(1/2+1/4+1/6+1/8+frac{1}{10}) eching

$$( \frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 6 } + \frac { 1 } { 8 } + \frac { 1 } { 10 } )$$

Baholash

$$\frac{137}{120}\approx 1,141666667$$

Yechim qadamlari

2 va 4 ning eng kichik umumiy karralisi 4 ga teng. \frac{1}{2} va \frac{1}{4} ni 4 maxraj bilan kasrlarga aylantirib oling.

$$\frac{2}{4}+\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}$$

\frac{2}{4} va \frac{1}{4} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2+1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}$$

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

$$\frac{3}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{10}$$

4 va 6 ning eng kichik umumiy karralisi 12 ga teng. \frac{3}{4} va \frac{1}{6} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{9}{12}+\frac{2}{12}+\frac{1}{8}+\frac{1}{10}$$

\frac{9}{12} va \frac{2}{12} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{9+2}{12}+\frac{1}{8}+\frac{1}{10}$$

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

$$\frac{11}{12}+\frac{1}{8}+\frac{1}{10}$$

12 va 8 ning eng kichik umumiy karralisi 24 ga teng. \frac{11}{12} va \frac{1}{8} ni 24 maxraj bilan kasrlarga aylantirib oling.

$$\frac{22}{24}+\frac{3}{24}+\frac{1}{10}$$

\frac{22}{24} va \frac{3}{24} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{22+3}{24}+\frac{1}{10}$$

25 olish uchun 22 va 3'ni qo'shing.

$$\frac{25}{24}+\frac{1}{10}$$

24 va 10 ning eng kichik umumiy karralisi 120 ga teng. \frac{25}{24} va \frac{1}{10} ni 120 maxraj bilan kasrlarga aylantirib oling.

$$\frac{125}{120}+\frac{12}{120}$$

\frac{125}{120} va \frac{12}{120} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{125+12}{120}$$

137 olish uchun 125 va 12'ni qo'shing.

$$\frac{137}{120}$$

Omil

$$\frac{137}{2 ^ {3} \cdot 3 \cdot 5} = 1\frac{17}{120} = 1,1416666666666666$$