Whakaoti i te 2/3-3/2*(2/3-3/2)+frac{1}{3}*(frac{3}{2}-3)=

$$\frac { 2 } { 3 } - \frac { 3 } { 2 } \cdot ( \frac { 2 } { 3 } - \frac { 3 } { 2 } ) + \frac { 1 } { 3 } \cdot ( \frac { 3 } { 2 } - 3 ) =$$

Aromātai

$$\frac{17}{12}\approx 1.416666667$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 3 me 2 ko 6. Me tahuri \frac{2}{3} me \frac{3}{2} ki te hautau me te tautūnga 6.

$$\frac{2}{3}-\frac{3}{2}\left(\frac{4}{6}-\frac{9}{6}\right)+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Tā te mea he rite te tauraro o \frac{4}{6} me \frac{9}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2}{3}-\frac{3}{2}\times \frac{4-9}{6}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Tangohia te 9 i te 4, ka -5.

$$\frac{2}{3}-\frac{3}{2}\left(-\frac{5}{6}\right)+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Me whakarea te \frac{3}{2} ki te -\frac{5}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{2}{3}-\frac{3\left(-5\right)}{2\times 6}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{3\left(-5\right)}{2\times 6}.

$$\frac{2}{3}-\frac{-15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Whakahekea te hautanga \frac{-15}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{2}{3}-\left(-\frac{5}{4}\right)+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Ko te tauaro o -\frac{5}{4} ko \frac{5}{4}.

$$\frac{2}{3}+\frac{5}{4}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Ko te maha noa iti rawa atu o 3 me 4 ko 12. Me tahuri \frac{2}{3} me \frac{5}{4} ki te hautau me te tautūnga 12.

$$\frac{8}{12}+\frac{15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Tā te mea he rite te tauraro o \frac{8}{12} me \frac{15}{12}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8+15}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Tāpirihia te 8 ki te 15, ka 23.

$$\frac{23}{12}+\frac{1}{3}\left(\frac{3}{2}-3\right)$$

Me tahuri te 3 ki te hautau \frac{6}{2}.

$$\frac{23}{12}+\frac{1}{3}\left(\frac{3}{2}-\frac{6}{2}\right)$$

Tā te mea he rite te tauraro o \frac{3}{2} me \frac{6}{2}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{23}{12}+\frac{1}{3}\times \frac{3-6}{2}$$

Tangohia te 6 i te 3, ka -3.

$$\frac{23}{12}+\frac{1}{3}\left(-\frac{3}{2}\right)$$

Me whakarea te \frac{1}{3} ki te -\frac{3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{23}{12}+\frac{1\left(-3\right)}{3\times 2}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\left(-3\right)}{3\times 2}.

$$\frac{23}{12}+\frac{-3}{6}$$

Whakahekea te hautanga \frac{-3}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{23}{12}-\frac{1}{2}$$

Ko te maha noa iti rawa atu o 12 me 2 ko 12. Me tahuri \frac{23}{12} me \frac{1}{2} ki te hautau me te tautūnga 12.

$$\frac{23}{12}-\frac{6}{12}$$

Tā te mea he rite te tauraro o \frac{23}{12} me \frac{6}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{23-6}{12}$$

Tangohia te 6 i te 23, ka 17.

$$\frac{17}{12}$$

Tauwehe

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$