Whakaoti i te 5|[(1/2+1/3-1/4)*(1/2-frac{1}{13})+frac{1}{4}:frac{1}{2}]

$$5 | [ ( \frac { 1 } { 2 } + \frac { 1 } { 3 } - \frac { 1 } { 4 } ) \cdot ( \frac { 1 } { 2 } - \frac { 1 } { 13 } ) + \frac { 1 } { 4 } : \frac { 1 } { 2 } ]$$

Aromātai

$$\frac{1165}{312}\approx 3.733974359$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 2 me 3 ko 6. Me tahuri \frac{1}{2} me \frac{1}{3} ki te hautau me te tautūnga 6.

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

Tā te mea he rite te tauraro o \frac{3}{6} me \frac{2}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 3 ki te 2, ka 5.

$$5|\left(\frac{5}{6}-\frac{1}{4}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Ko te maha noa iti rawa atu o 6 me 4 ko 12. Me tahuri \frac{5}{6} me \frac{1}{4} ki te hautau me te tautūnga 12.

$$5|\left(\frac{10}{12}-\frac{3}{12}\right)\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Tā te mea he rite te tauraro o \frac{10}{12} me \frac{3}{12}, me tango rāua mā te tango i ō raua taurunga.

$$5|\frac{10-3}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Tangohia te 3 i te 10, ka 7.

$$5|\frac{7}{12}\left(\frac{1}{2}-\frac{1}{13}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Ko te maha noa iti rawa atu o 2 me 13 ko 26. Me tahuri \frac{1}{2} me \frac{1}{13} ki te hautau me te tautūnga 26.

$$5|\frac{7}{12}\left(\frac{13}{26}-\frac{2}{26}\right)+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Tā te mea he rite te tauraro o \frac{13}{26} me \frac{2}{26}, me tango rāua mā te tango i ō raua taurunga.

$$5|\frac{7}{12}\times \frac{13-2}{26}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Tangohia te 2 i te 13, ka 11.

$$5|\frac{7}{12}\times \frac{11}{26}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Me whakarea te \frac{7}{12} ki te \frac{11}{26} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$5|\frac{7\times 11}{12\times 26}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Mahia ngā whakarea i roto i te hautanga \frac{7\times 11}{12\times 26}.

$$5|\frac{77}{312}+\frac{\frac{1}{4}}{\frac{1}{2}}|$$

Whakawehe \frac{1}{4} ki te \frac{1}{2} mā te whakarea \frac{1}{4} ki te tau huripoki o \frac{1}{2}.

$$5|\frac{77}{312}+\frac{1}{4}\times 2|$$

Whakareatia te \frac{1}{4} ki te 2, ka \frac{2}{4}.

$$5|\frac{77}{312}+\frac{2}{4}|$$

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

$$5|\frac{77}{312}+\frac{1}{2}|$$

Ko te maha noa iti rawa atu o 312 me 2 ko 312. Me tahuri \frac{77}{312} me \frac{1}{2} ki te hautau me te tautūnga 312.

$$5|\frac{77}{312}+\frac{156}{312}|$$

Tā te mea he rite te tauraro o \frac{77}{312} me \frac{156}{312}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$5|\frac{77+156}{312}|$$

Tāpirihia te 77 ki te 156, ka 233.

$$5|\frac{233}{312}|$$

Ko te uara pū o tētahi tau tūturu a ko a ina a\geq 0, ko -a rānei ina a<0. Ko te uara pū o \frac{233}{312} ko \frac{233}{312}.

$$5\times \frac{233}{312}$$

Tuhia te 5\times \frac{233}{312} hei hautanga kotahi.

$$\frac{5\times 233}{312}$$

Whakareatia te 5 ki te 233, ka 1165.

$$\frac{1165}{312}$$

Tauwehe

$$\frac{5 \cdot 233}{2 ^ {3} \cdot 3 \cdot 13} = 3\frac{229}{312} = 3.733974358974359$$