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

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

Aromātai

$$\frac{635}{504}\approx 1.259920635$$

Ngā Upane Otinga

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.

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

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

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

Tāpirihia te 8 ki te 9, ka 17.

$$\frac{17}{72}+\frac{-1}{7}+\frac{7}{6}$$

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

$$\frac{17}{72}-\frac{1}{7}+\frac{7}{6}$$

Ko te maha noa iti rawa atu o 72 me 7 ko 504. Me tahuri \frac{17}{72} me \frac{1}{7} ki te hautau me te tautūnga 504.

$$\frac{119}{504}-\frac{72}{504}+\frac{7}{6}$$

Tā te mea he rite te tauraro o \frac{119}{504} me \frac{72}{504}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{119-72}{504}+\frac{7}{6}$$

Tangohia te 72 i te 119, ka 47.

$$\frac{47}{504}+\frac{7}{6}$$

Ko te maha noa iti rawa atu o 504 me 6 ko 504. Me tahuri \frac{47}{504} me \frac{7}{6} ki te hautau me te tautūnga 504.

$$\frac{47}{504}+\frac{588}{504}$$

Tā te mea he rite te tauraro o \frac{47}{504} me \frac{588}{504}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{47+588}{504}$$

Tāpirihia te 47 ki te 588, ka 635.

$$\frac{635}{504}$$

Tauwehe

$$\frac{5 \cdot 127}{2 ^ {3} \cdot 3 ^ {2} \cdot 7} = 1\frac{131}{504} = 1.2599206349206349$$