1/2-[2/7-3/4-(5/14+1)+(frac{1}{4}+frac{1}{7}-frac{3}{4})+2] eching

$$\frac { 1 } { 2 } - [ \frac { 2 } { 7 } - \frac { 3 } { 4 } - ( \frac { 5 } { 14 } + 1 ) + ( \frac { 1 } { 4 } + \frac { 1 } { 7 } - \frac { 3 } { 4 } ) + 2 ]$$

Baholash

$$\frac{19}{28}\approx 0,678571429$$

Yechim qadamlari

7 va 4 ning eng kichik umumiy karralisi 28 ga teng. \frac{2}{7} va \frac{3}{4} ni 28 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{2}-\left(\frac{8}{28}-\frac{21}{28}-\left(\frac{5}{14}+1\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

\frac{8}{28} va \frac{21}{28} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{2}-\left(\frac{8-21}{28}-\left(\frac{5}{14}+1\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

-13 olish uchun 8 dan 21 ni ayirish.

$$\frac{1}{2}-\left(-\frac{13}{28}-\left(\frac{5}{14}+1\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

1 ni \frac{14}{14} kasrga o‘giring.

$$\frac{1}{2}-\left(-\frac{13}{28}-\left(\frac{5}{14}+\frac{14}{14}\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

\frac{5}{14} va \frac{14}{14} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}-\left(-\frac{13}{28}-\frac{5+14}{14}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

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

$$\frac{1}{2}-\left(-\frac{13}{28}-\frac{19}{14}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

28 va 14 ning eng kichik umumiy karralisi 28 ga teng. -\frac{13}{28} va \frac{19}{14} ni 28 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{2}-\left(-\frac{13}{28}-\frac{38}{28}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

-\frac{13}{28} va \frac{38}{28} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{2}-\left(\frac{-13-38}{28}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

-51 olish uchun -13 dan 38 ni ayirish.

$$\frac{1}{2}-\left(-\frac{51}{28}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

28 va 4 ning eng kichik umumiy karralisi 28 ga teng. -\frac{51}{28} va \frac{1}{4} ni 28 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{2}-\left(-\frac{51}{28}+\frac{7}{28}+\frac{1}{7}-\frac{3}{4}+2\right)$$

-\frac{51}{28} va \frac{7}{28} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}-\left(\frac{-51+7}{28}+\frac{1}{7}-\frac{3}{4}+2\right)$$

-44 olish uchun -51 va 7'ni qo'shing.

$$\frac{1}{2}-\left(\frac{-44}{28}+\frac{1}{7}-\frac{3}{4}+2\right)$$

\frac{-44}{28} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}-\left(-\frac{11}{7}+\frac{1}{7}-\frac{3}{4}+2\right)$$

-\frac{11}{7} va \frac{1}{7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}-\left(\frac{-11+1}{7}-\frac{3}{4}+2\right)$$

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

$$\frac{1}{2}-\left(-\frac{10}{7}-\frac{3}{4}+2\right)$$

7 va 4 ning eng kichik umumiy karralisi 28 ga teng. -\frac{10}{7} va \frac{3}{4} ni 28 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1}{2}-\left(-\frac{40}{28}-\frac{21}{28}+2\right)$$

-\frac{40}{28} va \frac{21}{28} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1}{2}-\left(\frac{-40-21}{28}+2\right)$$

-61 olish uchun -40 dan 21 ni ayirish.

$$\frac{1}{2}-\left(-\frac{61}{28}+2\right)$$

2 ni \frac{56}{28} kasrga o‘giring.

$$\frac{1}{2}-\left(-\frac{61}{28}+\frac{56}{28}\right)$$

-\frac{61}{28} va \frac{56}{28} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{1}{2}-\frac{-61+56}{28}$$

-5 olish uchun -61 va 56'ni qo'shing.

$$\frac{1}{2}-\left(-\frac{5}{28}\right)$$

-\frac{5}{28} ning teskarisi \frac{5}{28} ga teng.

$$\frac{1}{2}+\frac{5}{28}$$

2 va 28 ning eng kichik umumiy karralisi 28 ga teng. \frac{1}{2} va \frac{5}{28} ni 28 maxraj bilan kasrlarga aylantirib oling.

$$\frac{14}{28}+\frac{5}{28}$$

\frac{14}{28} va \frac{5}{28} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{14+5}{28}$$

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

$$\frac{19}{28}$$

Omil

$$\frac{19}{2 ^ {2} \cdot 7} = 0,6785714285714286$$