Whakaoti i te 7/8+11/4-3/2*frac{4/9}{2frac{1}{2}-1frac{1}{10}+frac{1}{14}*frac{7}{5}}

$$\frac { \frac { 7 } { 8 } + 1 \frac { 1 } { 4 } - \frac { 3 } { 2 } \times \frac { 4 } { 9 } } { 2 \frac { 1 } { 2 } - 1 \frac { 1 } { 10 } + \frac { 1 } { 14 } \times \frac { 7 } { 5 } }$$

Aromātai

$$\frac{35}{36}\approx 0.972222222$$

Ngā Upane Otinga

Whakareatia te 1 ki te 4, ka 4.

$$\frac{\frac{7}{8}+\frac{4+1}{4}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{7}{8}+\frac{5}{4}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Ko te maha noa iti rawa atu o 8 me 4 ko 8. Me tahuri \frac{7}{8} me \frac{5}{4} ki te hautau me te tautūnga 8.

$$\frac{\frac{7}{8}+\frac{10}{8}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tā te mea he rite te tauraro o \frac{7}{8} me \frac{10}{8}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{7+10}{8}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tāpirihia te 7 ki te 10, ka 17.

$$\frac{\frac{17}{8}-\frac{3}{2}\times \frac{4}{9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Me whakarea te \frac{3}{2} ki te \frac{4}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{17}{8}-\frac{3\times 4}{2\times 9}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 4}{2\times 9}.

$$\frac{\frac{17}{8}-\frac{12}{18}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Whakahekea te hautanga \frac{12}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{\frac{17}{8}-\frac{2}{3}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Ko te maha noa iti rawa atu o 8 me 3 ko 24. Me tahuri \frac{17}{8} me \frac{2}{3} ki te hautau me te tautūnga 24.

$$\frac{\frac{51}{24}-\frac{16}{24}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tā te mea he rite te tauraro o \frac{51}{24} me \frac{16}{24}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{51-16}{24}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tangohia te 16 i te 51, ka 35.

$$\frac{\frac{35}{24}}{\frac{2\times 2+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{35}{24}}{\frac{4+1}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{35}{24}}{\frac{5}{2}-\frac{1\times 10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Whakareatia te 1 ki te 10, ka 10.

$$\frac{\frac{35}{24}}{\frac{5}{2}-\frac{10+1}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tāpirihia te 10 ki te 1, ka 11.

$$\frac{\frac{35}{24}}{\frac{5}{2}-\frac{11}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Ko te maha noa iti rawa atu o 2 me 10 ko 10. Me tahuri \frac{5}{2} me \frac{11}{10} ki te hautau me te tautūnga 10.

$$\frac{\frac{35}{24}}{\frac{25}{10}-\frac{11}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tā te mea he rite te tauraro o \frac{25}{10} me \frac{11}{10}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{35}{24}}{\frac{25-11}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Tangohia te 11 i te 25, ka 14.

$$\frac{\frac{35}{24}}{\frac{14}{10}+\frac{1}{14}\times \frac{7}{5}}$$

Whakahekea te hautanga \frac{14}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{1}{14}\times \frac{7}{5}}$$

Me whakarea te \frac{1}{14} ki te \frac{7}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{1\times 7}{14\times 5}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 7}{14\times 5}.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{7}{70}}$$

Whakahekea te hautanga \frac{7}{70} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{\frac{35}{24}}{\frac{7}{5}+\frac{1}{10}}$$

Ko te maha noa iti rawa atu o 5 me 10 ko 10. Me tahuri \frac{7}{5} me \frac{1}{10} ki te hautau me te tautūnga 10.

$$\frac{\frac{35}{24}}{\frac{14}{10}+\frac{1}{10}}$$

Tā te mea he rite te tauraro o \frac{14}{10} me \frac{1}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{35}{24}}{\frac{14+1}{10}}$$

Tāpirihia te 14 ki te 1, ka 15.

$$\frac{\frac{35}{24}}{\frac{15}{10}}$$

Whakahekea te hautanga \frac{15}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{\frac{35}{24}}{\frac{3}{2}}$$

Whakawehe \frac{35}{24} ki te \frac{3}{2} mā te whakarea \frac{35}{24} ki te tau huripoki o \frac{3}{2}.

$$\frac{35}{24}\times \frac{2}{3}$$

Me whakarea te \frac{35}{24} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{35\times 2}{24\times 3}$$

Mahia ngā whakarea i roto i te hautanga \frac{35\times 2}{24\times 3}.

$$\frac{70}{72}$$

Whakahekea te hautanga \frac{70}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{35}{36}$$

Tauwehe

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3 ^ {2}} = 0.9722222222222222$$