Rešite (1-1/3)(1-1/5)(1-1/7)/(1+frac{1{3})(1+frac{1}{5})(1+frac{1}{7})}

$$\frac { ( 1 - \frac { 1 } { 3 } ) ( 1 - \frac { 1 } { 5 } ) ( 1 - \frac { 1 } { 7 } ) } { ( 1 + \frac { 1 } { 3 } ) ( 1 + \frac { 1 } { 5 } ) ( 1 + \frac { 1 } { 7 } ) }$$

Ovrednoti

$$\frac{1}{4}=0,25$$

Koraki rešitve

Pretvorite 1 v ulomek \frac{3}{3}.

$$\frac{\left(\frac{3}{3}-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Ker \frac{3}{3} in \frac{1}{3} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{\frac{3-1}{3}\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Odštejte 1 od 3, da dobite 2.

$$\frac{\frac{2}{3}\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Pretvorite 1 v ulomek \frac{5}{5}.

$$\frac{\frac{2}{3}\left(\frac{5}{5}-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Ker \frac{5}{5} in \frac{1}{5} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{\frac{2}{3}\times \frac{5-1}{5}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Odštejte 1 od 5, da dobite 4.

$$\frac{\frac{2}{3}\times \frac{4}{5}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Pomnožite \frac{2}{3} s/z \frac{4}{5} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{2\times 4}{3\times 5}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Izvedite množenja v ulomku \frac{2\times 4}{3\times 5}.

$$\frac{\frac{8}{15}\left(1-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Pretvorite 1 v ulomek \frac{7}{7}.

$$\frac{\frac{8}{15}\left(\frac{7}{7}-\frac{1}{7}\right)}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Ker \frac{7}{7} in \frac{1}{7} imata isti imenovalec, jih odštejte tako, da odštejete njihove števce.

$$\frac{\frac{8}{15}\times \frac{7-1}{7}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Odštejte 1 od 7, da dobite 6.

$$\frac{\frac{8}{15}\times \frac{6}{7}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Pomnožite \frac{8}{15} s/z \frac{6}{7} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{8\times 6}{15\times 7}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Izvedite množenja v ulomku \frac{8\times 6}{15\times 7}.

$$\frac{\frac{48}{105}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Zmanjšajte ulomek \frac{48}{105} na najmanjši imenovalec tako, da izpeljete in okrajšate 3.

$$\frac{\frac{16}{35}}{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Pretvorite 1 v ulomek \frac{3}{3}.

$$\frac{\frac{16}{35}}{\left(\frac{3}{3}+\frac{1}{3}\right)\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

\frac{3}{3} in \frac{1}{3} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{16}{35}}{\frac{3+1}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Seštejte 3 in 1, da dobite 4.

$$\frac{\frac{16}{35}}{\frac{4}{3}\left(1+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

Pretvorite 1 v ulomek \frac{5}{5}.

$$\frac{\frac{16}{35}}{\frac{4}{3}\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{7}\right)}$$

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

$$\frac{\frac{16}{35}}{\frac{4}{3}\times \frac{5+1}{5}\left(1+\frac{1}{7}\right)}$$

Seštejte 5 in 1, da dobite 6.

$$\frac{\frac{16}{35}}{\frac{4}{3}\times \frac{6}{5}\left(1+\frac{1}{7}\right)}$$

Pomnožite \frac{4}{3} s/z \frac{6}{5} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{16}{35}}{\frac{4\times 6}{3\times 5}\left(1+\frac{1}{7}\right)}$$

Izvedite množenja v ulomku \frac{4\times 6}{3\times 5}.

$$\frac{\frac{16}{35}}{\frac{24}{15}\left(1+\frac{1}{7}\right)}$$

Zmanjšajte ulomek \frac{24}{15} na najmanjši imenovalec tako, da izpeljete in okrajšate 3.

$$\frac{\frac{16}{35}}{\frac{8}{5}\left(1+\frac{1}{7}\right)}$$

Pretvorite 1 v ulomek \frac{7}{7}.

$$\frac{\frac{16}{35}}{\frac{8}{5}\left(\frac{7}{7}+\frac{1}{7}\right)}$$

\frac{7}{7} in \frac{1}{7} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{16}{35}}{\frac{8}{5}\times \frac{7+1}{7}}$$

Seštejte 7 in 1, da dobite 8.

$$\frac{\frac{16}{35}}{\frac{8}{5}\times \frac{8}{7}}$$

Pomnožite \frac{8}{5} s/z \frac{8}{7} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{16}{35}}{\frac{8\times 8}{5\times 7}}$$

Izvedite množenja v ulomku \frac{8\times 8}{5\times 7}.

$$\frac{\frac{16}{35}}{\frac{64}{35}}$$

Delite \frac{16}{35} s/z \frac{64}{35} tako, da pomnožite \frac{16}{35} z obratno vrednostjo \frac{64}{35}.

$$\frac{16}{35}\times \frac{35}{64}$$

Pomnožite \frac{16}{35} s/z \frac{35}{64} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{16\times 35}{35\times 64}$$

Okrajšaj 35 v števcu in imenovalcu.

$$\frac{16}{64}$$

Zmanjšajte ulomek \frac{16}{64} na najmanjši imenovalec tako, da izpeljete in okrajšate 16.

$$\frac{1}{4}$$

Faktoriziraj

$$\frac{1}{2 ^ {2}} = 0,25$$