2-2/3/4/5+3-1/3/4/3/frac{4-1/4{1/2}+frac{5-1/5}{24}}*(frac{7}{20}*frac{11}{2}) eching

$$\frac { \frac { 2 - \frac { 2 } { 3 } } { 4 / 5 } + \frac { 3 - 1 / 3 } { 4 / 3 } } { \frac { 4 - 1 / 4 } { 1 / 2 } + \frac { 5 - 1 / 5 } { 24 } } \times ( \frac { 7 } { 20 } \times \frac { 11 } { 2 } )$$

Baholash

$$\frac{11}{12}\approx 0,916666667$$

Yechim qadamlari

2 ni \frac{6}{3} kasrga o‘giring.

$$\frac{\frac{\frac{6}{3}-\frac{2}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{6}{3} va \frac{2}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{\frac{6-2}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

4 olish uchun 6 dan 2 ni ayirish.

$$\frac{\frac{\frac{4}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

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

$$\frac{\frac{4}{3}\times \frac{5}{4}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{5}{4} ga ko‘paytiring.

$$\frac{\frac{4\times 5}{3\times 4}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

$$\frac{\frac{5}{3}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

3 ni \frac{9}{3} kasrga o‘giring.

$$\frac{\frac{5}{3}+\frac{\frac{9}{3}-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{9}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{5}{3}+\frac{\frac{9-1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

8 olish uchun 9 dan 1 ni ayirish.

$$\frac{\frac{5}{3}+\frac{\frac{8}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{8}{3} ni \frac{4}{3} ga bo'lish \frac{8}{3} ga k'paytirish \frac{4}{3} ga qaytarish.

$$\frac{\frac{5}{3}+\frac{8}{3}\times \frac{3}{4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{3} ni \frac{3}{4} ga ko‘paytiring.

$$\frac{\frac{5}{3}+\frac{8\times 3}{3\times 4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{\frac{5}{3}+\frac{8}{4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

2 ni olish uchun 8 ni 4 ga bo‘ling.

$$\frac{\frac{5}{3}+2}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

2 ni \frac{6}{3} kasrga o‘giring.

$$\frac{\frac{5}{3}+\frac{6}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{5}{3} va \frac{6}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{5+6}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

11 olish uchun 5 va 6'ni qo'shing.

$$\frac{\frac{11}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

4 ni \frac{16}{4} kasrga o‘giring.

$$\frac{\frac{11}{3}}{\frac{\frac{16}{4}-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{16}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{11}{3}}{\frac{\frac{16-1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

15 olish uchun 16 dan 1 ni ayirish.

$$\frac{\frac{11}{3}}{\frac{\frac{15}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{15}{4} ni \frac{1}{2} ga bo'lish \frac{15}{4} ga k'paytirish \frac{1}{2} ga qaytarish.

$$\frac{\frac{11}{3}}{\frac{15}{4}\times 2+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{15}{4}\times 2 ni yagona kasrga aylantiring.

$$\frac{\frac{11}{3}}{\frac{15\times 2}{4}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

30 hosil qilish uchun 15 va 2 ni ko'paytirish.

$$\frac{\frac{11}{3}}{\frac{30}{4}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{30}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

5 ni \frac{25}{5} kasrga o‘giring.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{25}{5}-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{25}{5} va \frac{1}{5} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{25-1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

24 olish uchun 25 dan 1 ni ayirish.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{24}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{\frac{24}{5}}{24} ni yagona kasrga aylantiring.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{24}{5\times 24}}\times \frac{7}{20}\times \frac{11}{2}$$

Surat va maxrajdagi ikkala 24 ni qisqartiring.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{1}{5}}\times \frac{7}{20}\times \frac{11}{2}$$

2 va 5 ning eng kichik umumiy karralisi 10 ga teng. \frac{15}{2} va \frac{1}{5} ni 10 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{11}{3}}{\frac{75}{10}+\frac{2}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{75}{10} va \frac{2}{10} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{11}{3}}{\frac{75+2}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

77 olish uchun 75 va 2'ni qo'shing.

$$\frac{\frac{11}{3}}{\frac{77}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{11}{3} ni \frac{77}{10} ga bo'lish \frac{11}{3} ga k'paytirish \frac{77}{10} ga qaytarish.

$$\frac{11}{3}\times \frac{10}{77}\times \frac{7}{20}\times \frac{11}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{11}{3} ni \frac{10}{77} ga ko‘paytiring.

$$\frac{11\times 10}{3\times 77}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{11\times 10}{3\times 77} kasridagi ko‘paytirishlarni bajaring.

$$\frac{110}{231}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{110}{231} ulushini 11 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{10}{21}\times \frac{7}{20}\times \frac{11}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{10}{21} ni \frac{7}{20} ga ko‘paytiring.

$$\frac{10\times 7}{21\times 20}\times \frac{11}{2}$$

\frac{10\times 7}{21\times 20} kasridagi ko‘paytirishlarni bajaring.

$$\frac{70}{420}\times \frac{11}{2}$$

\frac{70}{420} ulushini 70 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}\times \frac{11}{2}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{6} ni \frac{11}{2} ga ko‘paytiring.

$$\frac{1\times 11}{6\times 2}$$

\frac{1\times 11}{6\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{11}{12}$$

Omil

$$\frac{11}{2 ^ {2} \cdot 3} = 0,9166666666666666$$