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

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

Baholash

$$1$$

Yechim qadamlari

1 ni \frac{4}{4} kasrga o‘giring.

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

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

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

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

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

\frac{5}{4} ni \frac{1}{2} ga bo'lish \frac{5}{4} ga k'paytirish \frac{1}{2} ga qaytarish.

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

\frac{5}{4}\times 2 ni yagona kasrga aylantiring.

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

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

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

\frac{10}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

1 ni \frac{4}{4} kasrga o‘giring.

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

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

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

3 olish uchun 4 dan 1 ni ayirish.

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

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

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

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

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

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

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

2 va 4 ning eng kichik umumiy karralisi 4 ga teng. \frac{5}{2} va \frac{9}{4} ni 4 maxraj bilan kasrlarga aylantirib oling.

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

\frac{10}{4} va \frac{9}{4} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

1 olish uchun 10 dan 9 ni ayirish.

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

1 ni \frac{3}{3} kasrga o‘giring.

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

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

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

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

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

\frac{1}{4} ni \frac{5}{3} ga bo'lish \frac{1}{4} ga k'paytirish \frac{5}{3} ga qaytarish.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{4} ni \frac{3}{5} ga ko‘paytiring.

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

\frac{1\times 3}{4\times 5} kasridagi ko‘paytirishlarni bajaring.

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

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

$$\frac{3}{20}\left(\frac{30+1}{3}-\frac{3\times 3+2}{3}\right)$$

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

$$\frac{3}{20}\left(\frac{31}{3}-\frac{3\times 3+2}{3}\right)$$

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

$$\frac{3}{20}\left(\frac{31}{3}-\frac{9+2}{3}\right)$$

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

$$\frac{3}{20}\left(\frac{31}{3}-\frac{11}{3}\right)$$

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

$$\frac{3}{20}\times \frac{31-11}{3}$$

20 olish uchun 31 dan 11 ni ayirish.

$$\frac{3}{20}\times \frac{20}{3}$$

\frac{3}{20} va uning teskari kasrini \frac{20}{3} ni qisqartiring.

$$1$$

Omil

$$1$$