11/4+15/9*15/8div61/2=? eching

$$1 \frac { 1 } { 4 } + 1 \frac { 5 } { 9 } \times 1 \frac { 5 } { 8 } \div 6 \frac { 1 } { 2 } = ?$$

Baholash

$$\frac{59}{36}\approx 1,638888889$$

Yechim qadamlari

4 hosil qilish uchun 1 va 4 ni ko'paytirish.

$$\frac{4+1}{4}+\frac{\frac{1\times 9+5}{9}\times \frac{1\times 8+5}{8}}{\frac{6\times 2+1}{2}}$$

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

$$\frac{5}{4}+\frac{\frac{1\times 9+5}{9}\times \frac{1\times 8+5}{8}}{\frac{6\times 2+1}{2}}$$

9 hosil qilish uchun 1 va 9 ni ko'paytirish.

$$\frac{5}{4}+\frac{\frac{9+5}{9}\times \frac{1\times 8+5}{8}}{\frac{6\times 2+1}{2}}$$

14 olish uchun 9 va 5'ni qo'shing.

$$\frac{5}{4}+\frac{\frac{14}{9}\times \frac{1\times 8+5}{8}}{\frac{6\times 2+1}{2}}$$

8 hosil qilish uchun 1 va 8 ni ko'paytirish.

$$\frac{5}{4}+\frac{\frac{14}{9}\times \frac{8+5}{8}}{\frac{6\times 2+1}{2}}$$

13 olish uchun 8 va 5'ni qo'shing.

$$\frac{5}{4}+\frac{\frac{14}{9}\times \frac{13}{8}}{\frac{6\times 2+1}{2}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{14}{9} ni \frac{13}{8} ga ko‘paytiring.

$$\frac{5}{4}+\frac{\frac{14\times 13}{9\times 8}}{\frac{6\times 2+1}{2}}$$

\frac{14\times 13}{9\times 8} kasridagi ko‘paytirishlarni bajaring.

$$\frac{5}{4}+\frac{\frac{182}{72}}{\frac{6\times 2+1}{2}}$$

\frac{182}{72} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{4}+\frac{\frac{91}{36}}{\frac{6\times 2+1}{2}}$$

12 hosil qilish uchun 6 va 2 ni ko'paytirish.

$$\frac{5}{4}+\frac{\frac{91}{36}}{\frac{12+1}{2}}$$

13 olish uchun 12 va 1'ni qo'shing.

$$\frac{5}{4}+\frac{\frac{91}{36}}{\frac{13}{2}}$$

\frac{91}{36} ni \frac{13}{2} ga bo'lish \frac{91}{36} ga k'paytirish \frac{13}{2} ga qaytarish.

$$\frac{5}{4}+\frac{91}{36}\times \frac{2}{13}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{91}{36} ni \frac{2}{13} ga ko‘paytiring.

$$\frac{5}{4}+\frac{91\times 2}{36\times 13}$$

\frac{91\times 2}{36\times 13} kasridagi ko‘paytirishlarni bajaring.

$$\frac{5}{4}+\frac{182}{468}$$

\frac{182}{468} ulushini 26 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{4}+\frac{7}{18}$$

4 va 18 ning eng kichik umumiy karralisi 36 ga teng. \frac{5}{4} va \frac{7}{18} ni 36 maxraj bilan kasrlarga aylantirib oling.

$$\frac{45}{36}+\frac{14}{36}$$

\frac{45}{36} va \frac{14}{36} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{45+14}{36}$$

59 olish uchun 45 va 14'ni qo'shing.

$$\frac{59}{36}$$

Omil

$$\frac{59}{2 ^ {2} \cdot 3 ^ {2}} = 1\frac{23}{36} = 1,6388888888888888$$