left(\frac{77}{312}+\frac{52}{312}\right)$$

\frac{77}{312} va \frac{52}{312} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$le\times \frac{3}{5}\times \frac{77+52}{312}$$

129 olish uchun 77 va 52'ni qo'shing.

$$le\times \frac{3}{5}\times \frac{129}{312}$$

\frac{129}{312} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$le\times \frac{3}{5}\times \frac{43}{104}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{5} ni \frac{43}{104} ga ko‘paytiring.

$$le\times \frac{3\times 43}{5\times 104}$$

\frac{3\times 43}{5\times 104} kasridagi ko‘paytirishlarni bajaring.

$$le\times \frac{129}{520}$$