[3/2+1/2+frac{1{3}}]div[1/frac{3{5}}+frac{2/5}{3}] eching

$$[ \frac { 3 } { 2 } + \frac { 1 } { 2 + \frac { 1 } { 3 } } ] \div [ \frac { 1 } { \frac { 3 } { 5 } } + \frac { \frac { 2 } { 5 } } { 3 } ]$$

Baholash

$$\frac{15}{14}\approx 1,071428571$$

Yechim qadamlari

2 ni \frac{6}{3} kasrga o‘giring.

$$\frac{\frac{3}{2}+\frac{1}{\frac{6}{3}+\frac{1}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

\frac{6}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{3}{2}+\frac{1}{\frac{6+1}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

7 olish uchun 6 va 1'ni qo'shing.

$$\frac{\frac{3}{2}+\frac{1}{\frac{7}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

1 ni \frac{7}{3} ga bo'lish 1 ga k'paytirish \frac{7}{3} ga qaytarish.

$$\frac{\frac{3}{2}+1\times \frac{3}{7}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

\frac{3}{7} hosil qilish uchun 1 va \frac{3}{7} ni ko'paytirish.

$$\frac{\frac{3}{2}+\frac{3}{7}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

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

$$\frac{\frac{21}{14}+\frac{6}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

\frac{21}{14} va \frac{6}{14} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{21+6}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

27 olish uchun 21 va 6'ni qo'shing.

$$\frac{\frac{27}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

1 ni \frac{3}{5} ga bo'lish 1 ga k'paytirish \frac{3}{5} ga qaytarish.

$$\frac{\frac{27}{14}}{1\times \frac{5}{3}+\frac{\frac{2}{5}}{3}}$$

\frac{5}{3} hosil qilish uchun 1 va \frac{5}{3} ni ko'paytirish.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{\frac{2}{5}}{3}}$$

\frac{\frac{2}{5}}{3} ni yagona kasrga aylantiring.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{2}{5\times 3}}$$

15 hosil qilish uchun 5 va 3 ni ko'paytirish.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{2}{15}}$$

3 va 15 ning eng kichik umumiy karralisi 15 ga teng. \frac{5}{3} va \frac{2}{15} ni 15 maxraj bilan kasrlarga aylantirib oling.

$$\frac{\frac{27}{14}}{\frac{25}{15}+\frac{2}{15}}$$

\frac{25}{15} va \frac{2}{15} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{27}{14}}{\frac{25+2}{15}}$$

27 olish uchun 25 va 2'ni qo'shing.

$$\frac{\frac{27}{14}}{\frac{27}{15}}$$

\frac{27}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{27}{14}}{\frac{9}{5}}$$

\frac{27}{14} ni \frac{9}{5} ga bo'lish \frac{27}{14} ga k'paytirish \frac{9}{5} ga qaytarish.

$$\frac{27}{14}\times \frac{5}{9}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{27}{14} ni \frac{5}{9} ga ko‘paytiring.

$$\frac{27\times 5}{14\times 9}$$

\frac{27\times 5}{14\times 9} kasridagi ko‘paytirishlarni bajaring.

$$\frac{135}{126}$$

\frac{135}{126} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{15}{14}$$

Omil

$$\frac{3 \cdot 5}{2 \cdot 7} = 1\frac{1}{14} = 1,0714285714285714$$