Whakaoti i te (65/18-511/15)div[22/7+(12-82/3)div14]

$$( 6 \frac { 5 } { 18 } - 5 \frac { 11 } { 15 } ) \div [ 2 \frac { 2 } { 7 } + ( 12 - 8 \frac { 2 } { 3 } ) \div 14 ]$$

Aromātai

$$\frac{343}{1590}\approx 0.21572327$$

Ngā Upane Otinga

Whakareatia te 6 ki te 18, ka 108.

$$\frac{\frac{108+5}{18}-\frac{5\times 15+11}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Tāpirihia te 108 ki te 5, ka 113.

$$\frac{\frac{113}{18}-\frac{5\times 15+11}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Whakareatia te 5 ki te 15, ka 75.

$$\frac{\frac{113}{18}-\frac{75+11}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Tāpirihia te 75 ki te 11, ka 86.

$$\frac{\frac{113}{18}-\frac{86}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Ko te maha noa iti rawa atu o 18 me 15 ko 90. Me tahuri \frac{113}{18} me \frac{86}{15} ki te hautau me te tautūnga 90.

$$\frac{\frac{565}{90}-\frac{516}{90}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Tā te mea he rite te tauraro o \frac{565}{90} me \frac{516}{90}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{565-516}{90}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Tangohia te 516 i te 565, ka 49.

$$\frac{\frac{49}{90}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Whakareatia te 2 ki te 7, ka 14.

$$\frac{\frac{49}{90}}{\frac{14+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Tāpirihia te 14 ki te 2, ka 16.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Whakareatia te 8 ki te 3, ka 24.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{12-\frac{24+2}{3}}{14}}$$

Tāpirihia te 24 ki te 2, ka 26.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{12-\frac{26}{3}}{14}}$$

Me tahuri te 12 ki te hautau \frac{36}{3}.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{\frac{36}{3}-\frac{26}{3}}{14}}$$

Tā te mea he rite te tauraro o \frac{36}{3} me \frac{26}{3}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{\frac{36-26}{3}}{14}}$$

Tangohia te 26 i te 36, ka 10.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{\frac{10}{3}}{14}}$$

Tuhia te \frac{\frac{10}{3}}{14} hei hautanga kotahi.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{10}{3\times 14}}$$

Whakareatia te 3 ki te 14, ka 42.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{10}{42}}$$

Whakahekea te hautanga \frac{10}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{5}{21}}$$

Ko te maha noa iti rawa atu o 7 me 21 ko 21. Me tahuri \frac{16}{7} me \frac{5}{21} ki te hautau me te tautūnga 21.

$$\frac{\frac{49}{90}}{\frac{48}{21}+\frac{5}{21}}$$

Tā te mea he rite te tauraro o \frac{48}{21} me \frac{5}{21}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{49}{90}}{\frac{48+5}{21}}$$

Tāpirihia te 48 ki te 5, ka 53.

$$\frac{\frac{49}{90}}{\frac{53}{21}}$$

Whakawehe \frac{49}{90} ki te \frac{53}{21} mā te whakarea \frac{49}{90} ki te tau huripoki o \frac{53}{21}.

$$\frac{49}{90}\times \frac{21}{53}$$

Me whakarea te \frac{49}{90} ki te \frac{21}{53} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{49\times 21}{90\times 53}$$

Mahia ngā whakarea i roto i te hautanga \frac{49\times 21}{90\times 53}.

$$\frac{1029}{4770}$$

Whakahekea te hautanga \frac{1029}{4770} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{343}{1590}$$

Tauwehe

$$\frac{7 ^ {3}}{2 \cdot 3 \cdot 5 \cdot 53} = 0.21572327044025158$$