Whakaoti i te [(31/4-41/3)-5/6]:{11/12-frac{1}{2}(2frac{1}{3}+1-1frac{1}{4})}

$$[ ( 3 \frac { 1 } { 4 } - 4 \frac { 1 } { 3 } ) - \frac { 5 } { 6 } ] : \{ \frac { 11 } { 12 } - \frac { 1 } { 2 } ( 2 \frac { 1 } { 3 } + 1 - 1 \frac { 1 } { 4 } ) \}$$

Aromātai

$$\frac{46}{3}\approx 15.333333333$$

Ngā Upane Otinga

Whakareatia te 3 ki te 4, ka 12.

$$\frac{\frac{12+1}{4}-\frac{4\times 3+1}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tāpirihia te 12 ki te 1, ka 13.

$$\frac{\frac{13}{4}-\frac{4\times 3+1}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{\frac{13}{4}-\frac{12+1}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tāpirihia te 12 ki te 1, ka 13.

$$\frac{\frac{13}{4}-\frac{13}{3}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Ko te maha noa iti rawa atu o 4 me 3 ko 12. Me tahuri \frac{13}{4} me \frac{13}{3} ki te hautau me te tautūnga 12.

$$\frac{\frac{39}{12}-\frac{52}{12}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{39}{12} me \frac{52}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{39-52}{12}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tangohia te 52 i te 39, ka -13.

$$\frac{-\frac{13}{12}-\frac{5}{6}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Ko te maha noa iti rawa atu o 12 me 6 ko 12. Me tahuri -\frac{13}{12} me \frac{5}{6} ki te hautau me te tautūnga 12.

$$\frac{-\frac{13}{12}-\frac{10}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tā te mea he rite te tauraro o -\frac{13}{12} me \frac{10}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{-13-10}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tangohia te 10 i te -13, ka -23.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{2\times 3+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{6+1}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{7}{3}+1-\frac{1\times 4+1}{4}\right)}$$

Me tahuri te 1 ki te hautau \frac{3}{3}.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{7}{3}+\frac{3}{3}-\frac{1\times 4+1}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{7}{3} me \frac{3}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{7+3}{3}-\frac{1\times 4+1}{4}\right)}$$

Tāpirihia te 7 ki te 3, ka 10.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{10}{3}-\frac{1\times 4+1}{4}\right)}$$

Whakareatia te 1 ki te 4, ka 4.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{10}{3}-\frac{4+1}{4}\right)}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{10}{3}-\frac{5}{4}\right)}$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri \frac{10}{3} me \frac{5}{4} ki te hautau me te tautūnga 12.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\left(\frac{40}{12}-\frac{15}{12}\right)}$$

Tā te mea he rite te tauraro o \frac{40}{12} me \frac{15}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\times \frac{40-15}{12}}$$

Tangohia te 15 i te 40, ka 25.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1}{2}\times \frac{25}{12}}$$

Me whakarea te \frac{1}{2} ki te \frac{25}{12} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{1\times 25}{2\times 12}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 25}{2\times 12}.

$$\frac{-\frac{23}{12}}{\frac{11}{12}-\frac{25}{24}}$$

Ko te maha noa iti rawa atu o 12 me 24 ko 24. Me tahuri \frac{11}{12} me \frac{25}{24} ki te hautau me te tautūnga 24.

$$\frac{-\frac{23}{12}}{\frac{22}{24}-\frac{25}{24}}$$

Tā te mea he rite te tauraro o \frac{22}{24} me \frac{25}{24}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-\frac{23}{12}}{\frac{22-25}{24}}$$

Tangohia te 25 i te 22, ka -3.

$$\frac{-\frac{23}{12}}{\frac{-3}{24}}$$

Whakahekea te hautanga \frac{-3}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{-\frac{23}{12}}{-\frac{1}{8}}$$

Whakawehe -\frac{23}{12} ki te -\frac{1}{8} mā te whakarea -\frac{23}{12} ki te tau huripoki o -\frac{1}{8}.

$$-\frac{23}{12}\left(-8\right)$$

Tuhia te -\frac{23}{12}\left(-8\right) hei hautanga kotahi.

$$\frac{-23\left(-8\right)}{12}$$

Whakareatia te -23 ki te -8, ka 184.

$$\frac{184}{12}$$

Whakahekea te hautanga \frac{184}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{46}{3}$$

Tauwehe

$$\frac{2 \cdot 23}{3} = 15\frac{1}{3} = 15.333333333333334$$