Whakaoti i te 2+1/3/7+1-frac{1/4/3}{frac{frac{1}{2}}{frac{1}{4}}-frac{frac{1}{4}}{frac{3}{5}}}left(frac{2}{7}+frac{4}{19}right)

$$\frac{ \frac{ 2+ \frac{ 1 }{ 3 } }{ 7 } + \frac{ 1- \frac{ 1 }{ 4 } }{ 3 } }{ \frac{ \frac{ 1 }{ 2 } }{ \frac{ 1 }{ 4 } } - \frac{ \frac{ 1 }{ 4 } }{ \frac{ 3 }{ 5 } } } \left( \frac{ 2 }{ 7 } + \frac{ 4 }{ 19 } \right)$$

Aromātai

$$\frac{66}{361}\approx 0.182825485$$

Ngā Upane Otinga

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

$$\frac{\frac{\frac{6}{3}+\frac{1}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tā te mea he rite te tauraro o \frac{6}{3} me \frac{1}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{\frac{6+1}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{\frac{\frac{7}{3}}{7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tuhia te \frac{\frac{7}{3}}{7} hei hautanga kotahi.

$$\frac{\frac{7}{3\times 7}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Me whakakore tahi te 7 i te taurunga me te tauraro.

$$\frac{\frac{1}{3}+\frac{1-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$\frac{\frac{1}{3}+\frac{\frac{4}{4}-\frac{1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{1}{3}+\frac{\frac{4-1}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tangohia te 1 i te 4, ka 3.

$$\frac{\frac{1}{3}+\frac{\frac{3}{4}}{3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tuhia te \frac{\frac{3}{4}}{3} hei hautanga kotahi.

$$\frac{\frac{1}{3}+\frac{3}{4\times 3}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{1}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{4}{12}+\frac{3}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tā te mea he rite te tauraro o \frac{4}{12} me \frac{3}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{4+3}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tāpirihia te 4 ki te 3, ka 7.

$$\frac{\frac{7}{12}}{\frac{\frac{1}{2}}{\frac{1}{4}}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{7}{12}}{\frac{1}{2}\times 4-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Whakareatia te \frac{1}{2} ki te 4, ka \frac{4}{2}.

$$\frac{\frac{7}{12}}{\frac{4}{2}-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

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

$$\frac{\frac{7}{12}}{2-\frac{\frac{1}{4}}{\frac{3}{5}}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Whakawehe \frac{1}{4} ki te \frac{3}{5} mā te whakarea \frac{1}{4} ki te tau huripoki o \frac{3}{5}.

$$\frac{\frac{7}{12}}{2-\frac{1}{4}\times \frac{5}{3}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Me whakarea te \frac{1}{4} ki te \frac{5}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{7}{12}}{2-\frac{1\times 5}{4\times 3}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 5}{4\times 3}.

$$\frac{\frac{7}{12}}{2-\frac{5}{12}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Me tahuri te 2 ki te hautau \frac{24}{12}.

$$\frac{\frac{7}{12}}{\frac{24}{12}-\frac{5}{12}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tā te mea he rite te tauraro o \frac{24}{12} me \frac{5}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{7}{12}}{\frac{24-5}{12}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Tangohia te 5 i te 24, ka 19.

$$\frac{\frac{7}{12}}{\frac{19}{12}}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Whakawehe \frac{7}{12} ki te \frac{19}{12} mā te whakarea \frac{7}{12} ki te tau huripoki o \frac{19}{12}.

$$\frac{7}{12}\times \frac{12}{19}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Me whakarea te \frac{7}{12} ki te \frac{12}{19} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7\times 12}{12\times 19}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Me whakakore tahi te 12 i te taurunga me te tauraro.

$$\frac{7}{19}\left(\frac{2}{7}+\frac{4}{19}\right)$$

Ko te maha noa iti rawa atu o 7 me 19 ko 133. Me tahuri \frac{2}{7} me \frac{4}{19} ki te hautau me te tautūnga 133.

$$\frac{7}{19}\left(\frac{38}{133}+\frac{28}{133}\right)$$

Tā te mea he rite te tauraro o \frac{38}{133} me \frac{28}{133}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7}{19}\times \frac{38+28}{133}$$

Tāpirihia te 38 ki te 28, ka 66.

$$\frac{7}{19}\times \frac{66}{133}$$

Me whakarea te \frac{7}{19} ki te \frac{66}{133} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7\times 66}{19\times 133}$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 66}{19\times 133}.

$$\frac{462}{2527}$$

Whakahekea te hautanga \frac{462}{2527} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{66}{361}$$

Tauwehe

$$\frac{2 \cdot 3 \cdot 11}{19 ^ {2}} = 0.18282548476454294$$