(1-5/7)*[(3-6/7-5/14):(5/6-frac{1}{3}-frac{3}{7})-frac{5}{12}] eching

$$( 1 - \frac { 5 } { 7 } ) \cdot [ ( 3 - \frac { 6 } { 7 } - \frac { 5 } { 14 } ) : ( \frac { 5 } { 6 } - \frac { 1 } { 3 } - \frac { 3 } { 7 } ) - \frac { 5 } { 12 } ]$$

Baholash

$$\frac{295}{42}\approx 7,023809524$$

Yechim qadamlari

1 ni \frac{7}{7} kasrga o‘giring.

$$\left(\frac{7}{7}-\frac{5}{7}\right)\left(\frac{3-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

\frac{7}{7} va \frac{5}{7} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{7-5}{7}\left(\frac{3-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

2 olish uchun 7 dan 5 ni ayirish.

$$\frac{2}{7}\left(\frac{3-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

3 ni \frac{21}{7} kasrga o‘giring.

$$\frac{2}{7}\left(\frac{\frac{21}{7}-\frac{6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

\frac{21}{7} va \frac{6}{7} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{7}\left(\frac{\frac{21-6}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

15 olish uchun 21 dan 6 ni ayirish.

$$\frac{2}{7}\left(\frac{\frac{15}{7}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

7 va 14 ning eng kichik umumiy karralisi 14 ga teng. \frac{15}{7} va \frac{5}{14} ni 14 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{7}\left(\frac{\frac{30}{14}-\frac{5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

\frac{30}{14} va \frac{5}{14} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{7}\left(\frac{\frac{30-5}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

25 olish uchun 30 dan 5 ni ayirish.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{5}{6}-\frac{1}{3}-\frac{3}{7}}-\frac{5}{12}\right)$$

6 va 3 ning eng kichik umumiy karralisi 6 ga teng. \frac{5}{6} va \frac{1}{3} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{5}{6}-\frac{2}{6}-\frac{3}{7}}-\frac{5}{12}\right)$$

\frac{5}{6} va \frac{2}{6} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{5-2}{6}-\frac{3}{7}}-\frac{5}{12}\right)$$

3 olish uchun 5 dan 2 ni ayirish.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{3}{6}-\frac{3}{7}}-\frac{5}{12}\right)$$

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

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{1}{2}-\frac{3}{7}}-\frac{5}{12}\right)$$

2 va 7 ning eng kichik umumiy karralisi 14 ga teng. \frac{1}{2} va \frac{3}{7} ni 14 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{7}{14}-\frac{6}{14}}-\frac{5}{12}\right)$$

\frac{7}{14} va \frac{6}{14} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{7-6}{14}}-\frac{5}{12}\right)$$

1 olish uchun 7 dan 6 ni ayirish.

$$\frac{2}{7}\left(\frac{\frac{25}{14}}{\frac{1}{14}}-\frac{5}{12}\right)$$

\frac{25}{14} ni \frac{1}{14} ga bo'lish \frac{25}{14} ga k'paytirish \frac{1}{14} ga qaytarish.

$$\frac{2}{7}\left(\frac{25}{14}\times 14-\frac{5}{12}\right)$$

14 va 14 ni qisqartiring.

$$\frac{2}{7}\left(25-\frac{5}{12}\right)$$

25 ni \frac{300}{12} kasrga o‘giring.

$$\frac{2}{7}\left(\frac{300}{12}-\frac{5}{12}\right)$$

\frac{300}{12} va \frac{5}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2}{7}\times \frac{300-5}{12}$$

295 olish uchun 300 dan 5 ni ayirish.

$$\frac{2}{7}\times \frac{295}{12}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2}{7} ni \frac{295}{12} ga ko‘paytiring.

$$\frac{2\times 295}{7\times 12}$$

\frac{2\times 295}{7\times 12} kasridagi ko‘paytirishlarni bajaring.

$$\frac{590}{84}$$

\frac{590}{84} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{295}{42}$$

Omil

$$\frac{5 \cdot 59}{2 \cdot 3 \cdot 7} = 7\frac{1}{42} = 7,023809523809524$$