Whakaoti i te 13/6-35/66+27/121*5/3-(frac{14}{15}+frac{8}{165})*(frac{2}{9}+frac{11}{18})

$$\frac { 13 } { 6 } - \frac { 35 } { 66 } + \frac { 27 } { 121 } \cdot \frac { 5 } { 3 } - ( \frac { 14 } { 15 } + \frac { 8 } { 165 } ) \cdot ( \frac { 2 } { 9 } + \frac { 11 } { 18 } )$$

Aromātai

$$\frac{144}{121}\approx 1.190082645$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 6 me 66 ko 66. Me tahuri \frac{13}{6} me \frac{35}{66} ki te hautau me te tautūnga 66.

$$\frac{143}{66}-\frac{35}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Tā te mea he rite te tauraro o \frac{143}{66} me \frac{35}{66}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{143-35}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Tangohia te 35 i te 143, ka 108.

$$\frac{108}{66}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Whakahekea te hautanga \frac{108}{66} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{18}{11}+\frac{27}{121}\times \frac{5}{3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Me whakarea te \frac{27}{121} ki te \frac{5}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{18}{11}+\frac{27\times 5}{121\times 3}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{27\times 5}{121\times 3}.

$$\frac{18}{11}+\frac{135}{363}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Whakahekea te hautanga \frac{135}{363} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{18}{11}+\frac{45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Ko te maha noa iti rawa atu o 11 me 121 ko 121. Me tahuri \frac{18}{11} me \frac{45}{121} ki te hautau me te tautūnga 121.

$$\frac{198}{121}+\frac{45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Tā te mea he rite te tauraro o \frac{198}{121} me \frac{45}{121}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{198+45}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Tāpirihia te 198 ki te 45, ka 243.

$$\frac{243}{121}-\left(\frac{14}{15}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Ko te maha noa iti rawa atu o 15 me 165 ko 165. Me tahuri \frac{14}{15} me \frac{8}{165} ki te hautau me te tautūnga 165.

$$\frac{243}{121}-\left(\frac{154}{165}+\frac{8}{165}\right)\left(\frac{2}{9}+\frac{11}{18}\right)$$

Tā te mea he rite te tauraro o \frac{154}{165} me \frac{8}{165}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{243}{121}-\frac{154+8}{165}\left(\frac{2}{9}+\frac{11}{18}\right)$$

Tāpirihia te 154 ki te 8, ka 162.

$$\frac{243}{121}-\frac{162}{165}\left(\frac{2}{9}+\frac{11}{18}\right)$$

Whakahekea te hautanga \frac{162}{165} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{243}{121}-\frac{54}{55}\left(\frac{2}{9}+\frac{11}{18}\right)$$

Ko te maha noa iti rawa atu o 9 me 18 ko 18. Me tahuri \frac{2}{9} me \frac{11}{18} ki te hautau me te tautūnga 18.

$$\frac{243}{121}-\frac{54}{55}\left(\frac{4}{18}+\frac{11}{18}\right)$$

Tā te mea he rite te tauraro o \frac{4}{18} me \frac{11}{18}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{243}{121}-\frac{54}{55}\times \frac{4+11}{18}$$

Tāpirihia te 4 ki te 11, ka 15.

$$\frac{243}{121}-\frac{54}{55}\times \frac{15}{18}$$

Whakahekea te hautanga \frac{15}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{243}{121}-\frac{54}{55}\times \frac{5}{6}$$

Me whakarea te \frac{54}{55} ki te \frac{5}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{243}{121}-\frac{54\times 5}{55\times 6}$$

Mahia ngā whakarea i roto i te hautanga \frac{54\times 5}{55\times 6}.

$$\frac{243}{121}-\frac{270}{330}$$

Whakahekea te hautanga \frac{270}{330} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 30.

$$\frac{243}{121}-\frac{9}{11}$$

Ko te maha noa iti rawa atu o 121 me 11 ko 121. Me tahuri \frac{243}{121} me \frac{9}{11} ki te hautau me te tautūnga 121.

$$\frac{243}{121}-\frac{99}{121}$$

Tā te mea he rite te tauraro o \frac{243}{121} me \frac{99}{121}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{243-99}{121}$$

Tangohia te 99 i te 243, ka 144.

$$\frac{144}{121}$$

Tauwehe

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{11 ^ {2}} = 1\frac{23}{121} = 1.1900826446280992$$