Whakaoti i te 43/7-27/14+37/2/6frac{2{3}+5frac{5}{9}-10frac{2}{15}}

$$\frac { 4 \frac { 3 } { 7 } - 2 \frac { 7 } { 14 } + 3 \frac { 7 } { 2 } } { 6 \frac { 2 } { 3 } + 5 \frac { 5 } { 9 } - 10 \frac { 2 } { 15 } }$$

Aromātai

$$\frac{2655}{658}\approx 4.034954407$$

Ngā Upane Otinga

Whakareatia te 4 ki te 7, ka 28.

$$\frac{\frac{28+3}{7}-\frac{2\times 14+7}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 28 ki te 3, ka 31.

$$\frac{\frac{31}{7}-\frac{2\times 14+7}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Whakareatia te 2 ki te 14, ka 28.

$$\frac{\frac{31}{7}-\frac{28+7}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 28 ki te 7, ka 35.

$$\frac{\frac{31}{7}-\frac{35}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Whakahekea te hautanga \frac{35}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{\frac{31}{7}-\frac{5}{2}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Ko te maha noa iti rawa atu o 7 me 2 ko 14. Me tahuri \frac{31}{7} me \frac{5}{2} ki te hautau me te tautūnga 14.

$$\frac{\frac{62}{14}-\frac{35}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tā te mea he rite te tauraro o \frac{62}{14} me \frac{35}{14}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{62-35}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tangohia te 35 i te 62, ka 27.

$$\frac{\frac{27}{14}+\frac{3\times 2+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{\frac{27}{14}+\frac{6+7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 6 ki te 7, ka 13.

$$\frac{\frac{27}{14}+\frac{13}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Ko te maha noa iti rawa atu o 14 me 2 ko 14. Me tahuri \frac{27}{14} me \frac{13}{2} ki te hautau me te tautūnga 14.

$$\frac{\frac{27}{14}+\frac{91}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tā te mea he rite te tauraro o \frac{27}{14} me \frac{91}{14}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{27+91}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 27 ki te 91, ka 118.

$$\frac{\frac{118}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Whakahekea te hautanga \frac{118}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{59}{7}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Whakareatia te 6 ki te 3, ka 18.

$$\frac{\frac{59}{7}}{\frac{18+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 18 ki te 2, ka 20.

$$\frac{\frac{59}{7}}{\frac{20}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+2}{15}}$$

Whakareatia te 5 ki te 9, ka 45.

$$\frac{\frac{59}{7}}{\frac{20}{3}+\frac{45+5}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 45 ki te 5, ka 50.

$$\frac{\frac{59}{7}}{\frac{20}{3}+\frac{50}{9}-\frac{10\times 15+2}{15}}$$

Ko te maha noa iti rawa atu o 3 me 9 ko 9. Me tahuri \frac{20}{3} me \frac{50}{9} ki te hautau me te tautūnga 9.

$$\frac{\frac{59}{7}}{\frac{60}{9}+\frac{50}{9}-\frac{10\times 15+2}{15}}$$

Tā te mea he rite te tauraro o \frac{60}{9} me \frac{50}{9}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{59}{7}}{\frac{60+50}{9}-\frac{10\times 15+2}{15}}$$

Tāpirihia te 60 ki te 50, ka 110.

$$\frac{\frac{59}{7}}{\frac{110}{9}-\frac{10\times 15+2}{15}}$$

Whakareatia te 10 ki te 15, ka 150.

$$\frac{\frac{59}{7}}{\frac{110}{9}-\frac{150+2}{15}}$$

Tāpirihia te 150 ki te 2, ka 152.

$$\frac{\frac{59}{7}}{\frac{110}{9}-\frac{152}{15}}$$

Ko te maha noa iti rawa atu o 9 me 15 ko 45. Me tahuri \frac{110}{9} me \frac{152}{15} ki te hautau me te tautūnga 45.

$$\frac{\frac{59}{7}}{\frac{550}{45}-\frac{456}{45}}$$

Tā te mea he rite te tauraro o \frac{550}{45} me \frac{456}{45}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{59}{7}}{\frac{550-456}{45}}$$

Tangohia te 456 i te 550, ka 94.

$$\frac{\frac{59}{7}}{\frac{94}{45}}$$

Whakawehe \frac{59}{7} ki te \frac{94}{45} mā te whakarea \frac{59}{7} ki te tau huripoki o \frac{94}{45}.

$$\frac{59}{7}\times \frac{45}{94}$$

Me whakarea te \frac{59}{7} ki te \frac{45}{94} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{59\times 45}{7\times 94}$$

Mahia ngā whakarea i roto i te hautanga \frac{59\times 45}{7\times 94}.

$$\frac{2655}{658}$$

Tauwehe

$$\frac{3 ^ {2} \cdot 5 \cdot 59}{2 \cdot 7 \cdot 47} = 4\frac{23}{658} = 4.0349544072948325$$