Whakaoti i te 3/4+40/frac{42{51}+7/frac{10{7}-4/35}}=

$$\frac{ 3 }{ 4 } + \frac{ 40 }{ \frac{ 42 }{ 51 } + \frac{ 7 }{ \frac{ 10 }{ 7 } - \frac{ 4 }{ 35 } } } =$$

Aromātai

$$\frac{139547}{19236}\approx 7.254470784$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{42}{51} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{10}{7}-\frac{4}{35}}}$$

Ko te maha noa iti rawa atu o 7 me 35 ko 35. Me tahuri \frac{10}{7} me \frac{4}{35} ki te hautau me te tautūnga 35.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{50}{35}-\frac{4}{35}}}$$

Tā te mea he rite te tauraro o \frac{50}{35} me \frac{4}{35}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{50-4}{35}}}$$

Tangohia te 4 i te 50, ka 46.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7}{\frac{46}{35}}}$$

Whakawehe 7 ki te \frac{46}{35} mā te whakarea 7 ki te tau huripoki o \frac{46}{35}.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+7\times \frac{35}{46}}$$

Tuhia te 7\times \frac{35}{46} hei hautanga kotahi.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{7\times 35}{46}}$$

Whakareatia te 7 ki te 35, ka 245.

$$\frac{3}{4}+\frac{40}{\frac{14}{17}+\frac{245}{46}}$$

Ko te maha noa iti rawa atu o 17 me 46 ko 782. Me tahuri \frac{14}{17} me \frac{245}{46} ki te hautau me te tautūnga 782.

$$\frac{3}{4}+\frac{40}{\frac{644}{782}+\frac{4165}{782}}$$

Tā te mea he rite te tauraro o \frac{644}{782} me \frac{4165}{782}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3}{4}+\frac{40}{\frac{644+4165}{782}}$$

Tāpirihia te 644 ki te 4165, ka 4809.

$$\frac{3}{4}+\frac{40}{\frac{4809}{782}}$$

Whakawehe 40 ki te \frac{4809}{782} mā te whakarea 40 ki te tau huripoki o \frac{4809}{782}.

$$\frac{3}{4}+40\times \frac{782}{4809}$$

Tuhia te 40\times \frac{782}{4809} hei hautanga kotahi.

$$\frac{3}{4}+\frac{40\times 782}{4809}$$

Whakareatia te 40 ki te 782, ka 31280.

$$\frac{3}{4}+\frac{31280}{4809}$$

Ko te maha noa iti rawa atu o 4 me 4809 ko 19236. Me tahuri \frac{3}{4} me \frac{31280}{4809} ki te hautau me te tautūnga 19236.

$$\frac{14427}{19236}+\frac{125120}{19236}$$

Tā te mea he rite te tauraro o \frac{14427}{19236} me \frac{125120}{19236}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{14427+125120}{19236}$$

Tāpirihia te 14427 ki te 125120, ka 139547.

$$\frac{139547}{19236}$$

Tauwehe

$$\frac{139547}{2 ^ {2} \cdot 3 \cdot 7 \cdot 229} = 7\frac{4895}{19236} = 7.254470783946767$$