1+1/1+3{1+frac{4/5}}=1+1/1+3{frac{9/3}} eching

$$1 + \frac { 1 } { 1 + \frac { 3 } { 1 + \frac { 4 } { 5 } } } = 1 + \frac { 1 } { 1 + \frac { 3 } { \frac { 9 } { 3 } } }$$

Tasdiqlamoq

Yechim qadamlari

1 ni \frac{5}{5} kasrga o‘giring.

$$1+\frac{1}{1+\frac{3}{\frac{5}{5}+\frac{4}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

\frac{5}{5} va \frac{4}{5} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$1+\frac{1}{1+\frac{3}{\frac{5+4}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

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

$$1+\frac{1}{1+\frac{3}{\frac{9}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

3 ni \frac{9}{5} ga bo'lish 3 ga k'paytirish \frac{9}{5} ga qaytarish.

$$1+\frac{1}{1+3\times \frac{5}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

3\times \frac{5}{9} ni yagona kasrga aylantiring.

$$1+\frac{1}{1+\frac{3\times 5}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

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

$$1+\frac{1}{1+\frac{15}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

\frac{15}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$1+\frac{1}{1+\frac{5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

1 ni \frac{3}{3} kasrga o‘giring.

$$1+\frac{1}{\frac{3}{3}+\frac{5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

\frac{3}{3} va \frac{5}{3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$1+\frac{1}{\frac{3+5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

8 olish uchun 3 va 5'ni qo'shing.

$$1+\frac{1}{\frac{8}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

1 ni \frac{8}{3} ga bo'lish 1 ga k'paytirish \frac{8}{3} ga qaytarish.

$$1+1\times \frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

\frac{3}{8} hosil qilish uchun 1 va \frac{3}{8} ni ko'paytirish.

$$1+\frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

1 ni \frac{8}{8} kasrga o‘giring.

$$\frac{8}{8}+\frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

\frac{8}{8} va \frac{3}{8} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8+3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

11 olish uchun 8 va 3'ni qo'shing.

$$\frac{11}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

3 ni \frac{9}{3} ga bo'lish 3 ga k'paytirish \frac{9}{3} ga qaytarish.

$$\frac{11}{8}=1+\frac{1}{1+\frac{3\times 3}{9}}$$

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

$$\frac{11}{8}=1+\frac{1}{1+\frac{9}{9}}$$

1 ni olish uchun 9 ni 9 ga bo‘ling.

$$\frac{11}{8}=1+\frac{1}{1+1}$$

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

$$\frac{11}{8}=1+\frac{1}{2}$$

1 ni \frac{2}{2} kasrga o‘giring.

$$\frac{11}{8}=\frac{2}{2}+\frac{1}{2}$$

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

$$\frac{11}{8}=\frac{2+1}{2}$$

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

$$\frac{11}{8}=\frac{3}{2}$$

8 va 2 ning eng kichik umumiy karralisi 8 ga teng. \frac{11}{8} va \frac{3}{2} ni 8 maxraj bilan kasrlarga aylantirib oling.

$$\frac{11}{8}=\frac{12}{8}$$

\frac{11}{8} va \frac{12}{8} ni taqqoslang.

$$\text{false}$$