7/12*2/7+1/3div5/6quad(frac{2}{3}+frac{1}{6}+frac{3}{8})*24 eching

$$\frac { 7 } { 12 } \times \frac { 2 } { 7 } + \frac { 1 } { 3 } \div \frac { 5 } { 6 } \quad ( \frac { 2 } { 3 } + \frac { 1 } { 6 } + \frac { 3 } { 8 } ) \times 24$$

Baholash

$$\frac{353}{30}\approx 11,766666667$$

Yechim qadamlari

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{12} ni \frac{2}{7} ga ko‘paytiring.

$$\frac{7\times 2}{12\times 7}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Surat va maxrajdagi ikkala 7 ni qisqartiring.

$$\frac{2}{12}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

\frac{2}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

\frac{1}{3} ni \frac{5}{6} ga bo'lish \frac{1}{3} ga k'paytirish \frac{5}{6} ga qaytarish.

$$\frac{1}{6}+\frac{1}{3}\times \frac{6}{5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{1}{3} ni \frac{6}{5} ga ko‘paytiring.

$$\frac{1}{6}+\frac{1\times 6}{3\times 5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

\frac{1\times 6}{3\times 5} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1}{6}+\frac{6}{15}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

\frac{6}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

3 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{2}{3} va \frac{1}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{4}{6}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

\frac{4}{6} va \frac{1}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{4+1}{6}+\frac{3}{8}\right)\times 24$$

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

$$\frac{1}{6}+\frac{2}{5}\left(\frac{5}{6}+\frac{3}{8}\right)\times 24$$

6 va 8 ning eng kichik umumiy karralisi 24 ga teng. \frac{5}{6} va \frac{3}{8} ni 24 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{20}{24}+\frac{9}{24}\right)\times 24$$

\frac{20}{24} va \frac{9}{24} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{6}+\frac{2}{5}\times \frac{20+9}{24}\times 24$$

29 olish uchun 20 va 9'ni qo'shing.

$$\frac{1}{6}+\frac{2}{5}\times \frac{29}{24}\times 24$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2}{5} ni \frac{29}{24} ga ko‘paytiring.

$$\frac{1}{6}+\frac{2\times 29}{5\times 24}\times 24$$

\frac{2\times 29}{5\times 24} kasridagi ko‘paytirishlarni bajaring.

$$\frac{1}{6}+\frac{58}{120}\times 24$$

\frac{58}{120} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}+\frac{29}{60}\times 24$$

\frac{29}{60}\times 24 ni yagona kasrga aylantiring.

$$\frac{1}{6}+\frac{29\times 24}{60}$$

696 hosil qilish uchun 29 va 24 ni ko'paytirish.

$$\frac{1}{6}+\frac{696}{60}$$

\frac{696}{60} ulushini 12 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}+\frac{58}{5}$$

6 va 5 ning eng kichik umumiy karralisi 30 ga teng. \frac{1}{6} va \frac{58}{5} ni 30 maxraj bilan kasrlarga aylantirib oling.

$$\frac{5}{30}+\frac{348}{30}$$

\frac{5}{30} va \frac{348}{30} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5+348}{30}$$

353 olish uchun 5 va 348'ni qo'shing.

$$\frac{353}{30}$$

Omil

$$\frac{353}{2 \cdot 3 \cdot 5} = 11\frac{23}{30} = 11,766666666666667$$