1/9+-1/8+-1/7+1/6 eching

$$\frac { 1 } { 9 } + \frac { - 1 } { 8 } + \frac { - 1 } { 7 } + \frac { 1 } { 6 }$$

Baholash

$$\frac{5}{504}\approx 0,009920635$$

Yechim qadamlari

\frac{-1}{8} kasri manfiy belgini olib tashlash bilan -\frac{1}{8} sifatida qayta yozilishi mumkin.

$$\frac{1}{9}-\frac{1}{8}+\frac{-1}{7}+\frac{1}{6}$$

9 va 8 ning eng kichik umumiy karralisi 72 ga teng. \frac{1}{9} va \frac{1}{8} ni 72 maxraj bilan kasrlarga aylantirib oling.

$$\frac{8}{72}-\frac{9}{72}+\frac{-1}{7}+\frac{1}{6}$$

\frac{8}{72} va \frac{9}{72} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{8-9}{72}+\frac{-1}{7}+\frac{1}{6}$$

-1 olish uchun 8 dan 9 ni ayirish.

$$-\frac{1}{72}+\frac{-1}{7}+\frac{1}{6}$$

\frac{-1}{7} kasri manfiy belgini olib tashlash bilan -\frac{1}{7} sifatida qayta yozilishi mumkin.

$$-\frac{1}{72}-\frac{1}{7}+\frac{1}{6}$$

72 va 7 ning eng kichik umumiy karralisi 504 ga teng. -\frac{1}{72} va \frac{1}{7} ni 504 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{7}{504}-\frac{72}{504}+\frac{1}{6}$$

-\frac{7}{504} va \frac{72}{504} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-7-72}{504}+\frac{1}{6}$$

-79 olish uchun -7 dan 72 ni ayirish.

$$-\frac{79}{504}+\frac{1}{6}$$

504 va 6 ning eng kichik umumiy karralisi 504 ga teng. -\frac{79}{504} va \frac{1}{6} ni 504 maxraj bilan kasrlarga aylantirib oling.

$$-\frac{79}{504}+\frac{84}{504}$$

-\frac{79}{504} va \frac{84}{504} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-79+84}{504}$$

5 olish uchun -79 va 84'ni qo'shing.

$$\frac{5}{504}$$

Omil

$$\frac{5}{2 ^ {3} \cdot 3 ^ {2} \cdot 7} = 0,00992063492063492$$