41/7-21/14+31/2/6frac{2{3}+5frac{5}{9}-10frac{1}{15}} eching

$$\frac { 4 \frac { 1 } { 7 } - 2 \frac { 1 } { 14 } + 3 \frac { 1 } { 2 } } { 6 \frac { 2 } { 3 } + 5 \frac { 5 } { 9 } - 10 \frac { 1 } { 15 } }$$

Baholash

$$\frac{1755}{679}\approx 2,584683358$$

Yechim qadamlari

28 hosil qilish uchun 4 va 7 ni ko'paytirish.

$$\frac{\frac{28+1}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

29 olish uchun 28 va 1'ni qo'shing.

$$\frac{\frac{29}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

28 hosil qilish uchun 2 va 14 ni ko'paytirish.

$$\frac{\frac{29}{7}-\frac{28+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

29 olish uchun 28 va 1'ni qo'shing.

$$\frac{\frac{29}{7}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

7 va 14 ning eng kichik umumiy karralisi 14 ga teng. \frac{29}{7} va \frac{29}{14} ni 14 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{58}{14}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

\frac{58}{14} va \frac{29}{14} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{58-29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

29 olish uchun 58 dan 29 ni ayirish.

$$\frac{\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

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

$$\frac{\frac{29}{14}+\frac{6+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

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

$$\frac{\frac{29}{14}+\frac{7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

14 va 2 ning eng kichik umumiy karralisi 14 ga teng. \frac{29}{14} va \frac{7}{2} ni 14 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{29}{14}+\frac{49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

\frac{29}{14} va \frac{49}{14} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{29+49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

78 olish uchun 29 va 49'ni qo'shing.

$$\frac{\frac{78}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

\frac{78}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{39}{7}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

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

$$\frac{\frac{39}{7}}{\frac{18+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

20 olish uchun 18 va 2'ni qo'shing.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

45 hosil qilish uchun 5 va 9 ni ko'paytirish.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{45+5}{9}-\frac{10\times 15+1}{15}}$$

50 olish uchun 45 va 5'ni qo'shing.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{50}{9}-\frac{10\times 15+1}{15}}$$

3 va 9 ning eng kichik umumiy karralisi 9 ga teng. \frac{20}{3} va \frac{50}{9} ni 9 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{39}{7}}{\frac{60}{9}+\frac{50}{9}-\frac{10\times 15+1}{15}}$$

\frac{60}{9} va \frac{50}{9} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{39}{7}}{\frac{60+50}{9}-\frac{10\times 15+1}{15}}$$

110 olish uchun 60 va 50'ni qo'shing.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{10\times 15+1}{15}}$$

150 hosil qilish uchun 10 va 15 ni ko'paytirish.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{150+1}{15}}$$

151 olish uchun 150 va 1'ni qo'shing.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{151}{15}}$$

9 va 15 ning eng kichik umumiy karralisi 45 ga teng. \frac{110}{9} va \frac{151}{15} ni 45 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{39}{7}}{\frac{550}{45}-\frac{453}{45}}$$

\frac{550}{45} va \frac{453}{45} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{39}{7}}{\frac{550-453}{45}}$$

97 olish uchun 550 dan 453 ni ayirish.

$$\frac{\frac{39}{7}}{\frac{97}{45}}$$

\frac{39}{7} ni \frac{97}{45} ga bo'lish \frac{39}{7} ga k'paytirish \frac{97}{45} ga qaytarish.

$$\frac{39}{7}\times \frac{45}{97}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{39}{7} ni \frac{45}{97} ga ko‘paytiring.

$$\frac{39\times 45}{7\times 97}$$

\frac{39\times 45}{7\times 97} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1755}{679}$$

Omil

$$\frac{3 ^ {3} \cdot 5 \cdot 13}{7 \cdot 97} = 2\frac{397}{679} = 2,5846833578792343$$