3/5+5{5+frac{5/5+5}} eching

$$\frac { 3 } { 5 + \frac { 5 } { 5 + \frac { 5 } { 5 + 5 } } }$$

Baholash

$$\frac{33}{65}\approx 0,507692308$$

Yechim qadamlari

10 olish uchun 5 va 5'ni qo'shing.

$$\frac{3}{5+\frac{5}{5+\frac{5}{10}}}$$

\frac{5}{10} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

5 ni \frac{10}{2} kasrga o‘giring.

$$\frac{3}{5+\frac{5}{\frac{10}{2}+\frac{1}{2}}}$$

\frac{10}{2} va \frac{1}{2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3}{5+\frac{5}{\frac{10+1}{2}}}$$

11 olish uchun 10 va 1'ni qo'shing.

$$\frac{3}{5+\frac{5}{\frac{11}{2}}}$$

5 ni \frac{11}{2} ga bo'lish 5 ga k'paytirish \frac{11}{2} ga qaytarish.

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

5\times \frac{2}{11} ni yagona kasrga aylantiring.

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

10 hosil qilish uchun 5 va 2 ni ko'paytirish.

$$\frac{3}{5+\frac{10}{11}}$$

5 ni \frac{55}{11} kasrga o‘giring.

$$\frac{3}{\frac{55}{11}+\frac{10}{11}}$$

\frac{55}{11} va \frac{10}{11} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3}{\frac{55+10}{11}}$$

65 olish uchun 55 va 10'ni qo'shing.

$$\frac{3}{\frac{65}{11}}$$

3 ni \frac{65}{11} ga bo'lish 3 ga k'paytirish \frac{65}{11} ga qaytarish.

$$3\times \frac{11}{65}$$

3\times \frac{11}{65} ni yagona kasrga aylantiring.

$$\frac{3\times 11}{65}$$

33 hosil qilish uchun 3 va 11 ni ko'paytirish.

$$\frac{33}{65}$$

Omil

$$\frac{3 \cdot 11}{5 \cdot 13} = 0,5076923076923077$$