Whakaoti i te 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})

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

Aromātai

$$\frac{11}{12}\approx 0.916666667$$

Ngā Upane Otinga

Me tahuri te 2 ki te hautau \frac{6}{3}.

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

Tā te mea he rite te tauraro o \frac{6}{3} me \frac{2}{3}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 2 i te 6, ka 4.

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

Whakawehe \frac{4}{3} ki te \frac{4}{5} mā te whakarea \frac{4}{3} ki te tau huripoki o \frac{4}{5}.

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

Me whakarea te \frac{4}{3} ki te \frac{5}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Me whakakore tahi te 4 i te taurunga me te tauraro.

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

Me tahuri te 3 ki te hautau \frac{9}{3}.

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

Tā te mea he rite te tauraro o \frac{9}{3} me \frac{1}{3}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 9, ka 8.

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

Whakawehe \frac{8}{3} ki te \frac{4}{3} mā te whakarea \frac{8}{3} ki te tau huripoki o \frac{4}{3}.

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

Me whakarea te \frac{8}{3} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Me whakakore tahi te 3 i te taurunga me te tauraro.

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

Whakawehea te 8 ki te 4, kia riro ko 2.

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

Me tahuri te 2 ki te hautau \frac{6}{3}.

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

Tā te mea he rite te tauraro o \frac{5}{3} me \frac{6}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 5 ki te 6, ka 11.

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

Me tahuri te 4 ki te hautau \frac{16}{4}.

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

Tā te mea he rite te tauraro o \frac{16}{4} me \frac{1}{4}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 16, ka 15.

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

Whakawehe \frac{15}{4} ki te \frac{1}{2} mā te whakarea \frac{15}{4} ki te tau huripoki o \frac{1}{2}.

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

Tuhia te \frac{15}{4}\times 2 hei hautanga kotahi.

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

Whakareatia te 15 ki te 2, ka 30.

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

Whakahekea te hautanga \frac{30}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Me tahuri te 5 ki te hautau \frac{25}{5}.

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

Tā te mea he rite te tauraro o \frac{25}{5} me \frac{1}{5}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 1 i te 25, ka 24.

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

Tuhia te \frac{\frac{24}{5}}{24} hei hautanga kotahi.

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

Me whakakore tahi te 24 i te taurunga me te tauraro.

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

Ko te maha noa iti rawa atu o 2 me 5 ko 10. Me tahuri \frac{15}{2} me \frac{1}{5} ki te hautau me te tautūnga 10.

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

Tā te mea he rite te tauraro o \frac{75}{10} me \frac{2}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 75 ki te 2, ka 77.

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

Whakawehe \frac{11}{3} ki te \frac{77}{10} mā te whakarea \frac{11}{3} ki te tau huripoki o \frac{77}{10}.

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

Me whakarea te \frac{11}{3} ki te \frac{10}{77} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{11\times 10}{3\times 77}.

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

Whakahekea te hautanga \frac{110}{231} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 11.

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

Me whakarea te \frac{10}{21} ki te \frac{7}{20} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{10\times 7}{21\times 20}.

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

Whakahekea te hautanga \frac{70}{420} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 70.

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

Me whakarea te \frac{1}{6} ki te \frac{11}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 11}{6\times 2}.

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

Tauwehe

$$\frac{11}{2 ^ {2} \cdot 3} = 0.9166666666666666$$