Rešite pi:11/2[31/2div21/3{11/4div(2+3frac{2}{3})}]

$$\pi : 1 \frac { 1 } { 2 } [ 3 \frac { 1 } { 2 } \div 2 \frac { 1 } { 3 } \{ 1 \frac { 1 } { 4 } \div ( 2 + 3 \frac { 2 } { 3 } ) \} ]$$

Ovrednoti

$$\frac{15\pi }{68}\approx 0,692998379$$

Koraki rešitve

Delite \pi s/z \frac{1\times 2+1}{2} tako, da pomnožite \pi z obratno vrednostjo \frac{1\times 2+1}{2}.

$$\frac{\pi \times 2}{1\times 2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Pomnožite 1 in 2, da dobite 2.

$$\frac{\pi \times 2}{2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Seštejte 2 in 1, da dobite 3.

$$\frac{\pi \times 2}{3}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Delite \frac{3\times 2+1}{2} s/z \frac{2\times 3+1}{3} tako, da pomnožite \frac{3\times 2+1}{2} z obratno vrednostjo \frac{2\times 3+1}{3}.

$$\frac{\pi \times 2}{3}\times \frac{\left(3\times 2+1\right)\times 3}{2\left(2\times 3+1\right)}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Okrajšaj 1+2\times 3 v števcu in imenovalcu.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Pomnožite 1 in 4, da dobite 4.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Seštejte 4 in 1, da dobite 5.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{3\times 3+2}{3}}$$

Pomnožite 3 in 3, da dobite 9.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{9+2}{3}}$$

Seštejte 9 in 2, da dobite 11.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}$$

Pretvorite 2 v ulomek \frac{6}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}$$

\frac{6}{3} in \frac{11}{3} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}$$

Seštejte 6 in 11, da dobite 17.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{17}{3}}$$

Delite \frac{5}{4} s/z \frac{17}{3} tako, da pomnožite \frac{5}{4} z obratno vrednostjo \frac{17}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5}{4}\times \frac{3}{17}$$

Pomnožite \frac{5}{4} s/z \frac{3}{17} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5\times 3}{4\times 17}$$

Izvedite množenja v ulomku \frac{5\times 3}{4\times 17}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{15}{68}$$

Pomnožite \frac{3}{2} s/z \frac{15}{68} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\pi \times 2}{3}\times \frac{3\times 15}{2\times 68}$$

Izvedite množenja v ulomku \frac{3\times 15}{2\times 68}.

$$\frac{\pi \times 2}{3}\times \frac{45}{136}$$

Pomnožite \frac{\pi \times 2}{3} s/z \frac{45}{136} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\pi \times 2\times 45}{3\times 136}$$

Okrajšaj 2\times 3 v števcu in imenovalcu.

$$\frac{15\pi }{68}$$

Razširi

$$\frac{15 \pi}{68} = 0,6929983794683366$$

Koraki rešitve

Delite \pi s/z \frac{1\times 2+1}{2} tako, da pomnožite \pi z obratno vrednostjo \frac{1\times 2+1}{2}.

$$\frac{\pi \times 2}{1\times 2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Pomnožite 1 in 2, da dobite 2.

$$\frac{\pi \times 2}{2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Seštejte 2 in 1, da dobite 3.

$$\frac{\pi \times 2}{3}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Delite \frac{3\times 2+1}{2} s/z \frac{2\times 3+1}{3} tako, da pomnožite \frac{3\times 2+1}{2} z obratno vrednostjo \frac{2\times 3+1}{3}.

$$\frac{\pi \times 2}{3}\times \frac{\left(3\times 2+1\right)\times 3}{2\left(2\times 3+1\right)}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Okrajšaj 1+2\times 3 v števcu in imenovalcu.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Pomnožite 1 in 4, da dobite 4.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Seštejte 4 in 1, da dobite 5.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{3\times 3+2}{3}}$$

Pomnožite 3 in 3, da dobite 9.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{9+2}{3}}$$

Seštejte 9 in 2, da dobite 11.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}$$

Pretvorite 2 v ulomek \frac{6}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}$$

\frac{6}{3} in \frac{11}{3} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}$$

Seštejte 6 in 11, da dobite 17.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{17}{3}}$$

Delite \frac{5}{4} s/z \frac{17}{3} tako, da pomnožite \frac{5}{4} z obratno vrednostjo \frac{17}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5}{4}\times \frac{3}{17}$$

Pomnožite \frac{5}{4} s/z \frac{3}{17} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5\times 3}{4\times 17}$$

Izvedite množenja v ulomku \frac{5\times 3}{4\times 17}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{15}{68}$$

Pomnožite \frac{3}{2} s/z \frac{15}{68} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\pi \times 2}{3}\times \frac{3\times 15}{2\times 68}$$

Izvedite množenja v ulomku \frac{3\times 15}{2\times 68}.

$$\frac{\pi \times 2}{3}\times \frac{45}{136}$$

Pomnožite \frac{\pi \times 2}{3} s/z \frac{45}{136} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\pi \times 2\times 45}{3\times 136}$$

Okrajšaj 2\times 3 v števcu in imenovalcu.

$$\frac{15\pi }{68}$$