Whakaoti i te 1div(2/3+4/21+8/15*7+16/31*15+frac{32}{63*31})*frac{4}{21}

$$1 \div ( \frac{ 2 }{ 3 } + \frac{ 4 }{ 21 } + \frac{ 8 }{ 15 \times 7 } + \frac{ 16 }{ 31 \times 15 } + \frac{ 32 }{ 63 \times 31 } ) \times \frac{ 4 }{ 21 }$$

Aromātai

$$\frac{6}{31}\approx 0.193548387$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 3 me 21 ko 21. Me tahuri \frac{2}{3} me \frac{4}{21} ki te hautau me te tautūnga 21.

$$\frac{1}{\frac{14}{21}+\frac{4}{21}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Tā te mea he rite te tauraro o \frac{14}{21} me \frac{4}{21}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{\frac{14+4}{21}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Tāpirihia te 14 ki te 4, ka 18.

$$\frac{1}{\frac{18}{21}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Whakahekea te hautanga \frac{18}{21} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{1}{\frac{6}{7}+\frac{8}{15\times 7}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Whakareatia te 15 ki te 7, ka 105.

$$\frac{1}{\frac{6}{7}+\frac{8}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Ko te maha noa iti rawa atu o 7 me 105 ko 105. Me tahuri \frac{6}{7} me \frac{8}{105} ki te hautau me te tautūnga 105.

$$\frac{1}{\frac{90}{105}+\frac{8}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Tā te mea he rite te tauraro o \frac{90}{105} me \frac{8}{105}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{\frac{90+8}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Tāpirihia te 90 ki te 8, ka 98.

$$\frac{1}{\frac{98}{105}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Whakahekea te hautanga \frac{98}{105} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{1}{\frac{14}{15}+\frac{16}{31\times 15}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Whakareatia te 31 ki te 15, ka 465.

$$\frac{1}{\frac{14}{15}+\frac{16}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Ko te maha noa iti rawa atu o 15 me 465 ko 465. Me tahuri \frac{14}{15} me \frac{16}{465} ki te hautau me te tautūnga 465.

$$\frac{1}{\frac{434}{465}+\frac{16}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Tā te mea he rite te tauraro o \frac{434}{465} me \frac{16}{465}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{\frac{434+16}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Tāpirihia te 434 ki te 16, ka 450.

$$\frac{1}{\frac{450}{465}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Whakahekea te hautanga \frac{450}{465} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 15.

$$\frac{1}{\frac{30}{31}+\frac{32}{63\times 31}}\times \frac{4}{21}$$

Whakareatia te 63 ki te 31, ka 1953.

$$\frac{1}{\frac{30}{31}+\frac{32}{1953}}\times \frac{4}{21}$$

Ko te maha noa iti rawa atu o 31 me 1953 ko 1953. Me tahuri \frac{30}{31} me \frac{32}{1953} ki te hautau me te tautūnga 1953.

$$\frac{1}{\frac{1890}{1953}+\frac{32}{1953}}\times \frac{4}{21}$$

Tā te mea he rite te tauraro o \frac{1890}{1953} me \frac{32}{1953}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{\frac{1890+32}{1953}}\times \frac{4}{21}$$

Tāpirihia te 1890 ki te 32, ka 1922.

$$\frac{1}{\frac{1922}{1953}}\times \frac{4}{21}$$

Whakahekea te hautanga \frac{1922}{1953} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 31.

$$\frac{1}{\frac{62}{63}}\times \frac{4}{21}$$

Whakawehe 1 ki te \frac{62}{63} mā te whakarea 1 ki te tau huripoki o \frac{62}{63}.

$$1\times \frac{63}{62}\times \frac{4}{21}$$

Whakareatia te 1 ki te \frac{63}{62}, ka \frac{63}{62}.

$$\frac{63}{62}\times \frac{4}{21}$$

Me whakarea te \frac{63}{62} ki te \frac{4}{21} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{63\times 4}{62\times 21}$$

Mahia ngā whakarea i roto i te hautanga \frac{63\times 4}{62\times 21}.

$$\frac{252}{1302}$$

Whakahekea te hautanga \frac{252}{1302} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 42.

$$\frac{6}{31}$$

Tauwehe

$$\frac{2 \cdot 3}{31} = 0.1935483870967742$$