Whakaoti i te 1+1/2/3+1-frac{1/3/2}{frac{2^1/2}{5/6}-frac{1/3}{1/8}}*(23^1/2divfrac{47}{12})

$$\frac { \frac { 1 + \frac { 1 } { 2 } } { 3 } + \frac { 1 - \frac { 1 } { 3 } } { 2 } } { \frac { 2 ^ { 1 } / 2 } { 5 / 6 } - \frac { 1 / 3 } { 1 / 8 } } \times ( 23 ^ { 1 } / 2 \div \frac { 47 } { 12 } )$$

Aromātai

$$-\frac{1725}{1034}\approx -1.66827853$$

Ngā Upane Otinga

Whakawehea te 2^{1} ki te 2, kia riro ko 1.

$$\frac{\frac{1+\frac{1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Me tahuri te 1 ki te hautau \frac{2}{2}.

$$\frac{\frac{\frac{2}{2}+\frac{1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tā te mea he rite te tauraro o \frac{2}{2} me \frac{1}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{\frac{2+1}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{\frac{\frac{3}{2}}{3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tuhia te \frac{\frac{3}{2}}{3} hei hautanga kotahi.

$$\frac{\frac{3}{2\times 3}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{1}{2}+\frac{1-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Me tahuri te 1 ki te hautau \frac{3}{3}.

$$\frac{\frac{1}{2}+\frac{\frac{3}{3}-\frac{1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{1}{2}+\frac{\frac{3-1}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tangohia te 1 i te 3, ka 2.

$$\frac{\frac{1}{2}+\frac{\frac{2}{3}}{2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tuhia te \frac{\frac{2}{3}}{2} hei hautanga kotahi.

$$\frac{\frac{1}{2}+\frac{2}{3\times 2}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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.

$$\frac{\frac{3}{6}+\frac{2}{6}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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.

$$\frac{\frac{3+2}{6}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{\frac{5}{6}}{\frac{1}{\frac{5}{6}}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

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

$$\frac{\frac{5}{6}}{1\times \frac{6}{5}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Whakareatia te 1 ki te \frac{6}{5}, ka \frac{6}{5}.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\frac{\frac{1}{3}}{\frac{1}{8}}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Whakawehe \frac{1}{3} ki te \frac{1}{8} mā te whakarea \frac{1}{3} ki te tau huripoki o \frac{1}{8}.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\frac{1}{3}\times 8}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Whakareatia te \frac{1}{3} ki te 8, ka \frac{8}{3}.

$$\frac{\frac{5}{6}}{\frac{6}{5}-\frac{8}{3}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri \frac{6}{5} me \frac{8}{3} ki te hautau me te tautūnga 15.

$$\frac{\frac{5}{6}}{\frac{18}{15}-\frac{40}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tā te mea he rite te tauraro o \frac{18}{15} me \frac{40}{15}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{5}{6}}{\frac{18-40}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Tangohia te 40 i te 18, ka -22.

$$\frac{\frac{5}{6}}{-\frac{22}{15}}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Whakawehe \frac{5}{6} ki te -\frac{22}{15} mā te whakarea \frac{5}{6} ki te tau huripoki o -\frac{22}{15}.

$$\frac{5}{6}\left(-\frac{15}{22}\right)\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Me whakarea te \frac{5}{6} ki te -\frac{15}{22} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{5\left(-15\right)}{6\times 22}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\left(-15\right)}{6\times 22}.

$$\frac{-75}{132}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Whakahekea te hautanga \frac{-75}{132} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$-\frac{25}{44}\times \frac{\frac{23^{1}}{2}}{\frac{47}{12}}$$

Whakawehe \frac{23^{1}}{2} ki te \frac{47}{12} mā te whakarea \frac{23^{1}}{2} ki te tau huripoki o \frac{47}{12}.

$$-\frac{25}{44}\times \frac{23^{1}\times 12}{2\times 47}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$-\frac{25}{44}\times \frac{6\times 23^{1}}{47}$$

Tātaihia te 23 mā te pū o 1, kia riro ko 23.

$$-\frac{25}{44}\times \frac{6\times 23}{47}$$

Whakareatia te 6 ki te 23, ka 138.

$$-\frac{25}{44}\times \frac{138}{47}$$

Me whakarea te -\frac{25}{44} ki te \frac{138}{47} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-25\times 138}{44\times 47}$$

Mahia ngā whakarea i roto i te hautanga \frac{-25\times 138}{44\times 47}.

$$\frac{-3450}{2068}$$

Whakahekea te hautanga \frac{-3450}{2068} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{1725}{1034}$$

Tauwehe

$$-\frac{1725}{1034} = -1\frac{691}{1034} = -1.6682785299806577$$