Whakaoti i te 11/4+(22/3*13/4-31/6div7frac{3}{5})

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

Aromātai

$$\frac{11}{2}=5.5$$

Ngā Upane Otinga

Whakareatia te 1 ki te 4, ka 4.

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

Tāpirihia te 4 ki te 1, ka 5.

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

Whakareatia te 2 ki te 3, ka 6.

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

Tāpirihia te 6 ki te 2, ka 8.

$$\frac{5}{4}+\frac{8}{3}\times \frac{1\times 4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Whakareatia te 1 ki te 4, ka 4.

$$\frac{5}{4}+\frac{8}{3}\times \frac{4+3}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Tāpirihia te 4 ki te 3, ka 7.

$$\frac{5}{4}+\frac{8}{3}\times \frac{7}{4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Me whakarea te \frac{8}{3} ki te \frac{7}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{5}{4}+\frac{8\times 7}{3\times 4}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Mahia ngā whakarea i roto i te hautanga \frac{8\times 7}{3\times 4}.

$$\frac{5}{4}+\frac{56}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Whakahekea te hautanga \frac{56}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{5}{4}+\frac{14}{3}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Ko te maha noa iti rawa atu o 4 me 3 ko 12. Me tahuri \frac{5}{4} me \frac{14}{3} ki te hautau me te tautūnga 12.

$$\frac{15}{12}+\frac{56}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Tā te mea he rite te tauraro o \frac{15}{12} me \frac{56}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{15+56}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Tāpirihia te 15 ki te 56, ka 71.

$$\frac{71}{12}-\frac{\frac{3\times 6+1}{6}}{\frac{7\times 5+3}{5}}$$

Whakawehe \frac{3\times 6+1}{6} ki te \frac{7\times 5+3}{5} mā te whakarea \frac{3\times 6+1}{6} ki te tau huripoki o \frac{7\times 5+3}{5}.

$$\frac{71}{12}-\frac{\left(3\times 6+1\right)\times 5}{6\left(7\times 5+3\right)}$$

Whakareatia te 3 ki te 6, ka 18.

$$\frac{71}{12}-\frac{\left(18+1\right)\times 5}{6\left(7\times 5+3\right)}$$

Tāpirihia te 18 ki te 1, ka 19.

$$\frac{71}{12}-\frac{19\times 5}{6\left(7\times 5+3\right)}$$

Whakareatia te 19 ki te 5, ka 95.

$$\frac{71}{12}-\frac{95}{6\left(7\times 5+3\right)}$$

Whakareatia te 7 ki te 5, ka 35.

$$\frac{71}{12}-\frac{95}{6\left(35+3\right)}$$

Tāpirihia te 35 ki te 3, ka 38.

$$\frac{71}{12}-\frac{95}{6\times 38}$$

Whakareatia te 6 ki te 38, ka 228.

$$\frac{71}{12}-\frac{95}{228}$$

Whakahekea te hautanga \frac{95}{228} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 19.

$$\frac{71}{12}-\frac{5}{12}$$

Tā te mea he rite te tauraro o \frac{71}{12} me \frac{5}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{71-5}{12}$$

Tangohia te 5 i te 71, ka 66.

$$\frac{66}{12}$$

Whakahekea te hautanga \frac{66}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{11}{2}$$

Tauwehe

$$\frac{11}{2} = 5\frac{1}{2} = 5.5$$