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

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

Izračunaj

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

Koraci rješenja

Podijelite \pi s \frac{1\times 2+1}{2} tako da pomnožite \pi s brojem recipročnim broju \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 i 2 da biste dobili 2.

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

Dodajte 2 broju 1 da biste dobili 3.

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

Podijelite \frac{3\times 2+1}{2} s \frac{2\times 3+1}{3} tako da pomnožite \frac{3\times 2+1}{2} s brojem recipročnim broju \frac{2\times 3+1}{3}.

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

Skratite 1+2\times 3 u brojniku i nazivniku.

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

Pomnožite 1 i 4 da biste dobili 4.

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

Dodajte 4 broju 1 da biste dobili 5.

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

Pomnožite 3 i 3 da biste dobili 9.

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

Dodajte 9 broju 2 da biste dobili 11.

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

Pretvorite 2 u razlomak \frac{6}{3}.

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

Budući da \frac{6}{3} i \frac{11}{3} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Dodajte 6 broju 11 da biste dobili 17.

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

Podijelite \frac{5}{4} s \frac{17}{3} tako da pomnožite \frac{5}{4} s brojem recipročnim broju \frac{17}{3}.

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

Pomnožite \frac{5}{4} i \frac{3}{17} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{5\times 3}{4\times 17}.

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

Pomnožite \frac{3}{2} i \frac{15}{68} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{3\times 15}{2\times 68}.

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

Pomnožite \frac{\pi \times 2}{3} i \frac{45}{136} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Skratite 2\times 3 u brojniku i nazivniku.

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

Proširi

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

Koraci rješenja

Podijelite \pi s \frac{1\times 2+1}{2} tako da pomnožite \pi s brojem recipročnim broju \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 i 2 da biste dobili 2.

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

Dodajte 2 broju 1 da biste dobili 3.

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

Podijelite \frac{3\times 2+1}{2} s \frac{2\times 3+1}{3} tako da pomnožite \frac{3\times 2+1}{2} s brojem recipročnim broju \frac{2\times 3+1}{3}.

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

Skratite 1+2\times 3 u brojniku i nazivniku.

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

Pomnožite 1 i 4 da biste dobili 4.

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

Dodajte 4 broju 1 da biste dobili 5.

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

Pomnožite 3 i 3 da biste dobili 9.

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

Dodajte 9 broju 2 da biste dobili 11.

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

Pretvorite 2 u razlomak \frac{6}{3}.

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

Budući da \frac{6}{3} i \frac{11}{3} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Dodajte 6 broju 11 da biste dobili 17.

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

Podijelite \frac{5}{4} s \frac{17}{3} tako da pomnožite \frac{5}{4} s brojem recipročnim broju \frac{17}{3}.

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

Pomnožite \frac{5}{4} i \frac{3}{17} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{5\times 3}{4\times 17}.

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

Pomnožite \frac{3}{2} i \frac{15}{68} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{3\times 15}{2\times 68}.

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

Pomnožite \frac{\pi \times 2}{3} i \frac{45}{136} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Skratite 2\times 3 u brojniku i nazivniku.

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