(1/1*4+1/4*7+1/7*1+1/10*13+frac{1}{13-16})= eching

$$( \frac { 1 } { 1 \cdot 4 } + \frac { 1 } { 4 \cdot 7 } + \frac { 1 } { 7 \cdot 1 } + \frac { 1 } { 10 \cdot 13 } + \frac { 1 } { 13 - 16 } ) =$$

Baholash

$$\frac{281}{2730}\approx 0,102930403$$

Yechim qadamlari

4 hosil qilish uchun 1 va 4 ni ko'paytirish.

$$\frac{1}{4}+\frac{1}{4\times 7}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

28 hosil qilish uchun 4 va 7 ni ko'paytirish.

$$\frac{1}{4}+\frac{1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

4 va 28 ning eng kichik umumiy karralisi 28 ga teng. \frac{1}{4} va \frac{1}{28} ni 28 maxraj bilan kasrlarga aylantirib oling.

$$\frac{7}{28}+\frac{1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

\frac{7}{28} va \frac{1}{28} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{7+1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

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

$$\frac{8}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

\frac{8}{28} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{2}{7}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

7 hosil qilish uchun 7 va 1 ni ko'paytirish.

$$\frac{2}{7}+\frac{1}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

\frac{2}{7} va \frac{1}{7} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2+1}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

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

$$\frac{3}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

130 hosil qilish uchun 10 va 13 ni ko'paytirish.

$$\frac{3}{7}+\frac{1}{130}+\frac{1}{13-16}$$

7 va 130 ning eng kichik umumiy karralisi 910 ga teng. \frac{3}{7} va \frac{1}{130} ni 910 maxraj bilan kasrlarga aylantirib oling.

$$\frac{390}{910}+\frac{7}{910}+\frac{1}{13-16}$$

\frac{390}{910} va \frac{7}{910} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{390+7}{910}+\frac{1}{13-16}$$

397 olish uchun 390 va 7'ni qo'shing.

$$\frac{397}{910}+\frac{1}{13-16}$$

-3 olish uchun 13 dan 16 ni ayirish.

$$\frac{397}{910}+\frac{1}{-3}$$

\frac{1}{-3} kasri manfiy belgini olib tashlash bilan -\frac{1}{3} sifatida qayta yozilishi mumkin.

$$\frac{397}{910}-\frac{1}{3}$$

910 va 3 ning eng kichik umumiy karralisi 2730 ga teng. \frac{397}{910} va \frac{1}{3} ni 2730 maxraj bilan kasrlarga aylantirib oling.

$$\frac{1191}{2730}-\frac{910}{2730}$$

\frac{1191}{2730} va \frac{910}{2730} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1191-910}{2730}$$

281 olish uchun 1191 dan 910 ni ayirish.

$$\frac{281}{2730}$$

Omil

$$\frac{281}{2 \cdot 3 \cdot 5 \cdot 7 \cdot 13} = 0,10293040293040293$$