Whakaoti i te 1+1/3/1+frac{2{2-frac{1/2}}+2-frac{1/3}{1-frac{2}{1+frac{1}{2}}}}{7+frac{1}{1-frac{1}{1+frac{7}{6}}}}

$$\frac { \frac { 1 + \frac { 1 } { 3 } } { 1 + \frac { 2 } { 2 - \frac { 1 } { 2 } } } + \frac { 2 - \frac { 1 } { 3 } } { 1 - \frac { 2 } { 1 + \frac { 1 } { 2 } } } } { 7 + \frac { 1 } { 1 - \frac { 1 } { 1 + \frac { 7 } { 6 } } } }$$

Aromātai

$$-\frac{1}{2}=-0.5$$

Ngā Upane Otinga

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

$$\frac{\frac{\frac{3}{3}+\frac{1}{3}}{1+\frac{2}{2-\frac{1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{3+1}{3}}{1+\frac{2}{2-\frac{1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tāpirihia te 3 ki te 1, ka 4.

$$\frac{\frac{\frac{4}{3}}{1+\frac{2}{2-\frac{1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Me tahuri te 2 ki te hautau \frac{4}{2}.

$$\frac{\frac{\frac{4}{3}}{1+\frac{2}{\frac{4}{2}-\frac{1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tā te mea he rite te tauraro o \frac{4}{2} me \frac{1}{2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{\frac{4}{3}}{1+\frac{2}{\frac{4-1}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tangohia te 1 i te 4, ka 3.

$$\frac{\frac{\frac{4}{3}}{1+\frac{2}{\frac{3}{2}}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{4}{3}}{1+2\times \frac{2}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{4}{3}}{1+\frac{2\times 2}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{\frac{4}{3}}{1+\frac{4}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{4}{3}}{\frac{3}{3}+\frac{4}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{\frac{4}{3}}{\frac{3+4}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tāpirihia te 3 ki te 4, ka 7.

$$\frac{\frac{\frac{4}{3}}{\frac{7}{3}}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Whakawehe \frac{4}{3} ki te \frac{7}{3} mā te whakarea \frac{4}{3} ki te tau huripoki o \frac{7}{3}.

$$\frac{\frac{4}{3}\times \frac{3}{7}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Me whakarea te \frac{4}{3} ki te \frac{3}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{4\times 3}{3\times 7}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{2-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{6}{3}-\frac{1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{6-1}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tangohia te 1 i te 6, ka 5.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{1+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{\frac{2}{2}+\frac{1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{\frac{2+1}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2}{\frac{3}{2}}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-2\times \frac{2}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{2\times 2}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{1-\frac{4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{\frac{3}{3}-\frac{4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{\frac{3-4}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tangohia te 4 i te 3, ka -1.

$$\frac{\frac{4}{7}+\frac{\frac{5}{3}}{-\frac{1}{3}}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

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

Tuhia te \frac{5}{3}\left(-3\right) hei hautanga kotahi.

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

Whakareatia te 5 ki te -3, ka -15.

$$\frac{\frac{4}{7}+\frac{-15}{3}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Whakawehea te -15 ki te 3, kia riro ko -5.

$$\frac{\frac{4}{7}-5}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Me tahuri te 5 ki te hautau \frac{35}{7}.

$$\frac{\frac{4}{7}-\frac{35}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tā te mea he rite te tauraro o \frac{4}{7} me \frac{35}{7}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{4-35}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

Tangohia te 35 i te 4, ka -31.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{1+\frac{7}{6}}}}$$

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

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{6}{6}+\frac{7}{6}}}}$$

Tā te mea he rite te tauraro o \frac{6}{6} me \frac{7}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{6+7}{6}}}}$$

Tāpirihia te 6 ki te 7, ka 13.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{1}{\frac{13}{6}}}}$$

Whakawehe 1 ki te \frac{13}{6} mā te whakarea 1 ki te tau huripoki o \frac{13}{6}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-1\times \frac{6}{13}}}$$

Whakareatia te 1 ki te \frac{6}{13}, ka \frac{6}{13}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{1-\frac{6}{13}}}$$

Me tahuri te 1 ki te hautau \frac{13}{13}.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{13}{13}-\frac{6}{13}}}$$

Tā te mea he rite te tauraro o \frac{13}{13} me \frac{6}{13}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{13-6}{13}}}$$

Tangohia te 6 i te 13, ka 7.

$$\frac{-\frac{31}{7}}{7+\frac{1}{\frac{7}{13}}}$$

Whakawehe 1 ki te \frac{7}{13} mā te whakarea 1 ki te tau huripoki o \frac{7}{13}.

$$\frac{-\frac{31}{7}}{7+1\times \frac{13}{7}}$$

Whakareatia te 1 ki te \frac{13}{7}, ka \frac{13}{7}.

$$\frac{-\frac{31}{7}}{7+\frac{13}{7}}$$

Me tahuri te 7 ki te hautau \frac{49}{7}.

$$\frac{-\frac{31}{7}}{\frac{49}{7}+\frac{13}{7}}$$

Tā te mea he rite te tauraro o \frac{49}{7} me \frac{13}{7}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-\frac{31}{7}}{\frac{49+13}{7}}$$

Tāpirihia te 49 ki te 13, ka 62.

$$\frac{-\frac{31}{7}}{\frac{62}{7}}$$

Whakawehe -\frac{31}{7} ki te \frac{62}{7} mā te whakarea -\frac{31}{7} ki te tau huripoki o \frac{62}{7}.

$$-\frac{31}{7}\times \frac{7}{62}$$

Me whakarea te -\frac{31}{7} ki te \frac{7}{62} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-31\times 7}{7\times 62}$$

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

$$\frac{-31}{62}$$

Whakahekea te hautanga \frac{-31}{62} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 31.

$$-\frac{1}{2}$$

Tauwehe

$$-\frac{1}{2} = -0.5$$