Whakaoti i te 12/3+(-56/13)+(-31/4)+(-27/13)+21frac{1}{3}+7frac{3}{4}

$$1 \frac{ 2 }{ 3 } +(-5 \frac{ 6 }{ 13 } )+(-3 \frac{ 1 }{ 4 } )+(-2 \frac{ 7 }{ 13 } )+21 \frac{ 1 }{ 3 } +7 \frac{ 3 }{ 4 }$$

Aromātai

$$\frac{39}{2}=19.5$$

Ngā Upane Otinga

Whakareatia te 1 ki te 3, ka 3.

$$\frac{3+2}{3}-\frac{5\times 13+6}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{5}{3}-\frac{5\times 13+6}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Whakareatia te 5 ki te 13, ka 65.

$$\frac{5}{3}-\frac{65+6}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tāpirihia te 65 ki te 6, ka 71.

$$\frac{5}{3}-\frac{71}{13}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Ko te maha noa iti rawa atu o 3 me 13 ko 39. Me tahuri \frac{5}{3} me \frac{71}{13} ki te hautau me te tautūnga 39.

$$\frac{65}{39}-\frac{213}{39}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tā te mea he rite te tauraro o \frac{65}{39} me \frac{213}{39}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{65-213}{39}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tangohia te 213 i te 65, ka -148.

$$-\frac{148}{39}-\frac{3\times 4+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Whakareatia te 3 ki te 4, ka 12.

$$-\frac{148}{39}-\frac{12+1}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tāpirihia te 12 ki te 1, ka 13.

$$-\frac{148}{39}-\frac{13}{4}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Ko te maha noa iti rawa atu o 39 me 4 ko 156. Me tahuri -\frac{148}{39} me \frac{13}{4} ki te hautau me te tautūnga 156.

$$-\frac{592}{156}-\frac{507}{156}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tā te mea he rite te tauraro o -\frac{592}{156} me \frac{507}{156}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-592-507}{156}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tangohia te 507 i te -592, ka -1099.

$$-\frac{1099}{156}-\frac{2\times 13+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Whakareatia te 2 ki te 13, ka 26.

$$-\frac{1099}{156}-\frac{26+7}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tāpirihia te 26 ki te 7, ka 33.

$$-\frac{1099}{156}-\frac{33}{13}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Ko te maha noa iti rawa atu o 156 me 13 ko 156. Me tahuri -\frac{1099}{156} me \frac{33}{13} ki te hautau me te tautūnga 156.

$$-\frac{1099}{156}-\frac{396}{156}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tā te mea he rite te tauraro o -\frac{1099}{156} me \frac{396}{156}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-1099-396}{156}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Tangohia te 396 i te -1099, ka -1495.

$$\frac{-1495}{156}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Whakahekea te hautanga \frac{-1495}{156} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 13.

$$-\frac{115}{12}+\frac{21\times 3+1}{3}+\frac{7\times 4+3}{4}$$

Whakareatia te 21 ki te 3, ka 63.

$$-\frac{115}{12}+\frac{63+1}{3}+\frac{7\times 4+3}{4}$$

Tāpirihia te 63 ki te 1, ka 64.

$$-\frac{115}{12}+\frac{64}{3}+\frac{7\times 4+3}{4}$$

Ko te maha noa iti rawa atu o 12 me 3 ko 12. Me tahuri -\frac{115}{12} me \frac{64}{3} ki te hautau me te tautūnga 12.

$$-\frac{115}{12}+\frac{256}{12}+\frac{7\times 4+3}{4}$$

Tā te mea he rite te tauraro o -\frac{115}{12} me \frac{256}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-115+256}{12}+\frac{7\times 4+3}{4}$$

Tāpirihia te -115 ki te 256, ka 141.

$$\frac{141}{12}+\frac{7\times 4+3}{4}$$

Whakahekea te hautanga \frac{141}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{47}{4}+\frac{7\times 4+3}{4}$$

Whakareatia te 7 ki te 4, ka 28.

$$\frac{47}{4}+\frac{28+3}{4}$$

Tāpirihia te 28 ki te 3, ka 31.

$$\frac{47}{4}+\frac{31}{4}$$

Tā te mea he rite te tauraro o \frac{47}{4} me \frac{31}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{47+31}{4}$$

Tāpirihia te 47 ki te 31, ka 78.

$$\frac{78}{4}$$

Whakahekea te hautanga \frac{78}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{39}{2}$$

Tauwehe

$$\frac{3 \cdot 13}{2} = 19\frac{1}{2} = 19.5$$