1/2+1/6+1/12+1/20+frac{1}{30}+frac{1}{42} eching

$$\frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 } + \frac { 1 } { 20 } + \frac { 1 } { 30 } + \frac { 1 } { 42 }$$

Baholash

$$\frac{6}{7}\approx 0,857142857$$

Yechim qadamlari

2 va 6 ning eng kichik umumiy karralisi 6 ga teng. \frac{1}{2} va \frac{1}{6} ni 6 maxraj bilan kasrlarga aylantirib oling.

$$\frac{3}{6}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

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

$$\frac{3+1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

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

$$\frac{4}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

\frac{4}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{3}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

3 va 12 ning eng kichik umumiy karralisi 12 ga teng. \frac{2}{3} va \frac{1}{12} ni 12 maxraj bilan kasrlarga aylantirib oling.

$$\frac{8}{12}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

\frac{8}{12} va \frac{1}{12} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8+1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

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

$$\frac{9}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

\frac{9}{12} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{3}{4}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

4 va 20 ning eng kichik umumiy karralisi 20 ga teng. \frac{3}{4} va \frac{1}{20} ni 20 maxraj bilan kasrlarga aylantirib oling.

$$\frac{15}{20}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}$$

\frac{15}{20} va \frac{1}{20} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{15+1}{20}+\frac{1}{30}+\frac{1}{42}$$

16 olish uchun 15 va 1'ni qo'shing.

$$\frac{16}{20}+\frac{1}{30}+\frac{1}{42}$$

\frac{16}{20} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{4}{5}+\frac{1}{30}+\frac{1}{42}$$

5 va 30 ning eng kichik umumiy karralisi 30 ga teng. \frac{4}{5} va \frac{1}{30} ni 30 maxraj bilan kasrlarga aylantirib oling.

$$\frac{24}{30}+\frac{1}{30}+\frac{1}{42}$$

\frac{24}{30} va \frac{1}{30} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{24+1}{30}+\frac{1}{42}$$

25 olish uchun 24 va 1'ni qo'shing.

$$\frac{25}{30}+\frac{1}{42}$$

\frac{25}{30} ulushini 5 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{6}+\frac{1}{42}$$

6 va 42 ning eng kichik umumiy karralisi 42 ga teng. \frac{5}{6} va \frac{1}{42} ni 42 maxraj bilan kasrlarga aylantirib oling.

$$\frac{35}{42}+\frac{1}{42}$$

\frac{35}{42} va \frac{1}{42} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{35+1}{42}$$

36 olish uchun 35 va 1'ni qo'shing.

$$\frac{36}{42}$$

\frac{36}{42} ulushini 6 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{6}{7}$$

Omil

$$\frac{2 \cdot 3}{7} = 0,8571428571428571$$