[(31/4-41/3)-5/6]:{11/12-frac{1}{2}(2frac{1}{3}+1-1frac{1}{4})} eching

$$[ ( 3 \frac { 1 } { 4 } - 4 \frac { 1 } { 3 } ) - \frac { 5 } { 6 } ] : \{ \frac { 11 } { 12 } - \frac { 1 } { 2 } ( 2 \frac { 1 } { 3 } + 1 - 1 \frac { 1 } { 4 } ) \}$$

Baholash

$$\frac{46}{3}\approx 15,333333333$$

Yechim qadamlari

12 hosil qilish uchun 3 va 4 ni ko'paytirish.

$$\frac{\frac{12+1}{4}-\frac{4\times 3+1}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

13 olish uchun 12 va 1'ni qo'shing.

$$\frac{\frac{13}{4}-\frac{4\times 3+1}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

12 hosil qilish uchun 4 va 3 ni ko'paytirish.

$$\frac{\frac{13}{4}-\frac{12+1}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

13 olish uchun 12 va 1'ni qo'shing.

$$\frac{\frac{13}{4}-\frac{13}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

4 va 3 ning eng kichik umumiy karralisi 12 ga teng. \frac{13}{4} va \frac{13}{3} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{39}{12}-\frac{52}{12}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

\frac{39}{12} va \frac{52}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{39-52}{12}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

-13 olish uchun 39 dan 52 ni ayirish.

$$\frac{-\frac{13}{12}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

12 va 6 ning eng kichik umumiy karralisi 12 ga teng. -\frac{13}{12} va \frac{5}{6} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{-\frac{13}{12}-\frac{10}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

-\frac{13}{12} va \frac{10}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{-13-10}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

-23 olish uchun -13 dan 10 ni ayirish.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{6+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

7 olish uchun 6 va 1'ni qo'shing.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{7}{3}+1-\frac{1\times 4+1}{4}\right)}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{7}{3}+\frac{3}{3}-\frac{1\times 4+1}{4}\right)}$$

\frac{7}{3} va \frac{3}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{7+3}{3}-\frac{1\times 4+1}{4}\right)}$$

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

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{10}{3}-\frac{1\times 4+1}{4}\right)}$$

4 hosil qilish uchun 1 va 4 ni ko'paytirish.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{10}{3}-\frac{4+1}{4}\right)}$$

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

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{10}{3}-\frac{5}{4}\right)}$$

3 va 4 ning eng kichik umumiy karralisi 12 ga teng. \frac{10}{3} va \frac{5}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{40}{12}-\frac{15}{12}\right)}$$

\frac{40}{12} va \frac{15}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\times \frac{40-15}{12}}$$

25 olish uchun 40 dan 15 ni ayirish.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\times \frac{25}{12}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{2} ni \frac{25}{12} ga ko‘paytiring.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1\times 25}{2\times 12}}$$

\frac{1\times 25}{2\times 12} kasridagi ko‘paytirishlarni bajaring.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{25}{24}}$$

12 va 24 ning eng kichik umumiy karralisi 24 ga teng. \frac{11}{12} va \frac{25}{24} ni 24 maxraj bilan kasrlarga aylantirib oling.

$$\frac{-\frac{23}{12}}{\frac{22}{24}-\frac{25}{24}}$$

\frac{22}{24} va \frac{25}{24} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-\frac{23}{12}}{\frac{22-25}{24}}$$

-3 olish uchun 22 dan 25 ni ayirish.

$$\frac{-\frac{23}{12}}{\frac{-3}{24}}$$

\frac{-3}{24} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{-\frac{23}{12}}{-\frac{1}{8}}$$

-\frac{23}{12} ni -\frac{1}{8} ga bo'lish -\frac{23}{12} ga k'paytirish -\frac{1}{8} ga qaytarish.

$$-\frac{23}{12}\left(-8\right)$$

-\frac{23}{12}\left(-8\right) ni yagona kasrga aylantiring.

$$\frac{-23\left(-8\right)}{12}$$

184 hosil qilish uchun -23 va -8 ni ko'paytirish.

$$\frac{184}{12}$$

\frac{184}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{46}{3}$$

Omil

$$\frac{2 \cdot 23}{3} = 15\frac{1}{3} = 15,333333333333334$$