(1-1/3)(1-1/5)(1-1/7)/(1+frac{1{3})(1+frac{1}{5})(1+frac{1}{7})} eching

$$\frac { ( 1 - \frac { 1 } { 3 } ) ( 1 - \frac { 1 } { 5 } ) ( 1 - \frac { 1 } { 7 } ) } { ( 1 + \frac { 1 } { 3 } ) ( 1 + \frac { 1 } { 5 } ) ( 1 + \frac { 1 } { 7 } ) }$$

Baholash

$$\frac{1}{4}=0,25$$

Yechim qadamlari

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{\left(\frac{3}{3}-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{3}{3} va \frac{1}{3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{3-1}{3}\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

2 olish uchun 3 dan 1 ni ayirish.

$$\frac{\frac{2}{3}\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

1 ni \frac{5}{5} kasrga o‘giring.

$$\frac{\frac{2}{3}\left(\frac{5}{5}-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{5}{5} va \frac{1}{5} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{2}{3}\times \frac{5-1}{5}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

4 olish uchun 5 dan 1 ni ayirish.

$$\frac{\frac{2}{3}\times \frac{4}{5}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{2}{3} ni \frac{4}{5} ga ko‘paytiring.

$$\frac{\frac{2\times 4}{3\times 5}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{2\times 4}{3\times 5} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{8}{15}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

1 ni \frac{7}{7} kasrga o‘giring.

$$\frac{\frac{8}{15}\left(\frac{7}{7}-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{7}{7} va \frac{1}{7} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{8}{15}\times \frac{7-1}{7}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

6 olish uchun 7 dan 1 ni ayirish.

$$\frac{\frac{8}{15}\times \frac{6}{7}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{15} ni \frac{6}{7} ga ko‘paytiring.

$$\frac{\frac{8\times 6}{15\times 7}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{8\times 6}{15\times 7} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{48}{105}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{48}{105} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{16}{35}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$\frac{\frac{16}{35}}{\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

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

$$\frac{\frac{16}{35}}{\frac{3+1}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

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

$$\frac{\frac{16}{35}}{\frac{4}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

1 ni \frac{5}{5} kasrga o‘giring.

$$\frac{\frac{16}{35}}{\frac{4}{3}\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{5}{5} va \frac{1}{5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{16}{35}}{\frac{4}{3}\times \frac{5+1}{5}\left(1+\frac{1}{7}\right)}$$

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

$$\frac{\frac{16}{35}}{\frac{4}{3}\times \frac{6}{5}\left(1+\frac{1}{7}\right)}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{6}{5} ga ko‘paytiring.

$$\frac{\frac{16}{35}}{\frac{4\times 6}{3\times 5}\left(1+\frac{1}{7}\right)}$$

\frac{4\times 6}{3\times 5} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{16}{35}}{\frac{24}{15}\left(1+\frac{1}{7}\right)}$$

\frac{24}{15} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{16}{35}}{\frac{8}{5}\left(1+\frac{1}{7}\right)}$$

1 ni \frac{7}{7} kasrga o‘giring.

$$\frac{\frac{16}{35}}{\frac{8}{5}\left(\frac{7}{7}+\frac{1}{7}\right)}$$

\frac{7}{7} va \frac{1}{7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{16}{35}}{\frac{8}{5}\times \frac{7+1}{7}}$$

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

$$\frac{\frac{16}{35}}{\frac{8}{5}\times \frac{8}{7}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8}{5} ni \frac{8}{7} ga ko‘paytiring.

$$\frac{\frac{16}{35}}{\frac{8\times 8}{5\times 7}}$$

\frac{8\times 8}{5\times 7} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{16}{35}}{\frac{64}{35}}$$

\frac{16}{35} ni \frac{64}{35} ga bo'lish \frac{16}{35} ga k'paytirish \frac{64}{35} ga qaytarish.

$$\frac{16}{35}\times \frac{35}{64}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{16}{35} ni \frac{35}{64} ga ko‘paytiring.

$$\frac{16\times 35}{35\times 64}$$

Surat va maxrajdagi ikkala 35 ni qisqartiring.

$$\frac{16}{64}$$

\frac{16}{64} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{4}$$

Omil

$$\frac{1}{2 ^ {2}} = 0,25$$