(1+1/37)+2(1/5+9/153)] eching

$$( 1 + \frac { 1 } { 37 } ) + 2 ( \frac { 1 } { 5 } + \frac { 9 } { 153 } ) ]$$

Baholash

$$\frac{4858}{3145}\approx 1,544674086$$

Yechim qadamlari

1 ni \frac{37}{37} kasrga o‘giring.

$$\frac{37}{37}+\frac{1}{37}+2\left(\frac{1}{5}+\frac{9}{153}\right)$$

\frac{37}{37} va \frac{1}{37} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{37+1}{37}+2\left(\frac{1}{5}+\frac{9}{153}\right)$$

38 olish uchun 37 va 1'ni qo'shing.

$$\frac{38}{37}+2\left(\frac{1}{5}+\frac{9}{153}\right)$$

\frac{9}{153} ulushini 9 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{38}{37}+2\left(\frac{1}{5}+\frac{1}{17}\right)$$

5 va 17 ning eng kichik umumiy karralisi 85 ga teng. \frac{1}{5} va \frac{1}{17} ni 85 maxraj bilan kasrlarga aylantirib oling.

$$\frac{38}{37}+2\left(\frac{17}{85}+\frac{5}{85}\right)$$

\frac{17}{85} va \frac{5}{85} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{38}{37}+2\times \frac{17+5}{85}$$

22 olish uchun 17 va 5'ni qo'shing.

$$\frac{38}{37}+2\times \frac{22}{85}$$

2\times \frac{22}{85} ni yagona kasrga aylantiring.

$$\frac{38}{37}+\frac{2\times 22}{85}$$

44 hosil qilish uchun 2 va 22 ni ko'paytirish.

$$\frac{38}{37}+\frac{44}{85}$$

37 va 85 ning eng kichik umumiy karralisi 3145 ga teng. \frac{38}{37} va \frac{44}{85} ni 3145 maxraj bilan kasrlarga aylantirib oling.

$$\frac{3230}{3145}+\frac{1628}{3145}$$

\frac{3230}{3145} va \frac{1628}{3145} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{3230+1628}{3145}$$

4858 olish uchun 3230 va 1628'ni qo'shing.

$$\frac{4858}{3145}$$

Omil

$$\frac{2 \cdot 7 \cdot 347}{5 \cdot 17 \cdot 37} = 1\frac{1713}{3145} = 1,5446740858505565$$