(3/5+1/2*2/3):(frac{1/5+frac{4}{2})}{(1-frac{5}{6})*(1+frac{5}{6})+frac{1}{36}}*(1+frac{2}{21}) eching

$$\frac { ( \frac { 3 } { 5 } + \frac { 1 } { 2 } \cdot \frac { 2 } { 3 } ) : ( \frac { 1 } { 5 } + \frac { 4 } { 2 } ) } { ( 1 - \frac { 5 } { 6 } ) \cdot ( 1 + \frac { 5 } { 6 } ) + \frac { 1 } { 36 } } \cdot ( 1 + \frac { 2 } { 21 } )$$

Baholash

$$\frac{46}{33}\approx 1,393939394$$

Yechim qadamlari

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

$$\frac{\frac{\frac{3}{5}+\frac{1\times 2}{2\times 3}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\frac{\frac{3}{5}+\frac{1}{3}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

5 va 3 ning eng kichik umumiy karralisi 15 ga teng. \frac{3}{5} va \frac{1}{3} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{\frac{9}{15}+\frac{5}{15}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{9}{15} va \frac{5}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{\frac{9+5}{15}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

14 olish uchun 9 va 5'ni qo'shing.

$$\frac{\frac{\frac{14}{15}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

2 ni olish uchun 4 ni 2 ga bo‘ling.

$$\frac{\frac{\frac{14}{15}}{\frac{1}{5}+2}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

2 ni \frac{10}{5} kasrga o‘giring.

$$\frac{\frac{\frac{14}{15}}{\frac{1}{5}+\frac{10}{5}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{1}{5} va \frac{10}{5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{\frac{14}{15}}{\frac{1+10}{5}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

11 olish uchun 1 va 10'ni qo'shing.

$$\frac{\frac{\frac{14}{15}}{\frac{11}{5}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{14}{15} ni \frac{11}{5} ga bo'lish \frac{14}{15} ga k'paytirish \frac{11}{5} ga qaytarish.

$$\frac{\frac{14}{15}\times \frac{5}{11}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{14}{15} ni \frac{5}{11} ga ko‘paytiring.

$$\frac{\frac{14\times 5}{15\times 11}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{14\times 5}{15\times 11} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{70}{165}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{70}{165} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{14}{33}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

1 ni \frac{6}{6} kasrga o‘giring.

$$\frac{\frac{14}{33}}{\left(\frac{6}{6}-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{6}{6} va \frac{5}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{14}{33}}{\frac{6-5}{6}\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

1 olish uchun 6 dan 5 ni ayirish.

$$\frac{\frac{14}{33}}{\frac{1}{6}\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

1 ni \frac{6}{6} kasrga o‘giring.

$$\frac{\frac{14}{33}}{\frac{1}{6}\left(\frac{6}{6}+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{6}{6} va \frac{5}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{14}{33}}{\frac{1}{6}\times \frac{6+5}{6}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

11 olish uchun 6 va 5'ni qo'shing.

$$\frac{\frac{14}{33}}{\frac{1}{6}\times \frac{11}{6}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{6} ni \frac{11}{6} ga ko‘paytiring.

$$\frac{\frac{14}{33}}{\frac{1\times 11}{6\times 6}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{1\times 11}{6\times 6} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{14}{33}}{\frac{11}{36}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{11}{36} va \frac{1}{36} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{14}{33}}{\frac{11+1}{36}}\left(1+\frac{2}{21}\right)$$

12 olish uchun 11 va 1'ni qo'shing.

$$\frac{\frac{14}{33}}{\frac{12}{36}}\left(1+\frac{2}{21}\right)$$

\frac{12}{36} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{14}{33}}{\frac{1}{3}}\left(1+\frac{2}{21}\right)$$

\frac{14}{33} ni \frac{1}{3} ga bo'lish \frac{14}{33} ga k'paytirish \frac{1}{3} ga qaytarish.

$$\frac{14}{33}\times 3\left(1+\frac{2}{21}\right)$$

\frac{14}{33}\times 3 ni yagona kasrga aylantiring.

$$\frac{14\times 3}{33}\left(1+\frac{2}{21}\right)$$

42 hosil qilish uchun 14 va 3 ni ko'paytirish.

$$\frac{42}{33}\left(1+\frac{2}{21}\right)$$

\frac{42}{33} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{14}{11}\left(1+\frac{2}{21}\right)$$

1 ni \frac{21}{21} kasrga o‘giring.

$$\frac{14}{11}\left(\frac{21}{21}+\frac{2}{21}\right)$$

\frac{21}{21} va \frac{2}{21} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{14}{11}\times \frac{21+2}{21}$$

23 olish uchun 21 va 2'ni qo'shing.

$$\frac{14}{11}\times \frac{23}{21}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{14}{11} ni \frac{23}{21} ga ko‘paytiring.

$$\frac{14\times 23}{11\times 21}$$

\frac{14\times 23}{11\times 21} kasridagi ko‘paytirishlarni bajaring.

$$\frac{322}{231}$$

\frac{322}{231} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{46}{33}$$

Omil

$$\frac{2 \cdot 23}{3 \cdot 11} = 1\frac{13}{33} = 1,393939393939394$$