Whakaoti i te 1/9+-1/8+-1/7+1/6

$$\frac { 1 } { 9 } + \frac { - 1 } { 8 } + \frac { - 1 } { 7 } + \frac { 1 } { 6 }$$

Aromātai

$$\frac{5}{504}\approx 0.009920635$$

Ngā Upane Otinga

Ka taea te hautanga \frac{-1}{8} te tuhi anō ko -\frac{1}{8} mā te tango i te tohu tōraro.

$$\frac{1}{9}-\frac{1}{8}+\frac{-1}{7}+\frac{1}{6}$$

Ko te maha noa iti rawa atu o 9 me 8 ko 72. Me tahuri \frac{1}{9} me \frac{1}{8} ki te hautau me te tautūnga 72.

$$\frac{8}{72}-\frac{9}{72}+\frac{-1}{7}+\frac{1}{6}$$

Tā te mea he rite te tauraro o \frac{8}{72} me \frac{9}{72}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{8-9}{72}+\frac{-1}{7}+\frac{1}{6}$$

Tangohia te 9 i te 8, ka -1.

$$-\frac{1}{72}+\frac{-1}{7}+\frac{1}{6}$$

Ka taea te hautanga \frac{-1}{7} te tuhi anō ko -\frac{1}{7} mā te tango i te tohu tōraro.

$$-\frac{1}{72}-\frac{1}{7}+\frac{1}{6}$$

Ko te maha noa iti rawa atu o 72 me 7 ko 504. Me tahuri -\frac{1}{72} me \frac{1}{7} ki te hautau me te tautūnga 504.

$$-\frac{7}{504}-\frac{72}{504}+\frac{1}{6}$$

Tā te mea he rite te tauraro o -\frac{7}{504} me \frac{72}{504}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-7-72}{504}+\frac{1}{6}$$

Tangohia te 72 i te -7, ka -79.

$$-\frac{79}{504}+\frac{1}{6}$$

Ko te maha noa iti rawa atu o 504 me 6 ko 504. Me tahuri -\frac{79}{504} me \frac{1}{6} ki te hautau me te tautūnga 504.

$$-\frac{79}{504}+\frac{84}{504}$$

Tā te mea he rite te tauraro o -\frac{79}{504} me \frac{84}{504}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-79+84}{504}$$

Tāpirihia te -79 ki te 84, ka 5.

$$\frac{5}{504}$$

Tauwehe

$$\frac{5}{2 ^ {3} \cdot 3 ^ {2} \cdot 7} = 0.00992063492063492$$