1+1/4/frac{frac{1{2}}{1+2/3}-1-frac{1/4}{frac{1}{3}}}*(10frac{1}{3}-3frac{2}{3}) eching

$$\frac { 1 + \frac { 1 } { 4 } } { \frac { \frac { 1 } { 2 } } { 1 + \frac { 2 } { 3 } } - \frac { 1 - \frac { 1 } { 4 } } { \frac { 1 } { 3 } } } \times ( 10 \frac { 1 } { 3 } - 3 \frac { 2 } { 3 } )$$

Baholash

$$-\frac{500}{117}\approx -4,273504274$$

Yechim qadamlari

1 ni \frac{4}{4} kasrga o‘giring.

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

\frac{4}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

5 olish uchun 4 va 1'ni qo'shing.

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

1 ni \frac{3}{3} kasrga o‘giring.

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

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

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

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

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni \frac{3}{5} ga ko‘paytiring.

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

\frac{1\times 3}{2\times 5} kasridagi ko‘paytirishlarni bajaring.

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

1 ni \frac{4}{4} kasrga o‘giring.

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

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

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

3 olish uchun 4 dan 1 ni ayirish.

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

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

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

\frac{3}{4}\times 3 ni yagona kasrga aylantiring.

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

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

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

10 va 4 ning eng kichik umumiy karralisi 20 ga teng. \frac{3}{10} va \frac{9}{4} ni 20 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{5}{4}}{\frac{6}{20}-\frac{45}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

\frac{6}{20} va \frac{45}{20} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{5}{4}}{\frac{6-45}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

-39 olish uchun 6 dan 45 ni ayirish.

$$\frac{\frac{5}{4}}{-\frac{39}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

\frac{5}{4} ni -\frac{39}{20} ga bo'lish \frac{5}{4} ga k'paytirish -\frac{39}{20} ga qaytarish.

$$\frac{5}{4}\left(-\frac{20}{39}\right)\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{4} ni -\frac{20}{39} ga ko‘paytiring.

$$\frac{5\left(-20\right)}{4\times 39}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

\frac{5\left(-20\right)}{4\times 39} kasridagi ko‘paytirishlarni bajaring.

$$\frac{-100}{156}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

\frac{-100}{156} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{25}{39}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

30 hosil qilish uchun 10 va 3 ni ko'paytirish.

$$-\frac{25}{39}\left(\frac{30+1}{3}-\frac{3\times 3+2}{3}\right)$$

31 olish uchun 30 va 1'ni qo'shing.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{3\times 3+2}{3}\right)$$

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

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{9+2}{3}\right)$$

11 olish uchun 9 va 2'ni qo'shing.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{11}{3}\right)$$

\frac{31}{3} va \frac{11}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{25}{39}\times \frac{31-11}{3}$$

20 olish uchun 31 dan 11 ni ayirish.

$$-\frac{25}{39}\times \frac{20}{3}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali -\frac{25}{39} ni \frac{20}{3} ga ko‘paytiring.

$$\frac{-25\times 20}{39\times 3}$$

\frac{-25\times 20}{39\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\frac{-500}{117}$$

\frac{-500}{117} kasri manfiy belgini olib tashlash bilan -\frac{500}{117} sifatida qayta yozilishi mumkin.

$$-\frac{500}{117}$$

Omil

$$-\frac{500}{117} = -4\frac{32}{117} = -4,273504273504273$$