Whakaoti i te 1:{2/19*|(3/2+27/5):3/5-(frac{11}{6}-frac{7}{4})|:frac{5}{6}}

$$1 : \{ \frac { 2 } { 19 } \times | ( \frac { 3 } { 2 } + \frac { 27 } { 5 } ) : \frac { 3 } { 5 } - ( \frac { 11 } { 6 } - \frac { 7 } { 4 } ) | : \frac { 5 } { 6 } \}$$

Aromātai

$$\frac{95}{137}\approx 0.693430657$$

Ngā Upane Otinga

Whakawehe 1 ki te \frac{\frac{2}{19}|\frac{\frac{3}{2}+\frac{27}{5}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}{\frac{5}{6}} mā te whakarea 1 ki te tau huripoki o \frac{\frac{2}{19}|\frac{\frac{3}{2}+\frac{27}{5}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}{\frac{5}{6}}.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{3}{2}+\frac{27}{5}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Ko te maha noa iti rawa atu o 2 me 5 ko 10. Me tahuri \frac{3}{2} me \frac{27}{5} ki te hautau me te tautūnga 10.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{15}{10}+\frac{54}{10}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Tā te mea he rite te tauraro o \frac{15}{10} me \frac{54}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{15+54}{10}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Tāpirihia te 15 ki te 54, ka 69.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{\frac{69}{10}}{\frac{3}{5}}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Whakawehe \frac{69}{10} ki te \frac{3}{5} mā te whakarea \frac{69}{10} ki te tau huripoki o \frac{3}{5}.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{69}{10}\times \frac{5}{3}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Me whakarea te \frac{69}{10} ki te \frac{5}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{69\times 5}{10\times 3}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Mahia ngā whakarea i roto i te hautanga \frac{69\times 5}{10\times 3}.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{345}{30}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Whakahekea te hautanga \frac{345}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 15.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\left(\frac{11}{6}-\frac{7}{4}\right)|}$$

Ko te maha noa iti rawa atu o 6 me 4 ko 12. Me tahuri \frac{11}{6} me \frac{7}{4} ki te hautau me te tautūnga 12.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\left(\frac{22}{12}-\frac{21}{12}\right)|}$$

Tā te mea he rite te tauraro o \frac{22}{12} me \frac{21}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\frac{22-21}{12}|}$$

Tangohia te 21 i te 22, ka 1.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{23}{2}-\frac{1}{12}|}$$

Ko te maha noa iti rawa atu o 2 me 12 ko 12. Me tahuri \frac{23}{2} me \frac{1}{12} ki te hautau me te tautūnga 12.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{138}{12}-\frac{1}{12}|}$$

Tā te mea he rite te tauraro o \frac{138}{12} me \frac{1}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{138-1}{12}|}$$

Tangohia te 1 i te 138, ka 137.

$$\frac{\frac{5}{6}}{\frac{2}{19}|\frac{137}{12}|}$$

Ko te uara pū o tētahi tau tūturu a ko a ina a\geq 0, ko -a rānei ina a<0. Ko te uara pū o \frac{137}{12} ko \frac{137}{12}.

$$\frac{\frac{5}{6}}{\frac{2}{19}\times \frac{137}{12}}$$

Me whakarea te \frac{2}{19} ki te \frac{137}{12} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{5}{6}}{\frac{2\times 137}{19\times 12}}$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 137}{19\times 12}.

$$\frac{\frac{5}{6}}{\frac{274}{228}}$$

Whakahekea te hautanga \frac{274}{228} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{5}{6}}{\frac{137}{114}}$$

Whakawehe \frac{5}{6} ki te \frac{137}{114} mā te whakarea \frac{5}{6} ki te tau huripoki o \frac{137}{114}.

$$\frac{5}{6}\times \frac{114}{137}$$

Me whakarea te \frac{5}{6} ki te \frac{114}{137} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{5\times 114}{6\times 137}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 114}{6\times 137}.

$$\frac{570}{822}$$

Whakahekea te hautanga \frac{570}{822} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{95}{137}$$

Tauwehe

$$\frac{5 \cdot 19}{137} = 0.6934306569343066$$