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

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

Ovrednoti

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

Koraki rešitve

Delite \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/z \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}}} z obratno vrednostjo \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 in 3, da dobite 12.

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

Seštejte 12 in 2, da dobite 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 in 75, da dobite 0.

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

Seštejte \frac{14}{3} in 0, da dobite \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 in 13, da dobite 39.

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

Seštejte 39 in 9, da dobite 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} s/z \frac{48}{13} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Izvedite množenja v ulomku \frac{14\times 48}{3\times 13}.

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

Zmanjšajte ulomek \frac{672}{39} na najmanjši imenovalec tako, da izpeljete in okrajšate 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 kot enojni ulomek.

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

Pomnožite 224 in 7, da dobite 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 in 45, da dobite 225.

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

Seštejte 225 in 4, da dobite 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 in 6, da dobite 24.

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

Seštejte 24 in 1, da dobite 25.

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

Najmanjši skupni mnogokratnik 45 in 6 je 90. Pretvorite \frac{229}{45} in \frac{25}{6} v ulomke z imenovalcem 90.

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

Ker \frac{458}{90} in \frac{375}{90} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

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

Odštejte 375 od 458, da dobite 83.

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

Pomnožite 5 in 15, da dobite 75.

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

Seštejte 75 in 8, da dobite 83.

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

Delite \frac{83}{90} s/z \frac{83}{15} tako, da pomnožite \frac{83}{90} z obratno vrednostjo \frac{83}{15}.

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

Pomnožite \frac{83}{90} s/z \frac{15}{83} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

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

Okrajšaj 83 v števcu in imenovalcu.

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

Zmanjšajte ulomek \frac{15}{90} na najmanjši imenovalec tako, da izpeljete in okrajšate 15.

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

Pomnožite 34 in 7, da dobite 238.

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

Seštejte 238 in 2, da dobite 240.

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

Pomnožite \frac{1}{6} in 240, da dobite \frac{240}{6}.

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

Delite 240 s/z 6, da dobite 40.

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

Izrazite \frac{\frac{1568}{13}}{40} kot enojni ulomek.

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

Pomnožite 13 in 40, da dobite 520.

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

Zmanjšajte ulomek \frac{1568}{520} na najmanjši imenovalec tako, da izpeljete in okrajšate 8.

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

Faktoriziraj

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