Riješi (1+1/5)*(1+1/6)*(1+1/7)*(1+1/8)*(1+frac{1}{9})*(1+frac{1}{10})

$$( 1 + \frac { 1 } { 5 } ) \cdot ( 1 + \frac { 1 } { 6 } ) \cdot ( 1 + \frac { 1 } { 7 } ) \cdot ( 1 + \frac { 1 } { 8 } ) \cdot ( 1 + \frac { 1 } { 9 } ) \cdot ( 1 + \frac { 1 } { 10 } )$$

Procijeni

$$\frac{11}{5}=2,2$$

Koraci za rješenje

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

$$\left(\frac{5}{5}+\frac{1}{5}\right)\left(1+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pošto \frac{5}{5} i \frac{1}{5} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{5+1}{5}\left(1+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Saberite 5 i 1 da biste dobili 6.

$$\frac{6}{5}\left(1+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Konvertirajte 1 u razlomak \frac{6}{6}.

$$\frac{6}{5}\left(\frac{6}{6}+\frac{1}{6}\right)\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pošto \frac{6}{6} i \frac{1}{6} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{6}{5}\times \frac{6+1}{6}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Saberite 6 i 1 da biste dobili 7.

$$\frac{6}{5}\times \frac{7}{6}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pomnožite \frac{6}{5} i \frac{7}{6} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

$$\frac{6\times 7}{5\times 6}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Otkaži 6 u brojiocu i imeniocu.

$$\frac{7}{5}\left(1+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

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

$$\frac{7}{5}\left(\frac{7}{7}+\frac{1}{7}\right)\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pošto \frac{7}{7} i \frac{1}{7} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{7}{5}\times \frac{7+1}{7}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Saberite 7 i 1 da biste dobili 8.

$$\frac{7}{5}\times \frac{8}{7}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pomnožite \frac{7}{5} i \frac{8}{7} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

$$\frac{7\times 8}{5\times 7}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Otkaži 7 u brojiocu i imeniocu.

$$\frac{8}{5}\left(1+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Konvertirajte 1 u razlomak \frac{8}{8}.

$$\frac{8}{5}\left(\frac{8}{8}+\frac{1}{8}\right)\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pošto \frac{8}{8} i \frac{1}{8} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{8}{5}\times \frac{8+1}{8}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Saberite 8 i 1 da biste dobili 9.

$$\frac{8}{5}\times \frac{9}{8}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pomnožite \frac{8}{5} i \frac{9}{8} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

$$\frac{8\times 9}{5\times 8}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Otkaži 8 u brojiocu i imeniocu.

$$\frac{9}{5}\left(1+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Konvertirajte 1 u razlomak \frac{9}{9}.

$$\frac{9}{5}\left(\frac{9}{9}+\frac{1}{9}\right)\left(1+\frac{1}{10}\right)$$

Pošto \frac{9}{9} i \frac{1}{9} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$\frac{9}{5}\times \frac{9+1}{9}\left(1+\frac{1}{10}\right)$$

Saberite 9 i 1 da biste dobili 10.

$$\frac{9}{5}\times \frac{10}{9}\left(1+\frac{1}{10}\right)$$

Pomnožite \frac{9}{5} i \frac{10}{9} tako što ćete pomnožiti brojilac s brojiocem i imenilac s imeniocem.

$$\frac{9\times 10}{5\times 9}\left(1+\frac{1}{10}\right)$$

Otkaži 9 u brojiocu i imeniocu.

$$\frac{10}{5}\left(1+\frac{1}{10}\right)$$

Podijelite 10 sa 5 da biste dobili 2.

$$2\left(1+\frac{1}{10}\right)$$

Konvertirajte 1 u razlomak \frac{10}{10}.

$$2\left(\frac{10}{10}+\frac{1}{10}\right)$$

Pošto \frac{10}{10} i \frac{1}{10} imaju isti imenilac, saberite ih tako što ćete sabrati njihove brojioce.

$$2\times \frac{10+1}{10}$$

Saberite 10 i 1 da biste dobili 11.

$$2\times \frac{11}{10}$$

Izrazite 2\times \frac{11}{10} kao jedan razlomak.

$$\frac{2\times 11}{10}$$

Pomnožite 2 i 11 da biste dobili 22.

$$\frac{22}{10}$$

Svedite razlomak \frac{22}{10} na najprostije elemente rastavlјanjem i kraćenjem 2.

$$\frac{11}{5}$$

Faktor

$$\frac{11}{5} = 2\frac{1}{5} = 2,2$$