13/6-35/66+27/121*5/3-(frac{14}{15}+frac{8}{165})*(frac{2}{9}+frac{11}{18}) eching

$$\frac { 13 } { 6 } - \frac { 35 } { 66 } + \frac { 27 } { 121 } \cdot \frac { 5 } { 3 } - ( \frac { 14 } { 15 } + \frac { 8 } { 165 } ) \cdot ( \frac { 2 } { 9 } + \frac { 11 } { 18 } )$$

Baholash

$$\frac{144}{121}\approx 1,190082645$$

Yechim qadamlari

6 va 66 ning eng kichik umumiy karralisi 66 ga teng. \frac{13}{6} va \frac{35}{66} ni 66 maxraj bilan kasrlarga aylantirib oling.

$$\frac{143}{66}-\frac{35}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{143}{66} va \frac{35}{66} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{143-35}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

108 olish uchun 143 dan 35 ni ayirish.

$$\frac{108}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{108}{66} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{18}{11}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{27}{121} ni \frac{5}{3} ga ko‘paytiring.

$$\frac{18}{11}+\frac{27\times 5}{121\times 3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{27\times 5}{121\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\frac{18}{11}+\frac{135}{363}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{135}{363} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{18}{11}+\frac{45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

11 va 121 ning eng kichik umumiy karralisi 121 ga teng. \frac{18}{11} va \frac{45}{121} ni 121 maxraj bilan kasrlarga aylantirib oling.

$$\frac{198}{121}+\frac{45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{198}{121} va \frac{45}{121} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{198+45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

243 olish uchun 198 va 45'ni qo'shing.

$$\frac{243}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

15 va 165 ning eng kichik umumiy karralisi 165 ga teng. \frac{14}{15} va \frac{8}{165} ni 165 maxraj bilan kasrlarga aylantirib oling.

$$\frac{243}{121}-\left(\frac{154}{165}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{154}{165} va \frac{8}{165} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{243}{121}-\frac{154+8}{165}\left(\frac{2}{9}+\frac{11}{18}\right)$$

162 olish uchun 154 va 8'ni qo'shing.

$$\frac{243}{121}-\frac{162}{165}\left(\frac{2}{9}+\frac{11}{18}\right)$$

\frac{162}{165} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{243}{121}-\frac{54}{55}\left(\frac{2}{9}+\frac{11}{18}\right)$$

9 va 18 ning eng kichik umumiy karralisi 18 ga teng. \frac{2}{9} va \frac{11}{18} ni 18 maxraj bilan kasrlarga aylantirib oling.

$$\frac{243}{121}-\frac{54}{55}\left(\frac{4}{18}+\frac{11}{18}\right)$$

\frac{4}{18} va \frac{11}{18} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{243}{121}-\frac{54}{55}\times \frac{4+11}{18}$$

15 olish uchun 4 va 11'ni qo'shing.

$$\frac{243}{121}-\frac{54}{55}\times \frac{15}{18}$$

\frac{15}{18} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{243}{121}-\frac{54}{55}\times \frac{5}{6}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{54}{55} ni \frac{5}{6} ga ko‘paytiring.

$$\frac{243}{121}-\frac{54\times 5}{55\times 6}$$

\frac{54\times 5}{55\times 6} kasridagi ko‘paytirishlarni bajaring.

$$\frac{243}{121}-\frac{270}{330}$$

\frac{270}{330} ulushini 30 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{243}{121}-\frac{9}{11}$$

121 va 11 ning eng kichik umumiy karralisi 121 ga teng. \frac{243}{121} va \frac{9}{11} ni 121 maxraj bilan kasrlarga aylantirib oling.

$$\frac{243}{121}-\frac{99}{121}$$

\frac{243}{121} va \frac{99}{121} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{243-99}{121}$$

144 olish uchun 243 dan 99 ni ayirish.

$$\frac{144}{121}$$

Omil

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{11 ^ {2}} = 1\frac{23}{121} = 1,1900826446280992$$