Whakaoti i te e(1-2/5)*((1/2+1/3-1/4)*(frac{1}{2}-frac{1}{13})+frac{3}{4}:frac{9}{2})

$$e ( 1 - \frac { 2 } { 5 } ) \cdot ( ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } ) \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 13 } ) + \frac { 3 } { 4 } : \frac { 9 } { 2 } )$$

Aromātai

$$\frac{129e}{520}\approx 0.674342992$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{5}{5}.

$$e\left(\frac{5}{5}-\frac{2}{5}\right)\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tā te mea he rite te tauraro o \frac{5}{5} me \frac{2}{5}, me tango rāua mā te tango i ō raua taurunga.

$$e\times \frac{5-2}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tangohia te 2 i te 5, ka 3.

$$e\times \frac{3}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$e\times \frac{3}{5}\left(\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$e\times \frac{3}{5}\left(\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tāpirihia te 3 ki te 2, ka 5.

$$e\times \frac{3}{5}\left(\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Ko te maha noa iti rawa atu o 6 me 4 ko 12. Me tahuri \frac{5}{6} me \frac{1}{4} ki te hautau me te tautūnga 12.

$$e\times \frac{3}{5}\left(\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tā te mea he rite te tauraro o \frac{10}{12} me \frac{3}{12}, me tango rāua mā te tango i ō raua taurunga.

$$e\times \frac{3}{5}\left(\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tangohia te 3 i te 10, ka 7.

$$e\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Ko te maha noa iti rawa atu o 2 me 13 ko 26. Me tahuri \frac{1}{2} me \frac{1}{13} ki te hautau me te tautūnga 26.

$$e\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tā te mea he rite te tauraro o \frac{13}{26} me \frac{2}{26}, me tango rāua mā te tango i ō raua taurunga.

$$e\times \frac{3}{5}\left(\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tangohia te 2 i te 13, ka 11.

$$e\times \frac{3}{5}\left(\frac{7}{12}\times \frac{11}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Me whakarea te \frac{7}{12} ki te \frac{11}{26} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$e\times \frac{3}{5}\left(\frac{7\times 11}{12\times 26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 11}{12\times 26}.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Whakawehe \frac{3}{4} ki te \frac{9}{2} mā te whakarea \frac{3}{4} ki te tau huripoki o \frac{9}{2}.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{3}{4}\times \frac{2}{9}\right)$$

Me whakarea te \frac{3}{4} ki te \frac{2}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{3\times 2}{4\times 9}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 2}{4\times 9}.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{6}{36}\right)$$

Whakahekea te hautanga \frac{6}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{1}{6}\right)$$

Ko te maha noa iti rawa atu o 312 me 6 ko 312. Me tahuri \frac{77}{312} me \frac{1}{6} ki te hautau me te tautūnga 312.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{52}{312}\right)$$

Tā te mea he rite te tauraro o \frac{77}{312} me \frac{52}{312}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$e\times \frac{3}{5}\times \frac{77+52}{312}$$

Tāpirihia te 77 ki te 52, ka 129.

$$e\times \frac{3}{5}\times \frac{129}{312}$$

Whakahekea te hautanga \frac{129}{312} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$e\times \frac{3}{5}\times \frac{43}{104}$$

Me whakarea te \frac{3}{5} ki te \frac{43}{104} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$e\times \frac{3\times 43}{5\times 104}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 43}{5\times 104}.

$$e\times \frac{129}{520}$$

Whakaroha

$$\frac{129e}{520}$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{5}{5}.

$$e\left(\frac{5}{5}-\frac{2}{5}\right)\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tā te mea he rite te tauraro o \frac{5}{5} me \frac{2}{5}, me tango rāua mā te tango i ō raua taurunga.

$$e\times \frac{5-2}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tangohia te 2 i te 5, ka 3.

$$e\times \frac{3}{5}\left(\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$e\times \frac{3}{5}\left(\left(\frac{3}{6}+\frac{2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

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

$$e\times \frac{3}{5}\left(\left(\frac{3+2}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tāpirihia te 3 ki te 2, ka 5.

$$e\times \frac{3}{5}\left(\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Ko te maha noa iti rawa atu o 6 me 4 ko 12. Me tahuri \frac{5}{6} me \frac{1}{4} ki te hautau me te tautūnga 12.

$$e\times \frac{3}{5}\left(\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tā te mea he rite te tauraro o \frac{10}{12} me \frac{3}{12}, me tango rāua mā te tango i ō raua taurunga.

$$e\times \frac{3}{5}\left(\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tangohia te 3 i te 10, ka 7.

$$e\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Ko te maha noa iti rawa atu o 2 me 13 ko 26. Me tahuri \frac{1}{2} me \frac{1}{13} ki te hautau me te tautūnga 26.

$$e\times \frac{3}{5}\left(\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tā te mea he rite te tauraro o \frac{13}{26} me \frac{2}{26}, me tango rāua mā te tango i ō raua taurunga.

$$e\times \frac{3}{5}\left(\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Tangohia te 2 i te 13, ka 11.

$$e\times \frac{3}{5}\left(\frac{7}{12}\times \frac{11}{26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Me whakarea te \frac{7}{12} ki te \frac{11}{26} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$e\times \frac{3}{5}\left(\frac{7\times 11}{12\times 26}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 11}{12\times 26}.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{\frac{3}{4}}{\frac{9}{2}}\right)$$

Whakawehe \frac{3}{4} ki te \frac{9}{2} mā te whakarea \frac{3}{4} ki te tau huripoki o \frac{9}{2}.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{3}{4}\times \frac{2}{9}\right)$$

Me whakarea te \frac{3}{4} ki te \frac{2}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{3\times 2}{4\times 9}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 2}{4\times 9}.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{6}{36}\right)$$

Whakahekea te hautanga \frac{6}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{1}{6}\right)$$

Ko te maha noa iti rawa atu o 312 me 6 ko 312. Me tahuri \frac{77}{312} me \frac{1}{6} ki te hautau me te tautūnga 312.

$$e\times \frac{3}{5}\left(\frac{77}{312}+\frac{52}{312}\right)$$

Tā te mea he rite te tauraro o \frac{77}{312} me \frac{52}{312}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$e\times \frac{3}{5}\times \frac{77+52}{312}$$

Tāpirihia te 77 ki te 52, ka 129.

$$e\times \frac{3}{5}\times \frac{129}{312}$$

Whakahekea te hautanga \frac{129}{312} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$e\times \frac{3}{5}\times \frac{43}{104}$$

Me whakarea te \frac{3}{5} ki te \frac{43}{104} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$e\times \frac{3\times 43}{5\times 104}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 43}{5\times 104}.

$$e\times \frac{129}{520}$$