Rešite (3/5+1/2*2/3):(frac{1/5+frac{4}{2})}{(1-frac{5}{6})*(1+frac{5}{6})+frac{1}{36}}*(1+frac{2}{21})

$$\frac { ( \frac { 3 } { 5 } + \frac { 1 } { 2 } \cdot \frac { 2 } { 3 } ) : ( \frac { 1 } { 5 } + \frac { 4 } { 2 } ) } { ( 1 - \frac { 5 } { 6 } ) \cdot ( 1 + \frac { 5 } { 6 } ) + \frac { 1 } { 36 } } \cdot ( 1 + \frac { 2 } { 21 } )$$

Ovrednoti

$$\frac{46}{33}\approx 1,393939394$$

Koraki rešitve

Pomnožite \frac{1}{2} s/z \frac{2}{3} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{\frac{3}{5}+\frac{1\times 2}{2\times 3}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Okrajšaj 2 v števcu in imenovalcu.

$$\frac{\frac{\frac{3}{5}+\frac{1}{3}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Najmanjši skupni mnogokratnik 5 in 3 je 15. Pretvorite \frac{3}{5} in \frac{1}{3} v ulomke z imenovalcem 15.

$$\frac{\frac{\frac{9}{15}+\frac{5}{15}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{9}{15} in \frac{5}{15} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{\frac{9+5}{15}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Seštejte 9 in 5, da dobite 14.

$$\frac{\frac{\frac{14}{15}}{\frac{1}{5}+\frac{4}{2}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Delite 4 s/z 2, da dobite 2.

$$\frac{\frac{\frac{14}{15}}{\frac{1}{5}+2}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Pretvorite 2 v ulomek \frac{10}{5}.

$$\frac{\frac{\frac{14}{15}}{\frac{1}{5}+\frac{10}{5}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{1}{5} in \frac{10}{5} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{\frac{14}{15}}{\frac{1+10}{5}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Seštejte 1 in 10, da dobite 11.

$$\frac{\frac{\frac{14}{15}}{\frac{11}{5}}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Delite \frac{14}{15} s/z \frac{11}{5} tako, da pomnožite \frac{14}{15} z obratno vrednostjo \frac{11}{5}.

$$\frac{\frac{14}{15}\times \frac{5}{11}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Pomnožite \frac{14}{15} s/z \frac{5}{11} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{14\times 5}{15\times 11}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Izvedite množenja v ulomku \frac{14\times 5}{15\times 11}.

$$\frac{\frac{70}{165}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Zmanjšajte ulomek \frac{70}{165} na najmanjši imenovalec tako, da izpeljete in okrajšate 5.

$$\frac{\frac{14}{33}}{\left(1-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Pretvorite 1 v ulomek \frac{6}{6}.

$$\frac{\frac{14}{33}}{\left(\frac{6}{6}-\frac{5}{6}\right)\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Ker \frac{6}{6} in \frac{5}{6} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{\frac{14}{33}}{\frac{6-5}{6}\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Odštejte 5 od 6, da dobite 1.

$$\frac{\frac{14}{33}}{\frac{1}{6}\left(1+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Pretvorite 1 v ulomek \frac{6}{6}.

$$\frac{\frac{14}{33}}{\frac{1}{6}\left(\frac{6}{6}+\frac{5}{6}\right)+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{6}{6} in \frac{5}{6} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{14}{33}}{\frac{1}{6}\times \frac{6+5}{6}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Seštejte 6 in 5, da dobite 11.

$$\frac{\frac{14}{33}}{\frac{1}{6}\times \frac{11}{6}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Pomnožite \frac{1}{6} s/z \frac{11}{6} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{14}{33}}{\frac{1\times 11}{6\times 6}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

Izvedite množenja v ulomku \frac{1\times 11}{6\times 6}.

$$\frac{\frac{14}{33}}{\frac{11}{36}+\frac{1}{36}}\left(1+\frac{2}{21}\right)$$

\frac{11}{36} in \frac{1}{36} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{14}{33}}{\frac{11+1}{36}}\left(1+\frac{2}{21}\right)$$

Seštejte 11 in 1, da dobite 12.

$$\frac{\frac{14}{33}}{\frac{12}{36}}\left(1+\frac{2}{21}\right)$$

Zmanjšajte ulomek \frac{12}{36} na najmanjši imenovalec tako, da izpeljete in okrajšate 12.

$$\frac{\frac{14}{33}}{\frac{1}{3}}\left(1+\frac{2}{21}\right)$$

Delite \frac{14}{33} s/z \frac{1}{3} tako, da pomnožite \frac{14}{33} z obratno vrednostjo \frac{1}{3}.

$$\frac{14}{33}\times 3\left(1+\frac{2}{21}\right)$$

Izrazite \frac{14}{33}\times 3 kot enojni ulomek.

$$\frac{14\times 3}{33}\left(1+\frac{2}{21}\right)$$

Pomnožite 14 in 3, da dobite 42.

$$\frac{42}{33}\left(1+\frac{2}{21}\right)$$

Zmanjšajte ulomek \frac{42}{33} na najmanjši imenovalec tako, da izpeljete in okrajšate 3.

$$\frac{14}{11}\left(1+\frac{2}{21}\right)$$

Pretvorite 1 v ulomek \frac{21}{21}.

$$\frac{14}{11}\left(\frac{21}{21}+\frac{2}{21}\right)$$

\frac{21}{21} in \frac{2}{21} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{14}{11}\times \frac{21+2}{21}$$

Seštejte 21 in 2, da dobite 23.

$$\frac{14}{11}\times \frac{23}{21}$$

Pomnožite \frac{14}{11} s/z \frac{23}{21} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{14\times 23}{11\times 21}$$

Izvedite množenja v ulomku \frac{14\times 23}{11\times 21}.

$$\frac{322}{231}$$

Zmanjšajte ulomek \frac{322}{231} na najmanjši imenovalec tako, da izpeljete in okrajšate 7.

$$\frac{46}{33}$$

Faktoriziraj

$$\frac{2 \cdot 23}{3 \cdot 11} = 1\frac{13}{33} = 1,393939393939394$$