Whakaoti i te (3/4-1/3)2/3/(1-frac{1{6})div5}*3+frac{frac{frac{2}{3}+frac{1}{2}}{frac{1}{2}-frac{2}{5}}}{2}

$$\frac { ( \frac { 3 } { 4 } - \frac { 1 } { 3 } ) \frac { 2 } { 3 } } { ( 1 - \frac { 1 } { 6 } ) \div 5 } \times 3 + \frac { \frac { \frac { 2 } { 3 } + \frac { 1 } { 2 } } { \frac { 1 } { 2 } - \frac { 2 } { 5 } } } { 2 }$$

Aromātai

$$\frac{65}{6}\approx 10.833333333$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 4 me 3 ko 12. Me tahuri \frac{3}{4} me \frac{1}{3} ki te hautau me te tautūnga 12.

$$\frac{\left(\frac{9}{12}-\frac{4}{12}\right)\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tā te mea he rite te tauraro o \frac{9}{12} me \frac{4}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{9-4}{12}\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tangohia te 4 i te 9, ka 5.

$$\frac{\frac{5}{12}\times \frac{2}{3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Me whakarea te \frac{5}{12} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{5\times 2}{12\times 3}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 2}{12\times 3}.

$$\frac{\frac{10}{36}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Whakahekea te hautanga \frac{10}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{5}{18}}{\frac{1-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Me tahuri te 1 ki te hautau \frac{6}{6}.

$$\frac{\frac{5}{18}}{\frac{\frac{6}{6}-\frac{1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tā te mea he rite te tauraro o \frac{6}{6} me \frac{1}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{5}{18}}{\frac{\frac{6-1}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tangohia te 1 i te 6, ka 5.

$$\frac{\frac{5}{18}}{\frac{\frac{5}{6}}{5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tuhia te \frac{\frac{5}{6}}{5} hei hautanga kotahi.

$$\frac{\frac{5}{18}}{\frac{5}{6\times 5}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$\frac{\frac{5}{18}}{\frac{1}{6}}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Whakawehe \frac{5}{18} ki te \frac{1}{6} mā te whakarea \frac{5}{18} ki te tau huripoki o \frac{1}{6}.

$$\frac{5}{18}\times 6\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tuhia te \frac{5}{18}\times 6 hei hautanga kotahi.

$$\frac{5\times 6}{18}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Whakareatia te 5 ki te 6, ka 30.

$$\frac{30}{18}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Whakahekea te hautanga \frac{30}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{5}{3}\times 3+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Me whakakore te 3 me te 3.

$$5+\frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2}$$

Tuhia te \frac{\frac{\frac{2}{3}+\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}}}{2} hei hautanga kotahi.

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

Ko te maha noa iti rawa atu o 3 me 2 ko 6. Me tahuri \frac{2}{3} me \frac{1}{2} ki te hautau me te tautūnga 6.

$$5+\frac{\frac{4}{6}+\frac{3}{6}}{\left(\frac{1}{2}-\frac{2}{5}\right)\times 2}$$

Tā te mea he rite te tauraro o \frac{4}{6} me \frac{3}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$5+\frac{\frac{4+3}{6}}{\left(\frac{1}{2}-\frac{2}{5}\right)\times 2}$$

Tāpirihia te 4 ki te 3, ka 7.

$$5+\frac{\frac{7}{6}}{\left(\frac{1}{2}-\frac{2}{5}\right)\times 2}$$

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

$$5+\frac{\frac{7}{6}}{\left(\frac{5}{10}-\frac{4}{10}\right)\times 2}$$

Tā te mea he rite te tauraro o \frac{5}{10} me \frac{4}{10}, me tango rāua mā te tango i ō raua taurunga.

$$5+\frac{\frac{7}{6}}{\frac{5-4}{10}\times 2}$$

Tangohia te 4 i te 5, ka 1.

$$5+\frac{\frac{7}{6}}{\frac{1}{10}\times 2}$$

Whakareatia te \frac{1}{10} ki te 2, ka \frac{2}{10}.

$$5+\frac{\frac{7}{6}}{\frac{2}{10}}$$

Whakahekea te hautanga \frac{2}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$5+\frac{\frac{7}{6}}{\frac{1}{5}}$$

Whakawehe \frac{7}{6} ki te \frac{1}{5} mā te whakarea \frac{7}{6} ki te tau huripoki o \frac{1}{5}.

$$5+\frac{7}{6}\times 5$$

Tuhia te \frac{7}{6}\times 5 hei hautanga kotahi.

$$5+\frac{7\times 5}{6}$$

Whakareatia te 7 ki te 5, ka 35.

$$5+\frac{35}{6}$$

Me tahuri te 5 ki te hautau \frac{30}{6}.

$$\frac{30}{6}+\frac{35}{6}$$

Tā te mea he rite te tauraro o \frac{30}{6} me \frac{35}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{30+35}{6}$$

Tāpirihia te 30 ki te 35, ka 65.

$$\frac{65}{6}$$

Tauwehe

$$\frac{5 \cdot 13}{2 \cdot 3} = 10\frac{5}{6} = 10.833333333333334$$