1+1/2/3+1-frac{1/3/2}{frac{2^1/2}{5/6}--frac{1/3}{1/8}}*(23^1/2divfrac{47}{12}) eching

$$\frac { \frac { 1 + \frac { 1 } { 2 } } { 3 } + \frac { 1 - \frac { 1 } { 3 } } { 2 } } { \frac { 2 ^ { 1 } / 2 } { 5 / 6 } - - \frac { 1 / 3 } { 1 / 8 } } \times ( 23 ^ { 1 } / 2 \div \frac { 47 } { 12 } )$$

Baholash

$$\frac{1725}{2726}\approx 0,632795304$$

Yechim qadamlari

1 ni olish uchun 2^{1} ni 2 ga bo‘ling.

$$\frac{\frac{1+\frac{1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

1 ni \frac{2}{2} kasrga o‘giring.

$$\frac{\frac{\frac{2}{2}+\frac{1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{2}{2} va \frac{1}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{\frac{2+1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

3 olish uchun 2 va 1'ni qo'shing.

$$\frac{\frac{\frac{3}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{\frac{3}{2}}{3} ni yagona kasrga aylantiring.

$$\frac{\frac{3}{2\times 3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{\frac{1}{2}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{\frac{1}{2}+\frac{\frac{3}{3}-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{1}{2}+\frac{\frac{3-1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

2 olish uchun 3 dan 1 ni ayirish.

$$\frac{\frac{1}{2}+\frac{\frac{2}{3}}{2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{\frac{2}{3}}{2} ni yagona kasrga aylantiring.

$$\frac{\frac{1}{2}+\frac{2}{3\times 2}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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.

$$\frac{\frac{3}{6}+\frac{2}{6}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{3+2}{6}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{5}{6}}{\frac{1}{\frac{5}{6}}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{5}{6}}{1\times \frac{6}{5}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{6}{5} hosil qilish uchun 1 va \frac{6}{5} ni ko'paytirish.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\left(-\frac{\frac{1}{3}}{\frac{1}{8}}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{1}{3} ni \frac{1}{8} ga bo'lish \frac{1}{3} ga k'paytirish \frac{1}{8} ga qaytarish.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\left(-\frac{1}{3}\times 8\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{8}{3} hosil qilish uchun \frac{1}{3} va 8 ni ko'paytirish.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\left(-\frac{8}{3}\right)}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

-\frac{8}{3} ning teskarisi \frac{8}{3} ga teng.

$$\frac{\frac{5}{6}}{\frac{6}{5}+\frac{8}{3}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

5 va 3 ning eng kichik umumiy karralisi 15 ga teng. \frac{6}{5} va \frac{8}{3} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{5}{6}}{\frac{18}{15}+\frac{40}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{18}{15} va \frac{40}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{5}{6}}{\frac{18+40}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

58 olish uchun 18 va 40'ni qo'shing.

$$\frac{\frac{5}{6}}{\frac{58}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{5}{6} ni \frac{58}{15} ga bo'lish \frac{5}{6} ga k'paytirish \frac{58}{15} ga qaytarish.

$$\frac{5}{6}\times \frac{15}{58}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{6} ni \frac{15}{58} ga ko‘paytiring.

$$\frac{5\times 15}{6\times 58}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{5\times 15}{6\times 58} kasridagi ko‘paytirishlarni bajaring.

$$\frac{75}{348}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{75}{348} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{25}{116}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

\frac{23^{1}}{2} ni \frac{47}{12} ga bo'lish \frac{23^{1}}{2} ga k'paytirish \frac{47}{12} ga qaytarish.

$$\frac{25}{116}\times \frac{23^{1}\times 12}{2\times 47}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{25}{116}\times \frac{6\times 23^{1}}{47}$$

1 daraja ko‘rsatkichini 23 ga hisoblang va 23 ni qiymatni oling.

$$\frac{25}{116}\times \frac{6\times 23}{47}$$

138 hosil qilish uchun 6 va 23 ni ko'paytirish.

$$\frac{25}{116}\times \frac{138}{47}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{25}{116} ni \frac{138}{47} ga ko‘paytiring.

$$\frac{25\times 138}{116\times 47}$$

\frac{25\times 138}{116\times 47} kasridagi ko‘paytirishlarni bajaring.

$$\frac{3450}{5452}$$

\frac{3450}{5452} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1725}{2726}$$

Omil

$$\frac{3 \cdot 5 ^ {2} \cdot 23}{2 \cdot 29 \cdot 47} = 0,6327953044754219$$