Whakaoti i te 2+1/2+1{2+frac{1/1+frac{1{11}}}}=67/24

$$2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \frac { 1 } { 1 + \frac { 1 } { 11 } } } } = \frac { 67 } { 24 }$$

Manatoko

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{11}{11}.

$$2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{11}{11}+\frac{1}{11}}}}=\frac{67}{24}$$

Tā te mea he rite te tauraro o \frac{11}{11} me \frac{1}{11}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{11+1}{11}}}}=\frac{67}{24}$$

Tāpirihia te 11 ki te 1, ka 12.

$$2+\frac{1}{2+\frac{1}{2+\frac{1}{\frac{12}{11}}}}=\frac{67}{24}$$

Whakawehe 1 ki te \frac{12}{11} mā te whakarea 1 ki te tau huripoki o \frac{12}{11}.

$$2+\frac{1}{2+\frac{1}{2+1\times \frac{11}{12}}}=\frac{67}{24}$$

Whakareatia te 1 ki te \frac{11}{12}, ka \frac{11}{12}.

$$2+\frac{1}{2+\frac{1}{2+\frac{11}{12}}}=\frac{67}{24}$$

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

$$2+\frac{1}{2+\frac{1}{\frac{24}{12}+\frac{11}{12}}}=\frac{67}{24}$$

Tā te mea he rite te tauraro o \frac{24}{12} me \frac{11}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$2+\frac{1}{2+\frac{1}{\frac{24+11}{12}}}=\frac{67}{24}$$

Tāpirihia te 24 ki te 11, ka 35.

$$2+\frac{1}{2+\frac{1}{\frac{35}{12}}}=\frac{67}{24}$$

Whakawehe 1 ki te \frac{35}{12} mā te whakarea 1 ki te tau huripoki o \frac{35}{12}.

$$2+\frac{1}{2+1\times \frac{12}{35}}=\frac{67}{24}$$

Whakareatia te 1 ki te \frac{12}{35}, ka \frac{12}{35}.

$$2+\frac{1}{2+\frac{12}{35}}=\frac{67}{24}$$

Me tahuri te 2 ki te hautau \frac{70}{35}.

$$2+\frac{1}{\frac{70}{35}+\frac{12}{35}}=\frac{67}{24}$$

Tā te mea he rite te tauraro o \frac{70}{35} me \frac{12}{35}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$2+\frac{1}{\frac{70+12}{35}}=\frac{67}{24}$$

Tāpirihia te 70 ki te 12, ka 82.

$$2+\frac{1}{\frac{82}{35}}=\frac{67}{24}$$

Whakawehe 1 ki te \frac{82}{35} mā te whakarea 1 ki te tau huripoki o \frac{82}{35}.

$$2+1\times \frac{35}{82}=\frac{67}{24}$$

Whakareatia te 1 ki te \frac{35}{82}, ka \frac{35}{82}.

$$2+\frac{35}{82}=\frac{67}{24}$$

Me tahuri te 2 ki te hautau \frac{164}{82}.

$$\frac{164}{82}+\frac{35}{82}=\frac{67}{24}$$

Tā te mea he rite te tauraro o \frac{164}{82} me \frac{35}{82}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{164+35}{82}=\frac{67}{24}$$

Tāpirihia te 164 ki te 35, ka 199.

$$\frac{199}{82}=\frac{67}{24}$$

Ko te maha noa iti rawa atu o 82 me 24 ko 984. Me tahuri \frac{199}{82} me \frac{67}{24} ki te hautau me te tautūnga 984.

$$\frac{2388}{984}=\frac{2747}{984}$$

Whakatauritea te \frac{2388}{984} me te \frac{2747}{984}.

$$\text{false}$$