Whakaoti i te (-7/18)*(-45)+1/6*(-1)^2000/(-13frac{1{3})*(-1)^1009-(-33/4)+(-frac{5}{16})}+2frac{7}{8}

$$\frac { ( - \frac { 7 } { 18 } ) \times ( - 45 ) + \frac { 1 } { 6 } \times ( - 1 ) ^ { 2000 } } { ( - 13 \frac { 1 } { 3 } ) \times ( - 1 ) ^ { 1009 } - ( - 3 \frac { 3 } { 4 } ) + ( - \frac { 5 } { 16 } ) } + 2 \frac { 7 } { 8 }$$

Aromātai

$$\frac{25299}{6440}\approx 3.928416149$$

Ngā Upane Otinga

Tuhia te -\frac{7}{18}\left(-45\right) hei hautanga kotahi.

$$\frac{\frac{-7\left(-45\right)}{18}+\frac{1}{6}\left(-1\right)^{2000}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakareatia te -7 ki te -45, ka 315.

$$\frac{\frac{315}{18}+\frac{1}{6}\left(-1\right)^{2000}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakahekea te hautanga \frac{315}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$\frac{\frac{35}{2}+\frac{1}{6}\left(-1\right)^{2000}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tātaihia te -1 mā te pū o 2000, kia riro ko 1.

$$\frac{\frac{35}{2}+\frac{1}{6}\times 1}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakareatia te \frac{1}{6} ki te 1, ka \frac{1}{6}.

$$\frac{\frac{35}{2}+\frac{1}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Ko te maha noa iti rawa atu o 2 me 6 ko 6. Me tahuri \frac{35}{2} me \frac{1}{6} ki te hautau me te tautūnga 6.

$$\frac{\frac{105}{6}+\frac{1}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tā te mea he rite te tauraro o \frac{105}{6} me \frac{1}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{105+1}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tāpirihia te 105 ki te 1, ka 106.

$$\frac{\frac{106}{6}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakahekea te hautanga \frac{106}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{53}{3}}{\left(-\frac{13\times 3+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakareatia te 13 ki te 3, ka 39.

$$\frac{\frac{53}{3}}{\left(-\frac{39+1}{3}\right)\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tāpirihia te 39 ki te 1, ka 40.

$$\frac{\frac{53}{3}}{-\frac{40}{3}\left(-1\right)^{1009}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tātaihia te -1 mā te pū o 1009, kia riro ko -1.

$$\frac{\frac{53}{3}}{-\frac{40}{3}\left(-1\right)-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakareatia te -\frac{40}{3} ki te -1, ka \frac{40}{3}.

$$\frac{\frac{53}{3}}{\frac{40}{3}-\left(-\frac{3\times 4+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Whakareatia te 3 ki te 4, ka 12.

$$\frac{\frac{53}{3}}{\frac{40}{3}-\left(-\frac{12+3}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tāpirihia te 12 ki te 3, ka 15.

$$\frac{\frac{53}{3}}{\frac{40}{3}-\left(-\frac{15}{4}\right)-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Ko te tauaro o -\frac{15}{4} ko \frac{15}{4}.

$$\frac{\frac{53}{3}}{\frac{40}{3}+\frac{15}{4}-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri \frac{40}{3} me \frac{15}{4} ki te hautau me te tautūnga 12.

$$\frac{\frac{53}{3}}{\frac{160}{12}+\frac{45}{12}-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tā te mea he rite te tauraro o \frac{160}{12} me \frac{45}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{53}{3}}{\frac{160+45}{12}-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Tāpirihia te 160 ki te 45, ka 205.

$$\frac{\frac{53}{3}}{\frac{205}{12}-\frac{5}{16}}+\frac{2\times 8+7}{8}$$

Ko te maha noa iti rawa atu o 12 me 16 ko 48. Me tahuri \frac{205}{12} me \frac{5}{16} ki te hautau me te tautūnga 48.

$$\frac{\frac{53}{3}}{\frac{820}{48}-\frac{15}{48}}+\frac{2\times 8+7}{8}$$

Tā te mea he rite te tauraro o \frac{820}{48} me \frac{15}{48}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{53}{3}}{\frac{820-15}{48}}+\frac{2\times 8+7}{8}$$

Tangohia te 15 i te 820, ka 805.

$$\frac{\frac{53}{3}}{\frac{805}{48}}+\frac{2\times 8+7}{8}$$

Whakawehe \frac{53}{3} ki te \frac{805}{48} mā te whakarea \frac{53}{3} ki te tau huripoki o \frac{805}{48}.

$$\frac{53}{3}\times \frac{48}{805}+\frac{2\times 8+7}{8}$$

Me whakarea te \frac{53}{3} ki te \frac{48}{805} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{53\times 48}{3\times 805}+\frac{2\times 8+7}{8}$$

Mahia ngā whakarea i roto i te hautanga \frac{53\times 48}{3\times 805}.

$$\frac{2544}{2415}+\frac{2\times 8+7}{8}$$

Whakahekea te hautanga \frac{2544}{2415} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{848}{805}+\frac{2\times 8+7}{8}$$

Whakareatia te 2 ki te 8, ka 16.

$$\frac{848}{805}+\frac{16+7}{8}$$

Tāpirihia te 16 ki te 7, ka 23.

$$\frac{848}{805}+\frac{23}{8}$$

Ko te maha noa iti rawa atu o 805 me 8 ko 6440. Me tahuri \frac{848}{805} me \frac{23}{8} ki te hautau me te tautūnga 6440.

$$\frac{6784}{6440}+\frac{18515}{6440}$$

Tā te mea he rite te tauraro o \frac{6784}{6440} me \frac{18515}{6440}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6784+18515}{6440}$$

Tāpirihia te 6784 ki te 18515, ka 25299.

$$\frac{25299}{6440}$$

Tauwehe

$$\frac{3 ^ {3} \cdot 937}{2 ^ {3} \cdot 5 \cdot 7 \cdot 23} = 3\frac{5979}{6440} = 3.928416149068323$$