Whakaoti i te S=1/9+1/18+1/30+1/45+frac{1}{63}

$$S = \frac { 1 } { 9 } + \frac { 1 } { 18 } + \frac { 1 } { 30 } + \frac { 1 } { 45 } + \frac { 1 } { 63 }$$

Whakaoti mō S

$$S=\frac{5}{21}\approx 0.238095238$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Ko te maha noa iti rawa atu o 9 me 18 ko 18. Me tahuri \frac{1}{9} me \frac{1}{18} ki te hautau me te tautūnga 18.

$$S=\frac{2}{18}+\frac{1}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Tā te mea he rite te tauraro o \frac{2}{18} me \frac{1}{18}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$S=\frac{2+1}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Tāpirihia te 2 ki te 1, ka 3.

$$S=\frac{3}{18}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

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

$$S=\frac{1}{6}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Ko te maha noa iti rawa atu o 6 me 30 ko 30. Me tahuri \frac{1}{6} me \frac{1}{30} ki te hautau me te tautūnga 30.

$$S=\frac{5}{30}+\frac{1}{30}+\frac{1}{45}+\frac{1}{63}$$

Tā te mea he rite te tauraro o \frac{5}{30} me \frac{1}{30}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$S=\frac{5+1}{30}+\frac{1}{45}+\frac{1}{63}$$

Tāpirihia te 5 ki te 1, ka 6.

$$S=\frac{6}{30}+\frac{1}{45}+\frac{1}{63}$$

Whakahekea te hautanga \frac{6}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$S=\frac{1}{5}+\frac{1}{45}+\frac{1}{63}$$

Ko te maha noa iti rawa atu o 5 me 45 ko 45. Me tahuri \frac{1}{5} me \frac{1}{45} ki te hautau me te tautūnga 45.

$$S=\frac{9}{45}+\frac{1}{45}+\frac{1}{63}$$

Tā te mea he rite te tauraro o \frac{9}{45} me \frac{1}{45}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$S=\frac{9+1}{45}+\frac{1}{63}$$

Tāpirihia te 9 ki te 1, ka 10.

$$S=\frac{10}{45}+\frac{1}{63}$$

Whakahekea te hautanga \frac{10}{45} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$S=\frac{2}{9}+\frac{1}{63}$$

Ko te maha noa iti rawa atu o 9 me 63 ko 63. Me tahuri \frac{2}{9} me \frac{1}{63} ki te hautau me te tautūnga 63.

$$S=\frac{14}{63}+\frac{1}{63}$$

Tā te mea he rite te tauraro o \frac{14}{63} me \frac{1}{63}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$S=\frac{14+1}{63}$$

Tāpirihia te 14 ki te 1, ka 15.

$$S=\frac{15}{63}$$

Whakahekea te hautanga \frac{15}{63} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$S=\frac{5}{21}$$

Tautapa S

$$S≔\frac{5}{21}$$