Whakaoti i te 52/3-31/3div22/3*4/5+2frac{1}{5}div2frac{3}{4}

$$5 \frac { 2 } { 3 } - 3 \frac { 1 } { 3 } \div 2 \frac { 2 } { 3 } \times \frac { 4 } { 5 } + 2 \frac { 1 } { 5 } \div 2 \frac { 3 } { 4 }$$

Aromātai

$$\frac{82}{15}\approx 5.466666667$$

Ngā Upane Otinga

Whakareatia te 5 ki te 3, ka 15.

$$\frac{15+2}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Tāpirihia te 15 ki te 2, ka 17.

$$\frac{17}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Whakawehe \frac{3\times 3+1}{3} ki te \frac{2\times 3+2}{3} mā te whakarea \frac{3\times 3+1}{3} ki te tau huripoki o \frac{2\times 3+2}{3}.

$$\frac{17}{3}-\frac{\left(3\times 3+1\right)\times 3}{3\left(2\times 3+2\right)}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{17}{3}-\frac{1+3\times 3}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{17}{3}-\frac{1+9}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Tāpirihia te 1 ki te 9, ka 10.

$$\frac{17}{3}-\frac{10}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Whakareatia te 2 ki te 3, ka 6.

$$\frac{17}{3}-\frac{10}{2+6}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Tāpirihia te 2 ki te 6, ka 8.

$$\frac{17}{3}-\frac{10}{8}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Whakahekea te hautanga \frac{10}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{17}{3}-\frac{5}{4}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Me whakakore atu te \frac{5}{4} me tōna tau utu \frac{4}{5}.

$$\frac{17}{3}-1+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

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

$$\frac{17}{3}-\frac{3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Tā te mea he rite te tauraro o \frac{17}{3} me \frac{3}{3}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{17-3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Tangohia te 3 i te 17, ka 14.

$$\frac{14}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Whakawehe \frac{2\times 5+1}{5} ki te \frac{2\times 4+3}{4} mā te whakarea \frac{2\times 5+1}{5} ki te tau huripoki o \frac{2\times 4+3}{4}.

$$\frac{14}{3}+\frac{\left(2\times 5+1\right)\times 4}{5\left(2\times 4+3\right)}$$

Whakareatia te 2 ki te 5, ka 10.

$$\frac{14}{3}+\frac{\left(10+1\right)\times 4}{5\left(2\times 4+3\right)}$$

Tāpirihia te 10 ki te 1, ka 11.

$$\frac{14}{3}+\frac{11\times 4}{5\left(2\times 4+3\right)}$$

Whakareatia te 11 ki te 4, ka 44.

$$\frac{14}{3}+\frac{44}{5\left(2\times 4+3\right)}$$

Whakareatia te 2 ki te 4, ka 8.

$$\frac{14}{3}+\frac{44}{5\left(8+3\right)}$$

Tāpirihia te 8 ki te 3, ka 11.

$$\frac{14}{3}+\frac{44}{5\times 11}$$

Whakareatia te 5 ki te 11, ka 55.

$$\frac{14}{3}+\frac{44}{55}$$

Whakahekea te hautanga \frac{44}{55} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 11.

$$\frac{14}{3}+\frac{4}{5}$$

Ko te maha noa iti rawa atu o 3 me 5 ko 15. Me tahuri \frac{14}{3} me \frac{4}{5} ki te hautau me te tautūnga 15.

$$\frac{70}{15}+\frac{12}{15}$$

Tā te mea he rite te tauraro o \frac{70}{15} me \frac{12}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{70+12}{15}$$

Tāpirihia te 70 ki te 12, ka 82.

$$\frac{82}{15}$$

Tauwehe

$$\frac{2 \cdot 41}{3 \cdot 5} = 5\frac{7}{15} = 5.466666666666667$$