Whakaoti i te (1/1*4+1/4*7+1/7*1+1/10*13+frac{1}{13-16})=

$$( \frac { 1 } { 1 \cdot 4 } + \frac { 1 } { 4 \cdot 7 } + \frac { 1 } { 7 \cdot 1 } + \frac { 1 } { 10 \cdot 13 } + \frac { 1 } { 13 - 16 } ) =$$

Aromātai

$$\frac{281}{2730}\approx 0.102930403$$

Ngā Upane Otinga

Whakareatia te 1 ki te 4, ka 4.

$$\frac{1}{4}+\frac{1}{4\times 7}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Whakareatia te 4 ki te 7, ka 28.

$$\frac{1}{4}+\frac{1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Ko te maha noa iti rawa atu o 4 me 28 ko 28. Me tahuri \frac{1}{4} me \frac{1}{28} ki te hautau me te tautūnga 28.

$$\frac{7}{28}+\frac{1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Tā te mea he rite te tauraro o \frac{7}{28} me \frac{1}{28}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{7+1}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Tāpirihia te 7 ki te 1, ka 8.

$$\frac{8}{28}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Whakahekea te hautanga \frac{8}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{2}{7}+\frac{1}{7\times 1}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Whakareatia te 7 ki te 1, ka 7.

$$\frac{2}{7}+\frac{1}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Tā te mea he rite te tauraro o \frac{2}{7} me \frac{1}{7}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{2+1}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{3}{7}+\frac{1}{10\times 13}+\frac{1}{13-16}$$

Whakareatia te 10 ki te 13, ka 130.

$$\frac{3}{7}+\frac{1}{130}+\frac{1}{13-16}$$

Ko te maha noa iti rawa atu o 7 me 130 ko 910. Me tahuri \frac{3}{7} me \frac{1}{130} ki te hautau me te tautūnga 910.

$$\frac{390}{910}+\frac{7}{910}+\frac{1}{13-16}$$

Tā te mea he rite te tauraro o \frac{390}{910} me \frac{7}{910}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{390+7}{910}+\frac{1}{13-16}$$

Tāpirihia te 390 ki te 7, ka 397.

$$\frac{397}{910}+\frac{1}{13-16}$$

Tangohia te 16 i te 13, ka -3.

$$\frac{397}{910}+\frac{1}{-3}$$

Ka taea te hautanga \frac{1}{-3} te tuhi anō ko -\frac{1}{3} mā te tango i te tohu tōraro.

$$\frac{397}{910}-\frac{1}{3}$$

Ko te maha noa iti rawa atu o 910 me 3 ko 2730. Me tahuri \frac{397}{910} me \frac{1}{3} ki te hautau me te tautūnga 2730.

$$\frac{1191}{2730}-\frac{910}{2730}$$

Tā te mea he rite te tauraro o \frac{1191}{2730} me \frac{910}{2730}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1191-910}{2730}$$

Tangohia te 910 i te 1191, ka 281.

$$\frac{281}{2730}$$

Tauwehe

$$\frac{281}{2 \cdot 3 \cdot 5 \cdot 7 \cdot 13} = 0.10293040293040293$$