5|[(1/2+1/3-1/4)*(1/2-frac{1}{13})+frac{1}{4}:frac{1}{2}] eching

$$5 | [ ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } ) \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 13 } ) + \frac { 1 } { 4 } : \frac { 1 } { 2 } ]$$

Baholash

$$\frac{1165}{312}\approx 3,733974359$$

Yechim qadamlari

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

$$5|\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

\frac{3}{6} va \frac{2}{6} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$5|\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

5 olish uchun 3 va 2'ni qo'shing.

$$5|\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

6 va 4 ning eng kichik umumiy karralisi 12 ga teng. \frac{5}{6} va \frac{1}{4} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$5|\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

\frac{10}{12} va \frac{3}{12} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$5|\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

7 olish uchun 10 dan 3 ni ayirish.

$$5|\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

2 va 13 ning eng kichik umumiy karralisi 26 ga teng. \frac{1}{2} va \frac{1}{13} ni 26 maxraj bilan kasrlarga aylantirib oling.

$$5|\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

\frac{13}{26} va \frac{2}{26} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$5|\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

11 olish uchun 13 dan 2 ni ayirish.

$$5|\frac{7}{12}\times \frac{11}{26}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{7}{12} ni \frac{11}{26} ga ko‘paytiring.

$$5|\frac{7\times 11}{12\times 26}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

\frac{7\times 11}{12\times 26} kasridagi ko‘paytirishlarni bajaring.

$$5|\frac{77}{312}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

\frac{1}{4} ni \frac{1}{2} ga bo'lish \frac{1}{4} ga k'paytirish \frac{1}{2} ga qaytarish.

$$5|\frac{77}{312}+\frac{1}{4}\times 2|$$

\frac{2}{4} hosil qilish uchun \frac{1}{4} va 2 ni ko'paytirish.

$$5|\frac{77}{312}+\frac{2}{4}|$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$5|\frac{77}{312}+\frac{1}{2}|$$

312 va 2 ning eng kichik umumiy karralisi 312 ga teng. \frac{77}{312} va \frac{1}{2} ni 312 maxraj bilan kasrlarga aylantirib oling.

$$5|\frac{77}{312}+\frac{156}{312}|$$

\frac{77}{312} va \frac{156}{312} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$5|\frac{77+156}{312}|$$

233 olish uchun 77 va 156'ni qo'shing.

$$5|\frac{233}{312}|$$

a haqiqiy sonining mutloq qiymati qachon a\geq 0 bo‘lganda, a yoki qachon a<0 bo‘lganda -a. \frac{233}{312} ning mutloq qiymati \frac{233}{312} ga teng.

$$5\times \frac{233}{312}$$

5\times \frac{233}{312} ni yagona kasrga aylantiring.

$$\frac{5\times 233}{312}$$

1165 hosil qilish uchun 5 va 233 ni ko'paytirish.

$$\frac{1165}{312}$$

Omil

$$\frac{5 \cdot 233}{2 ^ {3} \cdot 3 \cdot 13} = 3\frac{229}{312} = 3,733974358974359$$