Whakaoti i te 41/7-21/14+31/2/6frac{2{3}+5frac{5}{9}-10frac{1}{15}}

$$\frac { 4 \frac { 1 } { 7 } - 2 \frac { 1 } { 14 } + 3 \frac { 1 } { 2 } } { 6 \frac { 2 } { 3 } + 5 \frac { 5 } { 9 } - 10 \frac { 1 } { 15 } }$$

Aromātai

$$\frac{1755}{679}\approx 2.584683358$$

Ngā Upane Otinga

Whakareatia te 4 ki te 7, ka 28.

$$\frac{\frac{28+1}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 28 ki te 1, ka 29.

$$\frac{\frac{29}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Whakareatia te 2 ki te 14, ka 28.

$$\frac{\frac{29}{7}-\frac{28+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 28 ki te 1, ka 29.

$$\frac{\frac{29}{7}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Ko te maha noa iti rawa atu o 7 me 14 ko 14. Me tahuri \frac{29}{7} me \frac{29}{14} ki te hautau me te tautūnga 14.

$$\frac{\frac{58}{14}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tā te mea he rite te tauraro o \frac{58}{14} me \frac{29}{14}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{58-29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tangohia te 29 i te 58, ka 29.

$$\frac{\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{\frac{29}{14}+\frac{6+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{\frac{29}{14}+\frac{7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Ko te maha noa iti rawa atu o 14 me 2 ko 14. Me tahuri \frac{29}{14} me \frac{7}{2} ki te hautau me te tautūnga 14.

$$\frac{\frac{29}{14}+\frac{49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tā te mea he rite te tauraro o \frac{29}{14} me \frac{49}{14}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{29+49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 29 ki te 49, ka 78.

$$\frac{\frac{78}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Whakahekea te hautanga \frac{78}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{39}{7}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Whakareatia te 6 ki te 3, ka 18.

$$\frac{\frac{39}{7}}{\frac{18+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 18 ki te 2, ka 20.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{5\times 9+5}{9}-\frac{10\times 15+1}{15}}$$

Whakareatia te 5 ki te 9, ka 45.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{45+5}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 45 ki te 5, ka 50.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{50}{9}-\frac{10\times 15+1}{15}}$$

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.

$$\frac{\frac{39}{7}}{\frac{60}{9}+\frac{50}{9}-\frac{10\times 15+1}{15}}$$

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.

$$\frac{\frac{39}{7}}{\frac{60+50}{9}-\frac{10\times 15+1}{15}}$$

Tāpirihia te 60 ki te 50, ka 110.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{10\times 15+1}{15}}$$

Whakareatia te 10 ki te 15, ka 150.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{150+1}{15}}$$

Tāpirihia te 150 ki te 1, ka 151.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{151}{15}}$$

Ko te maha noa iti rawa atu o 9 me 15 ko 45. Me tahuri \frac{110}{9} me \frac{151}{15} ki te hautau me te tautūnga 45.

$$\frac{\frac{39}{7}}{\frac{550}{45}-\frac{453}{45}}$$

Tā te mea he rite te tauraro o \frac{550}{45} me \frac{453}{45}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{39}{7}}{\frac{550-453}{45}}$$

Tangohia te 453 i te 550, ka 97.

$$\frac{\frac{39}{7}}{\frac{97}{45}}$$

Whakawehe \frac{39}{7} ki te \frac{97}{45} mā te whakarea \frac{39}{7} ki te tau huripoki o \frac{97}{45}.

$$\frac{39}{7}\times \frac{45}{97}$$

Me whakarea te \frac{39}{7} ki te \frac{45}{97} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{39\times 45}{7\times 97}$$

Mahia ngā whakarea i roto i te hautanga \frac{39\times 45}{7\times 97}.

$$\frac{1755}{679}$$

Tauwehe

$$\frac{3 ^ {3} \cdot 5 \cdot 13}{7 \cdot 97} = 2\frac{397}{679} = 2.5846833578792343$$