11/2[31/2div21/3{11/4div(2+3frac{2}{3})}] eching

$$1 \frac { 1 } { 2 } [ 3 \frac { 1 } { 2 } \div 2 \frac { 1 } { 3 } \{ 1 \frac { 1 } { 4 } \div ( 2 + 3 \frac { 2 } { 3 } ) \} ]$$

Baholash

$$\frac{135}{272}\approx 0,496323529$$

Yechim qadamlari

2 hosil qilish uchun 1 va 2 ni ko'paytirish.

$$\frac{2+1}{2}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

3 olish uchun 2 va 1'ni qo'shing.

$$\frac{3}{2}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

\frac{3\times 2+1}{2} ni \frac{2\times 3+1}{3} ga bo'lish \frac{3\times 2+1}{2} ga k'paytirish \frac{2\times 3+1}{3} ga qaytarish.

$$\frac{3}{2}\times \frac{\left(3\times 2+1\right)\times 3}{2\left(2\times 3+1\right)}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Surat va maxrajdagi ikkala 1+2\times 3 ni qisqartiring.

$$\frac{3}{2}\times \frac{3}{2}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3}{2} ni \frac{3}{2} ga ko‘paytiring.

$$\frac{3\times 3}{2\times 2}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

\frac{3\times 3}{2\times 2} kasridagi ko‘paytirishlarni bajaring.

$$\frac{9}{4}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

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

$$\frac{9}{4}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

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

$$\frac{9}{4}\times \frac{\frac{5}{4}}{2+\frac{3\times 3+2}{3}}$$

9 hosil qilish uchun 3 va 3 ni ko'paytirish.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{2+\frac{9+2}{3}}$$

11 olish uchun 9 va 2'ni qo'shing.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}$$

2 ni \frac{6}{3} kasrga o‘giring.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}$$

\frac{6}{3} va \frac{11}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}$$

17 olish uchun 6 va 11'ni qo'shing.

$$\frac{9}{4}\times \frac{\frac{5}{4}}{\frac{17}{3}}$$

\frac{5}{4} ni \frac{17}{3} ga bo'lish \frac{5}{4} ga k'paytirish \frac{17}{3} ga qaytarish.

$$\frac{9}{4}\times \frac{5}{4}\times \frac{3}{17}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{5}{4} ni \frac{3}{17} ga ko‘paytiring.

$$\frac{9}{4}\times \frac{5\times 3}{4\times 17}$$

\frac{5\times 3}{4\times 17} kasridagi ko‘paytirishlarni bajaring.

$$\frac{9}{4}\times \frac{15}{68}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{9}{4} ni \frac{15}{68} ga ko‘paytiring.

$$\frac{9\times 15}{4\times 68}$$

\frac{9\times 15}{4\times 68} kasridagi ko‘paytirishlarni bajaring.

$$\frac{135}{272}$$

Omil

$$\frac{3 ^ {3} \cdot 5}{2 ^ {4} \cdot 17} = 0,4963235294117647$$