Rešite 2-2/3/4/5+3-1/3/4/3/frac{4-1/4{1/2}+frac{5-1/5}{24}}*(frac{7}{20}*frac{11}{2})

$$\frac { \frac { 2 - \frac { 2 } { 3 } } { 4 / 5 } + \frac { 3 - 1 / 3 } { 4 / 3 } } { \frac { 4 - 1 / 4 } { 1 / 2 } + \frac { 5 - 1 / 5 } { 24 } } \times ( \frac { 7 } { 20 } \times \frac { 11 } { 2 } )$$

Ovrednoti

$$\frac{11}{12}\approx 0,916666667$$

Koraki rešitve

Pretvorite 2 v ulomek \frac{6}{3}.

$$\frac{\frac{\frac{6}{3}-\frac{2}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{6}{3} in \frac{2}{3} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{\frac{6-2}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Odštejte 2 od 6, da dobite 4.

$$\frac{\frac{\frac{4}{3}}{\frac{4}{5}}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Delite \frac{4}{3} s/z \frac{4}{5} tako, da pomnožite \frac{4}{3} z obratno vrednostjo \frac{4}{5}.

$$\frac{\frac{4}{3}\times \frac{5}{4}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

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

$$\frac{\frac{4\times 5}{3\times 4}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Okrajšaj 4 v števcu in imenovalcu.

$$\frac{\frac{5}{3}+\frac{3-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Pretvorite 3 v ulomek \frac{9}{3}.

$$\frac{\frac{5}{3}+\frac{\frac{9}{3}-\frac{1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{9}{3} in \frac{1}{3} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{5}{3}+\frac{\frac{9-1}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Odštejte 1 od 9, da dobite 8.

$$\frac{\frac{5}{3}+\frac{\frac{8}{3}}{\frac{4}{3}}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Delite \frac{8}{3} s/z \frac{4}{3} tako, da pomnožite \frac{8}{3} z obratno vrednostjo \frac{4}{3}.

$$\frac{\frac{5}{3}+\frac{8}{3}\times \frac{3}{4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Pomnožite \frac{8}{3} s/z \frac{3}{4} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{5}{3}+\frac{8\times 3}{3\times 4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Okrajšaj 3 v števcu in imenovalcu.

$$\frac{\frac{5}{3}+\frac{8}{4}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Delite 8 s/z 4, da dobite 2.

$$\frac{\frac{5}{3}+2}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Pretvorite 2 v ulomek \frac{6}{3}.

$$\frac{\frac{5}{3}+\frac{6}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{5}{3} in \frac{6}{3} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{5+6}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Seštejte 5 in 6, da dobite 11.

$$\frac{\frac{11}{3}}{\frac{4-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Pretvorite 4 v ulomek \frac{16}{4}.

$$\frac{\frac{11}{3}}{\frac{\frac{16}{4}-\frac{1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{16}{4} in \frac{1}{4} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{11}{3}}{\frac{\frac{16-1}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Odštejte 1 od 16, da dobite 15.

$$\frac{\frac{11}{3}}{\frac{\frac{15}{4}}{\frac{1}{2}}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Delite \frac{15}{4} s/z \frac{1}{2} tako, da pomnožite \frac{15}{4} z obratno vrednostjo \frac{1}{2}.

$$\frac{\frac{11}{3}}{\frac{15}{4}\times 2+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Izrazite \frac{15}{4}\times 2 kot enojni ulomek.

$$\frac{\frac{11}{3}}{\frac{15\times 2}{4}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Pomnožite 15 in 2, da dobite 30.

$$\frac{\frac{11}{3}}{\frac{30}{4}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Zmanjšajte ulomek \frac{30}{4} na najmanjši imenovalec tako, da izpeljete in okrajšate 2.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{5-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Pretvorite 5 v ulomek \frac{25}{5}.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{25}{5}-\frac{1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{25}{5} in \frac{1}{5} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{25-1}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Odštejte 1 od 25, da dobite 24.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{\frac{24}{5}}{24}}\times \frac{7}{20}\times \frac{11}{2}$$

Izrazite \frac{\frac{24}{5}}{24} kot enojni ulomek.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{24}{5\times 24}}\times \frac{7}{20}\times \frac{11}{2}$$

Okrajšaj 24 v števcu in imenovalcu.

$$\frac{\frac{11}{3}}{\frac{15}{2}+\frac{1}{5}}\times \frac{7}{20}\times \frac{11}{2}$$

Najmanjši skupni mnogokratnik 2 in 5 je 10. Pretvorite \frac{15}{2} in \frac{1}{5} v ulomke z imenovalcem 10.

$$\frac{\frac{11}{3}}{\frac{75}{10}+\frac{2}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

\frac{75}{10} in \frac{2}{10} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{11}{3}}{\frac{75+2}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

Seštejte 75 in 2, da dobite 77.

$$\frac{\frac{11}{3}}{\frac{77}{10}}\times \frac{7}{20}\times \frac{11}{2}$$

Delite \frac{11}{3} s/z \frac{77}{10} tako, da pomnožite \frac{11}{3} z obratno vrednostjo \frac{77}{10}.

$$\frac{11}{3}\times \frac{10}{77}\times \frac{7}{20}\times \frac{11}{2}$$

Pomnožite \frac{11}{3} s/z \frac{10}{77} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{11\times 10}{3\times 77}\times \frac{7}{20}\times \frac{11}{2}$$

Izvedite množenja v ulomku \frac{11\times 10}{3\times 77}.

$$\frac{110}{231}\times \frac{7}{20}\times \frac{11}{2}$$

Zmanjšajte ulomek \frac{110}{231} na najmanjši imenovalec tako, da izpeljete in okrajšate 11.

$$\frac{10}{21}\times \frac{7}{20}\times \frac{11}{2}$$

Pomnožite \frac{10}{21} s/z \frac{7}{20} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{10\times 7}{21\times 20}\times \frac{11}{2}$$

Izvedite množenja v ulomku \frac{10\times 7}{21\times 20}.

$$\frac{70}{420}\times \frac{11}{2}$$

Zmanjšajte ulomek \frac{70}{420} na najmanjši imenovalec tako, da izpeljete in okrajšate 70.

$$\frac{1}{6}\times \frac{11}{2}$$

Pomnožite \frac{1}{6} s/z \frac{11}{2} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{1\times 11}{6\times 2}$$

Izvedite množenja v ulomku \frac{1\times 11}{6\times 2}.

$$\frac{11}{12}$$

Faktoriziraj

$$\frac{11}{2 ^ {2} \cdot 3} = 0,9166666666666666$$