Whakaoti i te 1+1/1+3{1+frac{4/5}}=1+1/1+3{frac{9/3}}

$$1 + \frac { 1 } { 1 + \frac { 3 } { 1 + \frac { 4 } { 5 } } } = 1 + \frac { 1 } { 1 + \frac { 3 } { \frac { 9 } { 3 } } }$$

Manatoko

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{5}{5}.

$$1+\frac{1}{1+\frac{3}{\frac{5}{5}+\frac{4}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tā te mea he rite te tauraro o \frac{5}{5} me \frac{4}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$1+\frac{1}{1+\frac{3}{\frac{5+4}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tāpirihia te 5 ki te 4, ka 9.

$$1+\frac{1}{1+\frac{3}{\frac{9}{5}}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Whakawehe 3 ki te \frac{9}{5} mā te whakarea 3 ki te tau huripoki o \frac{9}{5}.

$$1+\frac{1}{1+3\times \frac{5}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tuhia te 3\times \frac{5}{9} hei hautanga kotahi.

$$1+\frac{1}{1+\frac{3\times 5}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Whakareatia te 3 ki te 5, ka 15.

$$1+\frac{1}{1+\frac{15}{9}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Whakahekea te hautanga \frac{15}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$1+\frac{1}{1+\frac{5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

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

$$1+\frac{1}{\frac{3}{3}+\frac{5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tā te mea he rite te tauraro o \frac{3}{3} me \frac{5}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$1+\frac{1}{\frac{3+5}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tāpirihia te 3 ki te 5, ka 8.

$$1+\frac{1}{\frac{8}{3}}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

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

$$1+1\times \frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

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

$$1+\frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Me tahuri te 1 ki te hautau \frac{8}{8}.

$$\frac{8}{8}+\frac{3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tā te mea he rite te tauraro o \frac{8}{8} me \frac{3}{8}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8+3}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Tāpirihia te 8 ki te 3, ka 11.

$$\frac{11}{8}=1+\frac{1}{1+\frac{3}{\frac{9}{3}}}$$

Whakawehe 3 ki te \frac{9}{3} mā te whakarea 3 ki te tau huripoki o \frac{9}{3}.

$$\frac{11}{8}=1+\frac{1}{1+\frac{3\times 3}{9}}$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{11}{8}=1+\frac{1}{1+\frac{9}{9}}$$

Whakawehea te 9 ki te 9, kia riro ko 1.

$$\frac{11}{8}=1+\frac{1}{1+1}$$

Tāpirihia te 1 ki te 1, ka 2.

$$\frac{11}{8}=1+\frac{1}{2}$$

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

$$\frac{11}{8}=\frac{2}{2}+\frac{1}{2}$$

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.

$$\frac{11}{8}=\frac{2+1}{2}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{11}{8}=\frac{3}{2}$$

Ko te maha noa iti rawa atu o 8 me 2 ko 8. Me tahuri \frac{11}{8} me \frac{3}{2} ki te hautau me te tautūnga 8.

$$\frac{11}{8}=\frac{12}{8}$$

Whakatauritea te \frac{11}{8} me te \frac{12}{8}.

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