Whakaoti i te 11/5-1/3-{2/5-5/6-[frac{3}{4}-frac{1}{2}-(frac{7}{30}-frac{4}{5}-1)-frac{1}{4}]}-1

$$\frac { 11 } { 5 } - \frac { 1 } { 3 } - \{ \frac { 2 } { 5 } - \frac { 5 } { 6 } - [ \frac { 3 } { 4 } - \frac { 1 } { 2 } - ( \frac { 7 } { 30 } - \frac { 4 } { 5 } - 1 ) - \frac { 1 } { 4 } ] \} - 1$$

Aromātai

$$\frac{43}{15}\approx 2.866666667$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri \frac{11}{5} me \frac{1}{3} ki te hautau me te tautūnga 15.

$$\frac{33}{15}-\frac{5}{15}-\left(\frac{2}{5}-\frac{5}{6}-\left(\frac{3}{4}-\frac{1}{2}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Tā te mea he rite te tauraro o \frac{33}{15} me \frac{5}{15}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{33-5}{15}-\left(\frac{2}{5}-\frac{5}{6}-\left(\frac{3}{4}-\frac{1}{2}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Tangohia te 5 i te 33, ka 28.

$$\frac{28}{15}-\left(\frac{2}{5}-\frac{5}{6}-\left(\frac{3}{4}-\frac{1}{2}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Ko te maha noa iti rawa atu o 5 me 6 ko 30. Me tahuri \frac{2}{5} me \frac{5}{6} ki te hautau me te tautūnga 30.

$$\frac{28}{15}-\left(\frac{12}{30}-\frac{25}{30}-\left(\frac{3}{4}-\frac{1}{2}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Tā te mea he rite te tauraro o \frac{12}{30} me \frac{25}{30}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{15}-\left(\frac{12-25}{30}-\left(\frac{3}{4}-\frac{1}{2}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Tangohia te 25 i te 12, ka -13.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{3}{4}-\frac{1}{2}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Ko te maha noa iti rawa atu o 4 me 2 ko 4. Me tahuri \frac{3}{4} me \frac{1}{2} ki te hautau me te tautūnga 4.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{3}{4}-\frac{2}{4}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Tā te mea he rite te tauraro o \frac{3}{4} me \frac{2}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{3-2}{4}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Tangohia te 2 i te 3, ka 1.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\left(\frac{7}{30}-\frac{4}{5}-1\right)-\frac{1}{4}\right)\right)-1$$

Ko te maha noa iti rawa atu o 30 me 5 ko 30. Me tahuri \frac{7}{30} me \frac{4}{5} ki te hautau me te tautūnga 30.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\left(\frac{7}{30}-\frac{24}{30}-1\right)-\frac{1}{4}\right)\right)-1$$

Tā te mea he rite te tauraro o \frac{7}{30} me \frac{24}{30}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\left(\frac{7-24}{30}-1\right)-\frac{1}{4}\right)\right)-1$$

Tangohia te 24 i te 7, ka -17.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\left(-\frac{17}{30}-1\right)-\frac{1}{4}\right)\right)-1$$

Me tahuri te 1 ki te hautau \frac{30}{30}.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\left(-\frac{17}{30}-\frac{30}{30}\right)-\frac{1}{4}\right)\right)-1$$

Tā te mea he rite te tauraro o -\frac{17}{30} me \frac{30}{30}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\frac{-17-30}{30}-\frac{1}{4}\right)\right)-1$$

Tangohia te 30 i te -17, ka -47.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}-\left(-\frac{47}{30}\right)-\frac{1}{4}\right)\right)-1$$

Ko te tauaro o -\frac{47}{30} ko \frac{47}{30}.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{1}{4}+\frac{47}{30}-\frac{1}{4}\right)\right)-1$$

Ko te maha noa iti rawa atu o 4 me 30 ko 60. Me tahuri \frac{1}{4} me \frac{47}{30} ki te hautau me te tautūnga 60.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{15}{60}+\frac{94}{60}-\frac{1}{4}\right)\right)-1$$

Tā te mea he rite te tauraro o \frac{15}{60} me \frac{94}{60}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{15+94}{60}-\frac{1}{4}\right)\right)-1$$

Tāpirihia te 15 ki te 94, ka 109.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{109}{60}-\frac{1}{4}\right)\right)-1$$

Ko te maha noa iti rawa atu o 60 me 4 ko 60. Me tahuri \frac{109}{60} me \frac{1}{4} ki te hautau me te tautūnga 60.

$$\frac{28}{15}-\left(-\frac{13}{30}-\left(\frac{109}{60}-\frac{15}{60}\right)\right)-1$$

Tā te mea he rite te tauraro o \frac{109}{60} me \frac{15}{60}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{15}-\left(-\frac{13}{30}-\frac{109-15}{60}\right)-1$$

Tangohia te 15 i te 109, ka 94.

$$\frac{28}{15}-\left(-\frac{13}{30}-\frac{94}{60}\right)-1$$

Whakahekea te hautanga \frac{94}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{28}{15}-\left(-\frac{13}{30}-\frac{47}{30}\right)-1$$

Tā te mea he rite te tauraro o -\frac{13}{30} me \frac{47}{30}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{28}{15}-\frac{-13-47}{30}-1$$

Tangohia te 47 i te -13, ka -60.

$$\frac{28}{15}-\frac{-60}{30}-1$$

Whakawehea te -60 ki te 30, kia riro ko -2.

$$\frac{28}{15}-\left(-2\right)-1$$

Ko te tauaro o -2 ko 2.

$$\frac{28}{15}+2-1$$

Me tahuri te 2 ki te hautau \frac{30}{15}.

$$\frac{28}{15}+\frac{30}{15}-1$$

Tā te mea he rite te tauraro o \frac{28}{15} me \frac{30}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{28+30}{15}-1$$

Tāpirihia te 28 ki te 30, ka 58.

$$\frac{58}{15}-1$$

Me tahuri te 1 ki te hautau \frac{15}{15}.

$$\frac{58}{15}-\frac{15}{15}$$

Tā te mea he rite te tauraro o \frac{58}{15} me \frac{15}{15}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{58-15}{15}$$

Tangohia te 15 i te 58, ka 43.

$$\frac{43}{15}$$

Tauwehe

$$\frac{43}{3 \cdot 5} = 2\frac{13}{15} = 2.8666666666666667$$