(1/6+8/12)*(15/14-11/7)+(frac{10}{8}-frac{7}{6}):(-frac{1}{3})^3 eching

$$( \frac { 1 } { 6 } + \frac { 8 } { 12 } ) \cdot ( \frac { 15 } { 14 } - \frac { 11 } { 7 } ) + ( \frac { 10 } { 8 } - \frac { 7 } { 6 } ) : ( - \frac { 1 } { 3 } ) ^ { 3 }$$

Baholash

$$-\frac{8}{3}\approx -2,666666667$$

Yechim qadamlari

\frac{8}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\left(\frac{1}{6}+\frac{2}{3}\right)\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

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

$$\left(\frac{1}{6}+\frac{4}{6}\right)\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

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

$$\frac{1+4}{6}\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

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

$$\frac{5}{6}\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

14 va 7 ning eng kichik umumiy karralisi 14 ga teng. \frac{15}{14} va \frac{11}{7} ni 14 maxraj bilan kasrlarga aylantirib oling.

$$\frac{5}{6}\left(\frac{15}{14}-\frac{22}{14}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

\frac{15}{14} va \frac{22}{14} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5}{6}\times \frac{15-22}{14}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

-7 olish uchun 15 dan 22 ni ayirish.

$$\frac{5}{6}\times \frac{-7}{14}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

\frac{-7}{14} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{6}\left(-\frac{1}{2}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{6} ni -\frac{1}{2} ga ko‘paytiring.

$$\frac{5\left(-1\right)}{6\times 2}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

\frac{5\left(-1\right)}{6\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{-5}{12}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

\frac{-5}{12} kasri manfiy belgini olib tashlash bilan -\frac{5}{12} sifatida qayta yozilishi mumkin.

$$-\frac{5}{12}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

\frac{10}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{5}{12}+\frac{\frac{5}{4}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

4 va 6 ning eng kichik umumiy karralisi 12 ga teng. \frac{5}{4} va \frac{7}{6} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{5}{12}+\frac{\frac{15}{12}-\frac{14}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

\frac{15}{12} va \frac{14}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$-\frac{5}{12}+\frac{\frac{15-14}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

1 olish uchun 15 dan 14 ni ayirish.

$$-\frac{5}{12}+\frac{\frac{1}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

3 daraja ko‘rsatkichini -\frac{1}{3} ga hisoblang va -\frac{1}{27} ni qiymatni oling.

$$-\frac{5}{12}+\frac{\frac{1}{12}}{-\frac{1}{27}}$$

\frac{1}{12} ni -\frac{1}{27} ga bo'lish \frac{1}{12} ga k'paytirish -\frac{1}{27} ga qaytarish.

$$-\frac{5}{12}+\frac{1}{12}\left(-27\right)$$

\frac{-27}{12} hosil qilish uchun \frac{1}{12} va -27 ni ko'paytirish.

$$-\frac{5}{12}+\frac{-27}{12}$$

\frac{-27}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{5}{12}-\frac{9}{4}$$

12 va 4 ning eng kichik umumiy karralisi 12 ga teng. -\frac{5}{12} va \frac{9}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{5}{12}-\frac{27}{12}$$

-\frac{5}{12} va \frac{27}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-5-27}{12}$$

-32 olish uchun -5 dan 27 ni ayirish.

$$\frac{-32}{12}$$

\frac{-32}{12} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$-\frac{8}{3}$$

Omil

$$-\frac{8}{3} = -2\frac{2}{3} = -2,6666666666666665$$