Whakaoti i te [22/3*{21/4div(11/8+21/4-1frac{1}{2})}]-1frac{2}{3}-frac{2}{5}

$$[ 2 \frac { 2 } { 3 } \times \{ 2 \frac { 1 } { 4 } \div ( 1 \frac { 1 } { 8 } + 2 \frac { 1 } { 4 } - 1 \frac { 1 } { 2 } ) \} ] - 1 \frac { 2 } { 3 } - \frac { 2 } { 5 }$$

Aromātai

$$\frac{17}{15}\approx 1.133333333$$

Ngā Upane Otinga

Whakareatia te 2 ki te 3, ka 6.

$$\frac{6+2}{3}\times \frac{\frac{2\times 4+1}{4}}{\frac{1\times 8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tāpirihia te 6 ki te 2, ka 8.

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

Whakareatia te 2 ki te 4, ka 8.

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

Tāpirihia te 8 ki te 1, ka 9.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{1\times 8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakareatia te 1 ki te 8, ka 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{8+1}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tāpirihia te 8 ki te 1, ka 9.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{2\times 4+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakareatia te 2 ki te 4, ka 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{8+1}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tāpirihia te 8 ki te 1, ka 9.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{9}{4}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Ko te maha noa iti rawa atu o 8 me 4 ko 8. Me tahuri \frac{9}{8} me \frac{9}{4} ki te hautau me te tautūnga 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9}{8}+\frac{18}{8}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tā te mea he rite te tauraro o \frac{9}{8} me \frac{18}{8}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{9+18}{8}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tāpirihia te 9 ki te 18, ka 27.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{1\times 2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakareatia te 1 ki te 2, ka 2.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{2+1}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{3}{2}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Ko te maha noa iti rawa atu o 8 me 2 ko 8. Me tahuri \frac{27}{8} me \frac{3}{2} ki te hautau me te tautūnga 8.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27}{8}-\frac{12}{8}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tā te mea he rite te tauraro o \frac{27}{8} me \frac{12}{8}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{27-12}{8}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Tangohia te 12 i te 27, ka 15.

$$\frac{8}{3}\times \frac{\frac{9}{4}}{\frac{15}{8}}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakawehe \frac{9}{4} ki te \frac{15}{8} mā te whakarea \frac{9}{4} ki te tau huripoki o \frac{15}{8}.

$$\frac{8}{3}\times \frac{9}{4}\times \frac{8}{15}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Me whakarea te \frac{9}{4} ki te \frac{8}{15} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{8}{3}\times \frac{9\times 8}{4\times 15}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Mahia ngā whakarea i roto i te hautanga \frac{9\times 8}{4\times 15}.

$$\frac{8}{3}\times \frac{72}{60}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakahekea te hautanga \frac{72}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$\frac{8}{3}\times \frac{6}{5}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Me whakarea te \frac{8}{3} ki te \frac{6}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{8\times 6}{3\times 5}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Mahia ngā whakarea i roto i te hautanga \frac{8\times 6}{3\times 5}.

$$\frac{48}{15}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakahekea te hautanga \frac{48}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{16}{5}-\frac{1\times 3+2}{3}-\frac{2}{5}$$

Whakareatia te 1 ki te 3, ka 3.

$$\frac{16}{5}-\frac{3+2}{3}-\frac{2}{5}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{16}{5}-\frac{5}{3}-\frac{2}{5}$$

Ko te maha noa iti rawa atu o 5 me 3 ko 15. Me tahuri \frac{16}{5} me \frac{5}{3} ki te hautau me te tautūnga 15.

$$\frac{48}{15}-\frac{25}{15}-\frac{2}{5}$$

Tā te mea he rite te tauraro o \frac{48}{15} me \frac{25}{15}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{48-25}{15}-\frac{2}{5}$$

Tangohia te 25 i te 48, ka 23.

$$\frac{23}{15}-\frac{2}{5}$$

Ko te maha noa iti rawa atu o 15 me 5 ko 15. Me tahuri \frac{23}{15} me \frac{2}{5} ki te hautau me te tautūnga 15.

$$\frac{23}{15}-\frac{6}{15}$$

Tā te mea he rite te tauraro o \frac{23}{15} me \frac{6}{15}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{23-6}{15}$$

Tangohia te 6 i te 23, ka 17.

$$\frac{17}{15}$$

Tauwehe

$$\frac{17}{3 \cdot 5} = 1\frac{2}{15} = 1.1333333333333333$$