Whakaoti i te [(3/4-1/2)div4/3+1]div(-3/4+frac{1}{3})frac{3}{2}

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

Aromātai

$$-\frac{171}{40}=-4.275$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 4 me 2 ko 4. Me tahuri \frac{3}{4} me \frac{1}{2} ki te hautau me te tautūnga 4.

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

Tā te mea he rite te tauraro o \frac{3}{4} me \frac{2}{4}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 2 i te 3, ka 1.

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

Whakawehe \frac{1}{4} ki te \frac{4}{3} mā te whakarea \frac{1}{4} ki te tau huripoki o \frac{4}{3}.

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

Me whakarea te \frac{1}{4} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{4\times 4}.

$$\frac{\frac{3}{16}+1}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Me tahuri te 1 ki te hautau \frac{16}{16}.

$$\frac{\frac{3}{16}+\frac{16}{16}}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Tā te mea he rite te tauraro o \frac{3}{16} me \frac{16}{16}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{3+16}{16}}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Tāpirihia te 3 ki te 16, ka 19.

$$\frac{\frac{19}{16}}{-\frac{3}{4}+\frac{1}{3}}\times \frac{3}{2}$$

Ko te maha noa iti rawa atu o 4 me 3 ko 12. Me tahuri -\frac{3}{4} me \frac{1}{3} ki te hautau me te tautūnga 12.

$$\frac{\frac{19}{16}}{-\frac{9}{12}+\frac{4}{12}}\times \frac{3}{2}$$

Tā te mea he rite te tauraro o -\frac{9}{12} me \frac{4}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{19}{16}}{\frac{-9+4}{12}}\times \frac{3}{2}$$

Tāpirihia te -9 ki te 4, ka -5.

$$\frac{\frac{19}{16}}{-\frac{5}{12}}\times \frac{3}{2}$$

Whakawehe \frac{19}{16} ki te -\frac{5}{12} mā te whakarea \frac{19}{16} ki te tau huripoki o -\frac{5}{12}.

$$\frac{19}{16}\left(-\frac{12}{5}\right)\times \frac{3}{2}$$

Me whakarea te \frac{19}{16} ki te -\frac{12}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{19\left(-12\right)}{16\times 5}\times \frac{3}{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{19\left(-12\right)}{16\times 5}.

$$\frac{-228}{80}\times \frac{3}{2}$$

Whakahekea te hautanga \frac{-228}{80} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{57}{20}\times \frac{3}{2}$$

Me whakarea te -\frac{57}{20} ki te \frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-57\times 3}{20\times 2}$$

Mahia ngā whakarea i roto i te hautanga \frac{-57\times 3}{20\times 2}.

$$\frac{-171}{40}$$

Ka taea te hautanga \frac{-171}{40} te tuhi anō ko -\frac{171}{40} mā te tango i te tohu tōraro.

$$-\frac{171}{40}$$

Tauwehe

$$-\frac{171}{40} = -4\frac{11}{40} = -4.275$$