Whakaoti i te 1/3+1/5+1/7+1/9

$$\frac { 1 } { 3 } + \frac { 1 } { 5 } + \frac { 1 } { 7 } + \frac { 1 } { 9 }$$

Aromātai

$$\frac{248}{315}\approx 0.787301587$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 3 me 5 ko 15. Me tahuri \frac{1}{3} me \frac{1}{5} ki te hautau me te tautūnga 15.

$$\frac{5}{15}+\frac{3}{15}+\frac{1}{7}+\frac{1}{9}$$

Tā te mea he rite te tauraro o \frac{5}{15} me \frac{3}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5+3}{15}+\frac{1}{7}+\frac{1}{9}$$

Tāpirihia te 5 ki te 3, ka 8.

$$\frac{8}{15}+\frac{1}{7}+\frac{1}{9}$$

Ko te maha noa iti rawa atu o 15 me 7 ko 105. Me tahuri \frac{8}{15} me \frac{1}{7} ki te hautau me te tautūnga 105.

$$\frac{56}{105}+\frac{15}{105}+\frac{1}{9}$$

Tā te mea he rite te tauraro o \frac{56}{105} me \frac{15}{105}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{56+15}{105}+\frac{1}{9}$$

Tāpirihia te 56 ki te 15, ka 71.

$$\frac{71}{105}+\frac{1}{9}$$

Ko te maha noa iti rawa atu o 105 me 9 ko 315. Me tahuri \frac{71}{105} me \frac{1}{9} ki te hautau me te tautūnga 315.

$$\frac{213}{315}+\frac{35}{315}$$

Tā te mea he rite te tauraro o \frac{213}{315} me \frac{35}{315}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{213+35}{315}$$

Tāpirihia te 213 ki te 35, ka 248.

$$\frac{248}{315}$$

Tauwehe

$$\frac{2 ^ {3} \cdot 31}{3 ^ {2} \cdot 5 \cdot 7} = 0.7873015873015873$$