Whakaoti i te 1/8+4-(4/3*2/6-1/4)+frac{8}{5}:frac{1}{2}

$$\frac { 1 } { 8 } + 4 - ( \frac { 4 } { 3 } \cdot \frac { 2 } { 6 } - \frac { 1 } { 4 } ) + \frac { 8 } { 5 } : \frac { 1 } { 2 }$$

Aromātai

$$\frac{2567}{360}\approx 7.130555556$$

Ngā Upane Otinga

Me tahuri te 4 ki te hautau \frac{32}{8}.

$$\frac{1}{8}+\frac{32}{8}-\left(\frac{4}{3}\times \frac{2}{6}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Tā te mea he rite te tauraro o \frac{1}{8} me \frac{32}{8}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1+32}{8}-\left(\frac{4}{3}\times \frac{2}{6}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Tāpirihia te 1 ki te 32, ka 33.

$$\frac{33}{8}-\left(\frac{4}{3}\times \frac{2}{6}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Whakahekea te hautanga \frac{2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{33}{8}-\left(\frac{4}{3}\times \frac{1}{3}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Me whakarea te \frac{4}{3} ki te \frac{1}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{33}{8}-\left(\frac{4\times 1}{3\times 3}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Mahia ngā whakarea i roto i te hautanga \frac{4\times 1}{3\times 3}.

$$\frac{33}{8}-\left(\frac{4}{9}-\frac{1}{4}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Ko te maha noa iti rawa atu o 9 me 4 ko 36. Me tahuri \frac{4}{9} me \frac{1}{4} ki te hautau me te tautūnga 36.

$$\frac{33}{8}-\left(\frac{16}{36}-\frac{9}{36}\right)+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Tā te mea he rite te tauraro o \frac{16}{36} me \frac{9}{36}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{33}{8}-\frac{16-9}{36}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Tangohia te 9 i te 16, ka 7.

$$\frac{33}{8}-\frac{7}{36}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Ko te maha noa iti rawa atu o 8 me 36 ko 72. Me tahuri \frac{33}{8} me \frac{7}{36} ki te hautau me te tautūnga 72.

$$\frac{297}{72}-\frac{14}{72}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Tā te mea he rite te tauraro o \frac{297}{72} me \frac{14}{72}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{297-14}{72}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Tangohia te 14 i te 297, ka 283.

$$\frac{283}{72}+\frac{\frac{8}{5}}{\frac{1}{2}}$$

Whakawehe \frac{8}{5} ki te \frac{1}{2} mā te whakarea \frac{8}{5} ki te tau huripoki o \frac{1}{2}.

$$\frac{283}{72}+\frac{8}{5}\times 2$$

Tuhia te \frac{8}{5}\times 2 hei hautanga kotahi.

$$\frac{283}{72}+\frac{8\times 2}{5}$$

Whakareatia te 8 ki te 2, ka 16.

$$\frac{283}{72}+\frac{16}{5}$$

Ko te maha noa iti rawa atu o 72 me 5 ko 360. Me tahuri \frac{283}{72} me \frac{16}{5} ki te hautau me te tautūnga 360.

$$\frac{1415}{360}+\frac{1152}{360}$$

Tā te mea he rite te tauraro o \frac{1415}{360} me \frac{1152}{360}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1415+1152}{360}$$

Tāpirihia te 1415 ki te 1152, ka 2567.

$$\frac{2567}{360}$$

Tauwehe

$$\frac{17 \cdot 151}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 7\frac{47}{360} = 7.1305555555555555$$