Riješi (42/3+075)*39/13/(5frac{4{45}-41/6)div5frac{8}{15}}div34frac{2}{7}

$$\frac { ( 4 \frac { 2 } { 3 } + 075 ) \times 3 \frac { 9 } { 13 } } { ( 5 \frac { 4 } { 45 } - 4 \frac { 1 } { 6 } ) \div 5 \frac { 8 } { 15 } } \div 34 \frac { 2 } { 7 }$$

Izračunaj

$$\frac{196}{65}\approx 3,015384615$$

Koraci rješenja

Podijelite \frac{\left(\frac{4\times 3+2}{3}+0\times 75\right)\times \frac{3\times 13+9}{13}}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}} s \frac{34\times 7+2}{7} tako da pomnožite \frac{\left(\frac{4\times 3+2}{3}+0\times 75\right)\times \frac{3\times 13+9}{13}}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}} s brojem recipročnim broju \frac{34\times 7+2}{7}.

$$\frac{\left(\frac{4\times 3+2}{3}+0\times 75\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 4 i 3 da biste dobili 12.

$$\frac{\left(\frac{12+2}{3}+0\times 75\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Dodajte 12 broju 2 da biste dobili 14.

$$\frac{\left(\frac{14}{3}+0\times 75\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 0 i 75 da biste dobili 0.

$$\frac{\left(\frac{14}{3}+0\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Dodajte \frac{14}{3} broju 0 da biste dobili \frac{14}{3}.

$$\frac{\frac{14}{3}\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 3 i 13 da biste dobili 39.

$$\frac{\frac{14}{3}\times \frac{39+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Dodajte 39 broju 9 da biste dobili 48.

$$\frac{\frac{14}{3}\times \frac{48}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite \frac{14}{3} i \frac{48}{13} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

$$\frac{\frac{14\times 48}{3\times 13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Izvedite množenje u razlomku \frac{14\times 48}{3\times 13}.

$$\frac{\frac{672}{39}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Skratite razlomak \frac{672}{39} na najmanje vrijednosti tako da izlučite i poništite 3.

$$\frac{\frac{224}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Izrazite \frac{224}{13}\times 7 kao jedan razlomak.

$$\frac{\frac{224\times 7}{13}}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 224 i 7 da biste dobili 1568.

$$\frac{\frac{1568}{13}}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 5 i 45 da biste dobili 225.

$$\frac{\frac{1568}{13}}{\frac{\frac{225+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Dodajte 225 broju 4 da biste dobili 229.

$$\frac{\frac{1568}{13}}{\frac{\frac{229}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 4 i 6 da biste dobili 24.

$$\frac{\frac{1568}{13}}{\frac{\frac{229}{45}-\frac{24+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Dodajte 24 broju 1 da biste dobili 25.

$$\frac{\frac{1568}{13}}{\frac{\frac{229}{45}-\frac{25}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Najmanji zajednički višekratnik brojeva 45 i 6 je 90. Pretvorite \frac{229}{45} i \frac{25}{6} u razlomak s nazivnikom 90.

$$\frac{\frac{1568}{13}}{\frac{\frac{458}{90}-\frac{375}{90}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Budući da \frac{458}{90} i \frac{375}{90} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{\frac{1568}{13}}{\frac{\frac{458-375}{90}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Oduzmite 375 od 458 da biste dobili 83.

$$\frac{\frac{1568}{13}}{\frac{\frac{83}{90}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Pomnožite 5 i 15 da biste dobili 75.

$$\frac{\frac{1568}{13}}{\frac{\frac{83}{90}}{\frac{75+8}{15}}\left(34\times 7+2\right)}$$

Dodajte 75 broju 8 da biste dobili 83.

$$\frac{\frac{1568}{13}}{\frac{\frac{83}{90}}{\frac{83}{15}}\left(34\times 7+2\right)}$$

Podijelite \frac{83}{90} s \frac{83}{15} tako da pomnožite \frac{83}{90} s brojem recipročnim broju \frac{83}{15}.

$$\frac{\frac{1568}{13}}{\frac{83}{90}\times \frac{15}{83}\left(34\times 7+2\right)}$$

Pomnožite \frac{83}{90} i \frac{15}{83} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

$$\frac{\frac{1568}{13}}{\frac{83\times 15}{90\times 83}\left(34\times 7+2\right)}$$

Skratite 83 u brojniku i nazivniku.

$$\frac{\frac{1568}{13}}{\frac{15}{90}\left(34\times 7+2\right)}$$

Skratite razlomak \frac{15}{90} na najmanje vrijednosti tako da izlučite i poništite 15.

$$\frac{\frac{1568}{13}}{\frac{1}{6}\left(34\times 7+2\right)}$$

Pomnožite 34 i 7 da biste dobili 238.

$$\frac{\frac{1568}{13}}{\frac{1}{6}\left(238+2\right)}$$

Dodajte 238 broju 2 da biste dobili 240.

$$\frac{\frac{1568}{13}}{\frac{1}{6}\times 240}$$

Pomnožite \frac{1}{6} i 240 da biste dobili \frac{240}{6}.

$$\frac{\frac{1568}{13}}{\frac{240}{6}}$$

Podijelite 240 s 6 da biste dobili 40.

$$\frac{\frac{1568}{13}}{40}$$

Izrazite \frac{\frac{1568}{13}}{40} kao jedan razlomak.

$$\frac{1568}{13\times 40}$$

Pomnožite 13 i 40 da biste dobili 520.

$$\frac{1568}{520}$$

Skratite razlomak \frac{1568}{520} na najmanje vrijednosti tako da izlučite i poništite 8.

$$\frac{196}{65}$$

Faktor

$$\frac{2 ^ {2} \cdot 7 ^ {2}}{5 \cdot 13} = 3\frac{1}{65} = 3,0153846153846153$$