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

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

Izračunaj

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

Koraci rješenja

Pretvorite 1 u razlomak \frac{3}{3}.

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

Budući da \frac{3}{3} i \frac{1}{3} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Oduzmite 1 od 3 da biste dobili 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 u razlomak \frac{5}{5}.

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

Budući da \frac{5}{5} i \frac{1}{5} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Oduzmite 1 od 5 da biste dobili 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} i \frac{4}{5} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \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 u razlomak \frac{7}{7}.

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

Budući da \frac{7}{7} i \frac{1}{7} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

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

Oduzmite 1 od 7 da biste dobili 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} i \frac{6}{7} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{8\times 6}{15\times 7}.

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

Skratite razlomak \frac{48}{105} na najmanje vrijednosti tako da izlučite i poništite 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 u razlomak \frac{3}{3}.

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

Budući da \frac{3}{3} i \frac{1}{3} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Dodajte 3 broju 1 da biste dobili 4.

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

Pretvorite 1 u razlomak \frac{5}{5}.

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

Budući da \frac{5}{5} i \frac{1}{5} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Dodajte 5 broju 1 da biste dobili 6.

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

Pomnožite \frac{4}{3} i \frac{6}{5} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{4\times 6}{3\times 5}.

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

Skratite razlomak \frac{24}{15} na najmanje vrijednosti tako da izlučite i poništite 3.

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

Pretvorite 1 u razlomak \frac{7}{7}.

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

Budući da \frac{7}{7} i \frac{1}{7} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

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

Dodajte 7 broju 1 da biste dobili 8.

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

Pomnožite \frac{8}{5} i \frac{8}{7} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Izvedite množenje u razlomku \frac{8\times 8}{5\times 7}.

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

Podijelite \frac{16}{35} s \frac{64}{35} tako da pomnožite \frac{16}{35} s brojem recipročnim broju \frac{64}{35}.

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

Pomnožite \frac{16}{35} i \frac{35}{64} tako da pomnožite brojnik s brojnikom i nazivnik s nazivnikom.

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

Skratite 35 u brojniku i nazivniku.

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

Skratite razlomak \frac{16}{64} na najmanje vrijednosti tako da izlučite i poništite 16.

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

Faktor

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